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y(than)j(all)f(other)j(games)d(put)i(together.)24 b(The)16 b(game)e(app)q(eals)i(to)f(all)f(ages)i(and)g(abilities)262 1397 y(from)c(b)q(eginner)i(to)g(exp)q(ert.)365 1480 y("Chess)d(is)f(a)g(sea) g(in)g(whic)o(h)f(a)h(gnat)g(ma)o(y)e(drink)h(or)h(an)g(elephan)o(t)g(ma)o(y) e(bathe.")1319 1547 y Fm(Indian)k(pr)n(overb.)324 1665 y Fp(Chess)18 b(epitomises)e(man)o(y)e(of)i(the)i(problems)e(facing)f(the)j(\014eld)e(of)h (arti\014cial)e(in)o(telli-)262 1715 y(gence,)j(that)f(of)g(the)h(storage,)g (represen)o(tation,)h(retriev)n(al)e(and)g(application)f(of)h(kno)o(wl-)262 1765 y(edge;)12 b(searc)o(hing)h(in\014nite)e(domains)f(and)i(problem)f (solving)f(using)i(inexact)g(information.)262 1815 y(Chess)h(therefore)h(pro) o(vides)f(an)f(almost)f(p)q(erfect)j(en)o(vironmen)o(t)e(in)g(whic)o(h)g(to)h (exp)q(erimen)o(t)262 1864 y(with)e(new)g(ideas.)18 b(Unlik)o(e)10 b(most)g(other)i(problem)e(domains,)g(progress)i(can)g(b)q(e)g(accurately)262 1914 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y(t)o(yp)q(e)d(C)h(program)d(in)i(1958)f([42].) 17 b(This)12 b(w)o(as)g(the)h(\014rst)g(ev)o(er)g(practical)f(application)f (of)h(the)262 1443 y(alpha-b)q(eta)f(algorithm.)k(A)e(n)o(um)o(b)q(er)e(of)h (programs)f(follo)o(w)o(ed,)g(but)h(all)f(pla)o(y)o(ed)h(v)o(ery)h(p)q(o)q (or)262 1493 y(c)o(hess.)25 b(Despite)16 b(this,)g(man)o(y)e(researc)o(hers) 19 b(in)c(the)h(\014eld)g(of)f(arti\014cial)g(in)o(telligence)h(w)o(ere)262 1543 y(v)o(ery)e(con\014den)o(t)g(ab)q(out)g(the)h(p)q(oten)o(tial)e(of)g (their)i(mac)o(hines.)365 1619 y("Within)d(10)g(y)o(ears)h(a)g(digital)e (computer)i(will)e(b)q(e)i(the)h(w)o(orld's)e(c)o(hess)i(c)o(ham-)365 1669 y(pion,)f(unless)i(rules)f(bar)g(it)g(from)e(comp)q(etition")1088 1734 y Fm(Herb)n(ert)h(Simon,)j(1957.)324 1846 y Fp(It)h(w)o(as)h(not)f(un)o (til)g(1966)f(that)i(real)g(progress)g(w)o(as)g(made)e(b)o(y)h(Ric)o(hard)g (Green)o(blatt)262 1895 y(at)g(MIT)g([23)o(].)27 b(His)17 b(program)f(MacHac) 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Fl(+19)81 b(+21)817 1775 y(+8)269 b(+12)817 1941 y Ff(\000)p Fl(12)250 b Ff(\000)p Fl(8)899 2024 y Ff(\000)p Fl(21)86 b Ff(\000)p Fl(19)447 2151 y Fp(Figure)14 b(2.4:)j(Mo)o(v)o(e)d(generation)g(of)f(knigh)o(t)h(mo)o(v)o(es)e(using)i (o\013sets.)262 2277 y(Eac)o(h)g(of)f(these)i(p)q(oten)o(tial)f("to-squares") g(m)o(ust)f(b)q(e)h(tested)i(for)d(2)h(p)q(ossibilities:)324 2360 y Ff(\017)20 b Fp(Is)14 b(the)h(to-square)f(on)g(the)h(b)q(oard)e(?)324 2443 y Ff(\017)20 b Fp(Is)14 b(the)h(to-square)f(uno)q(ccupied)h(b)o(y)f(a)g (friendly)f(piece)i(?)957 2574 y(13)p eop %%Page: 14 16 14 15 bop 262 307 a Fp(If)9 b(b)q(oth)h(these)h(tests)g(pro)o(v)o(e)f(to)g(b) q(e)g(true,)h(then)g(a)e(pseudo)i(legal)e(mo)o(v)o(e)f(has)i(b)q(een)h (generated.)262 357 y(Note)i(that)g(this)g(do)q(es)h(not)e(determine)h (whether)i(the)e(mo)o(v)o(e)e(actually)h(lea)o(v)o(es)h(the)h(king)e(in)262 407 y(c)o(hec)o(k,)h(hence)h(it)e(is)h(called)g(pseudo)g(legal.)k(Nearly)12 b(all)g(programs)f(lea)o(v)o(e)i(this)g(calculation)262 457 y(un)o(til)h(a)h(more)f(con)o(v)o(enien)o(t)i(time.)21 b(As)15 b(y)o(ou)g(can)h(see)g(this)g(metho)q(d)e(of)h(mo)o(v)o(e)e(generation)262 506 y(is)g(quiet)h(simple.)324 592 y(Using)f(a)f(bitmap)g(represen)o(tation,) i(mo)o(v)o(e)d(generation)j(is)e(m)o(uc)o(h)g(more)g(e\016cien)o(t)i(with)262 641 y(resp)q(ect)h(to)f(time,)e(than)h(with)g(the)h(previous)g(metho)q(d.)j (The)d(reason)h(for)e(this)g(adv)n(an)o(tage)262 691 y(lies)e(in)g(the)h (fact)g(that)f(mo)o(v)o(es)f(are)i(generated)h(b)o(y)f(using)f(bit)o(wise)g (logical)f(op)q(erations)i(suc)o(h)262 741 y(as)h("and",)g("or")h(and)f ("not".)324 826 y(In)k(order)h(for)g(this)f(metho)q(d)g(to)g(generate)i(all)d (white)h(knigh)o(t)g(mo)o(v)o(es)f(from)g(a)h(giv)o(en)262 876 y(square,)f(a)g(bitmap)e(needs)j(to)f(b)q(e)h(fetc)o(hed)g(whic)o(h)f (represen)o(ts)i(all)d(mo)o(v)o(es)g(a)g(knigh)o(t)g(can)262 926 y(mak)o(e)10 b(from)g(the)i(giv)o(en)f(square,)i(call)e(this)h(bitmap)e 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b(it)g(is)g(still)g(feasible)g(with)g(a)g(16)g(or)g(32)g(bit)g(w)o(ord,)262 1410 y(it)j(is)i(signi\014can)o(tly)e(less)i(e\016cien)o(t.)29 b(Also)17 b(it)g(is)g(v)o(ery)g(imp)q(ortan)o(t)f(for)h(the)h(computer)f(to) 262 1460 y(ha)o(v)o(e)11 b(a)h(mac)o(hine)f(instruction)h(whic)o(h)g(can)h (giv)o(e)e(the)i(lo)q(cation)e(of)g(the)i(\014rst)g(bit)f(set)g(in)g(an)o(y) 262 1509 y(w)o(ord;)18 b(without)f(this,)h(the)g(metho)q(d)e(ma)o(y)f(b)q(e)j (to)q(o)g(ine\016cien)o(t.)28 b(F)m(or)17 b(a)g(more)f(complete)262 1559 y(explanation)c(of)i(this)g(tec)o(hnique)g(see)i([15)o(].)324 1644 y(In)10 b(b)q(oth)g(metho)q(ds)f(the)h(mo)o(v)o(es)f(of)g(v)o(ector)i (pieces)g(suc)o(h)f(as)g(bishops,)h(ro)q(oks)f(and)f(queens)262 1694 y(are)14 b(more)f(complex)g(to)h(generate.)20 b(P)o(a)o(wn)14 b(mo)o(v)o(es)f(and)h(sp)q(ecial)g(mo)o(v)o(es)f(suc)o(h)i(as)f(castling)262 1744 y(and)c(en-passan)o(t)g(are)h(also)f(more)f(complicated,)g(but)i(can)f (still)f(b)q(e)i(generated)h(using)e(either)262 1794 y(represen)o(tation.)262 1967 y Fr(2.3)69 b(Ev)l(aluation)23 b(F)-6 b(unctions)262 2093 y Fp(Giv)o(en)11 b(that)h(mo)o(v)o(es)f(can)i(b)q(e)g(generated)g(ho)o(w)f (can)h(the)f(relativ)o(e)g(merits)g(of)g(eac)o(h)g(mo)o(v)o(e)f(b)q(e)262 2143 y(determined)i(?)18 b(That)c(is)g(the)g(purp)q(ose)h(of)f(the)g Fm(Evaluation)i(F)m(unction)p Fp(.)324 2228 y(Shannon)f(prop)q(osed)g(that)g (an)g(ev)n(aluation)f(function)g(should)h(tak)o(e)g(accoun)o(t)h(of)e(suc)o (h)262 2278 y(features)j(as)f(material,)e(mobilit)o(y)m(,)f(p)q(osition)j(of) f(pieces)j(and)e(pa)o(wn)g(structure.)27 b(Eac)o(h)16 b(of)262 2328 y(these)21 b(factors)f(required)i(an)d(imp)q(ortance)h(w)o(eigh)o(ting)f (to)h(b)q(e)g(asso)q(ciated)h(with)f(them.)262 2377 y(Eac)o(h)e(factor)g(w)o (ould)f(then)i(b)q(e)f(v)n(alued)g(dep)q(ending)g(on)g(its)g(presence)j(or)d (absence)h(in)f(a)262 2427 y(giv)o(en)11 b(p)q(osition,)h(and)g(the)h(asso)q (ciated)g(w)o(eigh)o(tings)f(applied.)17 b(All)12 b(the)h(v)n(alues)f(could)g (then)957 2574 y(14)p eop %%Page: 15 17 15 16 bop 262 307 a Fp(b)q(e)14 b(added)h(together)g(to)f(giv)o(e)g(a)f (single)h(discrete)i(v)n(alue)e(for)g(the)g(p)q(osition.)k(The)d(mo)o(v)o(e)e (or)262 357 y(series)j(of)e(mo)o(v)o(es)g(whic)o(h)h(pro)q(duce)i(the)e(most) f(desirable)i(p)q(osition)e(from)f(the)j(ev)n(aluation)262 407 y(function's)d(p)q(oin)o(t)g(of)h(view)f(can)h(then)h(b)q(e)g(c)o(hosen.) 324 492 y(Almost)9 b(all)g(ev)n(aluation)g(functions)h(use)i(material)c(as)j (an)f(o)o(v)o(erriding)f(factor,)i(it)f(is)g(v)o(ery)262 542 y(rare)k(for)f(ev)o(en)i(the)f(sum)f(of)g(all)f(other)j(factors)f(to)g (exceed)h(the)f(v)n(alue)f(of)h(one)g(pa)o(wn.)j(The)262 592 y(reason)11 b(for)g(this)f(is)h(that)g(b)q(ecause)i(the)e(p)q(ositional)f(v)n (alues)g(are)i(so)f(crude,)h(if)e(material)f(w)o(ere)262 641 y(to)15 b(b)q(e)h(giv)o(en)f(a)o(w)o(a)o(y)f(in)h(exc)o(hange)h(for)g(p)q (ositional)e(comp)q(ensation,)g(the)i(mac)o(hine)e(w)o(ould)262 691 y(more)c(than)h(lik)o(ely)f(lose)h(b)q(ecause)i(its)e(ev)n(aluation)f(of) h(the)h(comp)q(ensation)e(w)o(as)h(inaccurate.)324 777 y(In)k(the)g(fort)o(y) g(y)o(ears)h(since)f(Shannon's)g(pap)q(er,)h(man)o(y)d(additional)g(ev)n (aluation)h(func-)262 826 y(tion)19 b(factors)h(ha)o(v)o(e)f(b)q(een)i (suggested)g(and)e(built)g(up)q(on.)36 b(They)20 b(include)g(king)e(safet)o (y)m(,)262 876 y(o)q(ccupation)e(of)g(w)o(eak)g(squares,)i(dev)o(elopmen)o (t,)e(piece)i(exc)o(hange)f(term)f(etc.)27 b(Ho)o(w)o(ev)o(er,)262 926 y(ev)o(en)16 b(to)q(da)o(y)f(v)o(ery)g(few)h(ev)n(aluation)e(functions)h (w)o(ould)g(ev)o(en)h(consider)g(exc)o(hanging)f(ma-)262 976 y(terial)e(for)h(other)g(factors)g(suc)o(h)h(as)f(activ)o(e)g(pla)o(y)m(.)324 1061 y(In)c(programs)e(whic)o(h)i(searc)o(h)h(only)e(a)g(few)h(p)q(ositions,) g(the)g(ev)n(aluation)f(function)g(can)h(b)q(e)262 1111 y(quite)15 b(complex)e(and)i(time)f(consuming.)19 b(Ho)o(w)o(ev)o(er,)d(all)d (successful)k(programs)d(searc)o(h)i(a)262 1161 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(material)e(during)i(its)g(searc)o(h.)20 b(A)14 b(one)h(ply)e(p)q(ositional)g (v)n(alue)h(is)g(com)o(bined)f(at)262 1559 y(the)h(end)g(of)g(the)g(searc)o (h)h(to)f(distinguish)f(b)q(et)o(w)o(een)j(mo)o(v)o(es)c(of)h(equal)h (material)e(outcome.)324 1644 y(A)f(go)q(o)q(d)h(explanation)e(of)h(a)g(con)o (v)o(en)o(tional)g(c)o(hess)i(ev)n(aluation)d(function)h(can)h(b)q(e)g(found) 262 1694 y(in)j([4)o(].)24 b(Ev)n(aluation)15 b(functions)h(will)e(b)q(e)j (lo)q(ok)o(ed)f(at)f(in)h(m)o(uc)o(h)f(greater)i(detail)e(in)h(future)262 1744 y(c)o(hapters.)262 1917 y Fr(2.4)69 b(Lo)r(ok)24 b(Ahead)262 2043 y Fp(In)16 b(order)h(to)f(lo)q(ok)g(ahead)g(in)o(to)g(p)q(ossibilities)g (whic)o(h)g(ma)o(y)e(dev)o(elop)j(in)f(the)h(game,)e(it)h(is)262 2093 y(necessary)c(generate)g(what)f(is)g(called)f(a)h("Game)d(tree".)18 b(A)11 b(game)e(tree)j(is)f(a)f(diagrammati)o(c)262 2143 y(represen)o(tation) i(of)e(p)q(ossible)h(mo)o(v)o(e)e(sequences.)20 b(This)11 b(is)f(ac)o(hiev)o (ed)h(b)o(y)g(generating)g(mo)o(v)o(es)262 2193 y(for)k(the)h(side)f(to)g (pla)o(y)m(,)f(then)i(replies)g(for)f(the)h(opp)q(onen)o(t,)g(then)g(coun)o (ter)g(replies)g(and)g(so)262 2242 y(on,)c(dep)q(ending)h(on)g(the)g(depth)h (of)e(lo)q(ok)g(ahead)g(required.)19 b(Figure)13 b(2.5)f(sho)o(ws)h(a)f(p)q (ossible)957 2574 y(15)p eop %%Page: 16 18 16 17 bop 262 307 a Fp(lo)q(ok)12 b(ahead)i(game)f(tree)i(from)d(the)j(op)q (ening)e(c)o(hess)j(p)q(osition.)623 1489 y(Figure)e(2.5:)j(A)d(P)o(ossible)g (lo)q(ok)f(ahead)h(tree.)324 1607 y(Strictly)i(sp)q(eaking)g(the)h(game)e (tree)j(is)e(not)g(a)g(tree,)i(but)e(rather)i(a)e(directed)h(graph.)262 1657 y(This)12 b(is)h(b)q(ecause)i(some)d(no)q(des)i(can)f(b)q(e)h(reac)o (hed)g(through)f(di\013eren)o(t)h(paths,)f(kno)o(wn)g(as)g(a)262 1707 y(transp)q(osition)i(of)f(mo)o(v)o(es.)20 b(F)m(or)15 b(the)h(purp)q(ose)g(of)f(consistency)h(with)f(other)h(material)d(on)262 1757 y(the)h(sub)r(ject)h(I)f(will)f(also)g(use)i(the)f(term)f(searc)o(h)i (or)f(game)f(tree.)324 1842 y(There)i(are)f(a)g(n)o(um)o(b)q(er)f(of)g(w)o(a) o(ys)h(the)g(game)f(tree)i(can)f(b)q(e)g(expanded)h(and)f(searc)o(hed:)324 1925 y Ff(\017)20 b Fl(Depth)c(\014rst)g(searc)o(h)p Fp(:)k(The)15 b(\014rst)h(branc)o(h)g(is)f(explored)h(to)f(the)h(required)g(depth)365 1975 y(b)q(efore)k(the)f(mac)o(hine)e(starts)j(on)e(the)h(next)h(unexplored)f (branc)o(h)g(one)g(lev)o(el)f(up.)365 2024 y(This)c(con)o(tin)o(ues)g(un)o (til)g(all)e(no)q(des)j(ha)o(v)o(e)f(b)q(een)h(explored)f(to)g(the)g (required)h(depth.)324 2107 y Ff(\017)20 b Fl(Breadth)d(\014rst)f(searc)o(h)p Fp(:)21 b(All)15 b(no)q(des)i(at)e(one)h(lev)o(el)g(are)g(examined)e(b)q (efore)j(pro-)365 2157 y(gressing)i(one)f(lev)o(el)g(do)o(wn)f(the)i(tree)g (and)f(examining)d(all)i(no)q(des)i(at)e(that)h(lev)o(el.)365 2207 y(This)c(con)o(tin)o(ues)g(un)o(til)g(all)e(no)q(des)j(ha)o(v)o(e)f(b)q (een)h(explored)f(to)g(the)g(required)h(depth.)324 2290 y Ff(\017)20 b Fl(Best)13 b(\014rst)f(searc)o(h)p Fp(:)j(A)o(t)d(eac)o(h)g(step)h(the)f (most)e(promising)g(no)q(de)i(is)f(selected)i(from)365 2340 y(all)h(the)h(no)q(des)g(generated)h(so)f(far)f(in)g(the)h(tree.)22 b(New)15 b(no)q(des)g(are)g(then)g(generated)365 2390 y(from)g(the)i (selected)h(no)q(de,)g(and)e(again,)f(the)i(most)f(promising)e(no)q(de)j(is)f (selected.)365 2440 y(A)f(no)q(de)g(can)f(b)q(e)h(selected)h(as)f(most)e (promising)f(no)i(matter)g(where)h(in)f(the)h(tree)h(it)957 2574 y(16)p eop %%Page: 17 19 17 18 bop 365 307 a Fp(o)q(ccurs.)19 b(Also)12 b(no)q(des)h(previously)f (searc)o(hed,)i(but)f(rejected)h(as)e(unpromising,)f(ma)o(y)365 357 y(again)i(b)q(ecome)h(promising)d(and)j(b)q(e)h(re-searc)o(hed.)324 440 y(Note)20 b(that)g(the)h(required)f(depth)h(will)d(b)q(e)j(the)f (limiting)d(factor)j(for)f(the)i(breadth)262 490 y(\014rst)e(and)g(depth)h (\014rst)g(searc)o(hes.)36 b(The)20 b(b)q(est)g(\014rst)g(searc)o(h)g(m)o (ust)e(ha)o(v)o(e)h(some)g(w)o(a)o(y)f(of)262 540 y(terminating,)11 b(although)i(depth)i(ma)o(y)d(not)h(b)q(e)i(the)f(limiting)d(factor.)324 625 y(I)g(kno)o(w)g(of)f(no)h(activ)o(e)h(programs)e(whic)o(h)h(uses)h(the)g (breadth)g(\014rst)g(searc)o(h.)19 b(Most)11 b(c)o(hess)262 675 y(programs)i(use)i(a)f(mo)q(di\014ed)f(v)o(ersion)i(of)f(the)h(depth)g (\014rst)g(searc)o(h.)21 b(These)15 b(mo)q(di\014cations)262 725 y(will)10 b(b)q(e)i(explained)g(in)f(c)o(hapter)i(3.)k(The)12 b(b)q(est)h(\014rst)f(pro)q(cedure)i(is)e(used)g(in)g(some)f(selectiv)o(e)262 774 y(searc)o(h)20 b(programs.)35 b(Of)20 b(particular)f(in)o(terest)i(is)f (the)g(B*)g(tree)h(searc)o(h)g(algorithm)c([6],)262 824 y(a)g(dev)o(elopmen)o (t)g(of)g(the)h(b)q(est)h(\014rst)g(searc)o(h.)30 b(This)18 b(algorithm)d(attempts)i(to)h(allo)o(w)e(for)262 874 y(uncertain)o(t)o(y)e (to)g(b)q(e)g(expressed)i(in)e(the)g(searc)o(h)h(tree.)324 959 y(The)20 b(searc)o(h)g(of)f(a)g(t)o(w)o(o-pla)o(y)o(er)g(game)f(tree)i (can)g(b)q(e)g(ac)o(hiev)o(ed)g(b)o(y)f(the)h(use)g(of)f(the)262 1009 y(minim)o(ax)11 b(pro)q(cedure.)20 b(This)14 b(is)g(based)h(on)f(the)g (idea)g(that)g(t)o(w)o(o)g(pla)o(y)o(ers)g(exist,)g(Max)g(and)262 1059 y(Min.)23 b(Max)16 b(c)o(ho)q(oses)h(mo)o(v)o(es)e(leading)g(to)h(high)f (scores,)j(where)f(as)f(Min)g(c)o(ho)q(oses)h(mo)o(v)o(es)262 1109 y(leading)10 b(to)i(lo)o(w)f(scores.)19 b(Max)12 b(and)f(Min)h(c)o(ho)q (ose)g(mo)o(v)o(es)f(at)h(alternate)g(lev)o(els)g(of)f(the)i(tree,)262 1158 y(o)q(dd)g(and)h(ev)o(en)h(resp)q(ectiv)o(ely)m(.)262 1331 y Fr(2.5)69 b(Selectiv)n(e)20 b(Searc)n(hing)262 1458 y Fp(It)13 b(has)g(b)q(een)i(sho)o(wn)e(b)o(y)g(de)h(Gro)q(ot)f([16)o(,)f (17])h(that)g(there)h(are)g(on)f(a)o(v)o(erage)g(38)g(mo)o(v)o(es)f(in)h(a) 262 1507 y(giv)o(en)d(p)q(osition,)h(y)o(et)g(only)f(an)h(a)o(v)o(erage)g(of) g(1.76)e(go)q(o)q(d)i(mo)o(v)o(es)1229 1492 y Fk(1)1257 1507 y Fp(exist)h(in)f(eac)o(h)g(p)q(osition.)17 b(A)262 1557 y(h)o(uman)11 b(c)o(hess)k(master's)d(searc)o(h)j(tree)f(t)o(ypically)e(in)o(v)o(olv)o(es)g (a)h(total)g(of)g(around)g(35)f(mo)o(v)o(es;)262 1607 y(v)n(ariations)18 b(are)i(explored)h(to)e(an)h(a)o(v)o(erage)g(depth)g(of)g(7)f(plies.)36 b(It)20 b(is)g(clear)g(from)e(the)262 1657 y(researc)o(h)e(of)f(de)g(Gro)q (ot)g(that)g(the)h(h)o(uman)d(c)o(hess)k(master)d(is)h(v)o(ery)g(e\016cien)o (t)h(at)f(selecting)262 1707 y(mo)o(v)o(es)8 b(to)h(explore)h(further.)17 b(It)10 b(therefore)h(seems)e(logical)f(to)h(program)f(a)i(computer)f(whic)o (h)262 1756 y(selects)18 b(the)g(most)e(plausible)g(mo)o(v)o(es)g(to)g(b)q(e) i(explored)f(next)h(from)d(those)j(a)o(v)n(ailable.)25 b(If)262 1806 y(suc)o(h)18 b(a)g(program)e(had)i(a)g(selection)h(mec)o(hanism)c(as)j (sophisticated)h(as)f(a)g(master's,)g(it)262 1856 y(w)o(ould)c(almost)f (certainly)i(pla)o(y)f(at)g(master)h(lev)o(el)g(or)f(ab)q(o)o(v)o(e.)21 b(This)15 b(metho)q(d)f(is)h(kno)o(w)g(as)262 1906 y Fm(Sele)n(ctive)f(Se)n (ar)n(ching)g Fp(or)g(a)g(Shannon)g(t)o(yp)q(e)g(B/C)g(strategy)m(.)324 1991 y(The)j(Green)o(blatt)f(program)f(w)o(as)i(the)g(\014rst)g(successful)h ('selectiv)o(e')f(searc)o(hing)g(c)o(hess)262 2041 y(program)12 b(whic)o(h)j(could)f(pla)o(y)f(at)h(a)h(reasonable)f(lev)o(el.)20 b(The)14 b(program)f(placed)i(limits)d(on)262 2091 y(the)i(n)o(um)o(b)q(er)f (of)g(mo)o(v)o(es)f(whic)o(h)i(could)f(b)q(e)i(searc)o(hed)g(at)e(di\013eren) o(t)i(depths.)k(The)14 b(n)o(um)o(b)q(er)262 2141 y(of)h(branc)o(hes)j (explored)f(in)f(the)i(\014rst)f(5)f(plies)h(w)o(ere)g(as)g(follo)o(ws:)22 b(15,)16 b(15,)g(9,)g(9,)h(7.)26 b(This)262 2190 y(tap)q(ering)11 b(of)h(the)g(searc)o(h)h(mean)o(t)e(that)h(deep)q(er)h(searc)o(hes)h(w)o(ere) f(p)q(ossible)f(when)g(compared)262 2240 y(with)k(the)i(full)e(width)h (approac)o(h)h(at)f(the)h(time.)26 b(In)18 b(the)g(early)f(1970's,)f(Hans)i (Berliner)262 2290 y(considered)c(v)o(ery)g(selectiv)o(e)h(searc)o(hing)f(as) f(the)i(w)o(a)o(y)d(forw)o(ard)h(and)h(exp)q(ected)h(the)f(searc)o(h)262 2340 y(tree)j(w)o(ould)d(con)o(tain)i(less)g(than)g(500)f(no)q(des.)24 b(It)16 b(is)g(ironic)f(that)h(Hans)g(is)f(no)o(w)h(a)f(ma)r(jor)p 262 2374 573 2 v 308 2401 a Fj(1)325 2413 y Fi(Grandmaster)8 b(standard)h(mo)o(v)o(es)957 2574 y Fp(17)p eop %%Page: 18 20 18 19 bop 262 307 a Fp(force)11 b(b)q(ehind)g(Hitec)o(h,)h(a)f(v)o(ery)g (strong)g(brute)h(force)g(searc)o(hing)f(program)e(from)h(Carnegie-)262 357 y(Mellon)j(Univ)o(ersit)o(y)m(.)324 442 y(The)21 b(b)q(est)h(attempt)e (at)g(selectiv)o(e)i(searc)o(hing)f(w)o(as)f(made)g(b)o(y)g(Wilkins)f([61],)i (who)262 492 y(pro)q(duced)14 b(a)f(kno)o(wledge)g(based)h(program,)d(P)m (ARADISE.)i(The)g(program)f(p)q(erformed)h(at)262 542 y(the)h(exp)q(ert)h (lev)o(el)f(in)f(the)i(relativ)o(ely)e(narro)o(w)h(domain)d(of)j(tactical)f (problems.)324 627 y(All)e(the)h(attempts)g(to)f(create)j(a)d(go)q(o)q(d)h (selectiv)o(e)h(searc)o(h)g(program)d(to)i(pla)o(y)e(the)j(whole)262 677 y(game)j(ha)o(v)o(e)j(hit)f(problems.)30 b(This)18 b(is)g(b)q(ecause)i (it)e(is)g(vital)g(to)g(include)g(all)f(imp)q(ortan)o(t)262 727 y(mo)o(v)o(es)f(in)g(the)i(selectiv)o(e)h(searc)o(h,)g(as)e(an)o(y)g(mo)o (v)o(es)f(not)h(selected)i(can)f(nev)o(er)g(b)q(e)g(pla)o(y)o(ed)262 777 y(o)o(v)o(er)13 b(the)i(b)q(oard.)j(This)c(can)g(cause)h(serious)f (tactical)g(threats)h(to)f(b)q(e)g(o)o(v)o(erlo)q(ok)o(ed.)324 862 y(Some)c(mo)o(v)o(es)h(ma)o(y)e(not)j(app)q(ear)g(immediately)c (plausible,)j(although)g(they)h(ma)o(y)e(turn)262 912 y(out)16 b(to)h(b)q(e)g(v)o(ery)g(strong)g(some)e(mo)o(v)o(es)h(later.)26 b(F)m(or)16 b(these)i(reasons)g(man)o(y)d(go)q(o)q(d)h(mo)o(v)o(es)262 961 y(are)d(o)o(v)o(erlo)q(ok)o(ed)f(and)h(not)g(selected)i(b)o(y)e(a)f (plausible)g(mo)o(v)o(e)g(generator.)18 b(These)d(problems)262 1011 y(are)f(b)q(est)h(illustrated)f(b)o(y)f(some)g(examples.)p 641 1105 673 5 v 641 1769 5 665 v 646 1188 a Fg(rm0Z0skZ)646 1271 y(o0l0mpop)646 1354 y(bo0ZpZ0Z)646 1437 y(Z0opO0Z0)646 1520 y(PZ0O0Z0Z)646 1603 y(Z0OBZNZ0)646 1686 y(0ZPZ0OPO)646 1769 y(S0AQJ0ZR)p 1310 1769 V 641 1773 673 5 v 659 1892 a Fp(Figure)h(2.6:)j (White)d(to)f(pla)o(y)g(and)h(win.)324 2010 y(In)g(\014gure)i(2.6,)d(white)i (can)f(pla)o(y)g(1.)20 b(Bxh7+)15 b(Kxh7)f(2.)20 b(Ng5+)15 b(Kg8)f(3.)20 b(Qh5)15 b(leading)262 2060 y(to)j(mate.)31 b(The)20 b(initial)c(mo)o(v)o(e)h(ma)o(y)g(ho)o(w)o(ev)o(er,)j(not)e(app)q(ear)i (plausible)e(to)g(a)h(selectiv)o(e)262 2110 y(searc)o(h)13 b(program)e(b)q(ecause)k(it)d(app)q(ears)h(to)g(lose)f(the)i(bishop)e(for)g (a)h(pa)o(wn.)k(An)o(y)12 b(plausible)262 2159 y(mo)o(v)o(e)i(generator)i (whic)o(h)g(did)f(consider)h(Bxh7+)g(plausible)f(w)o(ould)g(need)i(to)f ('recognise')262 2209 y(in)e(\014gure)i(2.7,)e(an)h(almost)f(iden)o(tical)g (p)q(osition,)h(that)g(1.)22 b(Bxh7+)16 b(Kxh7)f(2.)22 b(Ng5+)15 b(Kg8)262 2259 y(3.)i(Qh5)d(fails)f(to)h(3.)j(...)g(Bd3.)957 2574 y(18)p eop %%Page: 19 21 19 20 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(rm0Z0skZ)646 482 y(o0l0mpop)646 565 y(bo0ZpZ0Z)646 648 y(Z0opO0Z0)646 731 y(PZ0O0Z0Z)646 814 y(Z0OBZNZ0)646 897 y(0O0Z0OPO)646 980 y(S0AQJ0ZR)p 1310 980 V 641 984 673 5 v 605 1101 a Fp(Figure)14 b(2.7:)j(White)c(to)h(pla) o(y)m(,)e(no)i(forced)g(win.)324 1218 y(These)f(di\016culties)g(illustrate)f (that)g(to)h(k)o(eep)g(the)g(branc)o(hing)f(factor)g(do)o(wn)g(the)h(plau-) 262 1268 y(sible)g(mo)o(v)o(e)f(generator)i(needs)h(to)e(b)q(e)h(v)o(ery)f (selectiv)o(e,)i(while)d(not)i(excluding)f(k)o(ey)g(mo)o(v)o(es.)262 1318 y(A)o(t)f(the)g(presen)o(t)i(time)c(w)o(e)i(do)g(not)g(ha)o(v)o(e)g(the) g(capabilit)o(y)e(to)i(instill)f(enough)h(h)o(uman)e(c)o(hess)262 1368 y(kno)o(wledge)j(in)o(to)g(a)h(program)e(to)i(mak)o(e)e(this)i(metho)q (d)f(e\013ectiv)o(e)j(for)d(the)i(whole)e(game.)262 1540 y Fr(2.6)69 b(F)-6 b(ull)22 b(Width)g(Searc)n(hing)262 1667 y Fp(Instead)10 b(of)g(selecting)g(promising)e(lines)i(to)g(in)o(v)o(estigate)g (further,)h(it)e(is)h(p)q(ossible)g(to)g(explore)262 1716 y(all)15 b(mo)o(v)o(es)g(to)h(a)g(giv)o(en)f(depth.)26 b(This)16 b(Shannon)g(t)o(yp)q (e)h(A)f(metho)q(d)g(is)g(kno)o(wn)g(as)g(a)g Fm(F)m(ul)r(l)262 1766 y(Width)f(Se)n(ar)n(ch)f Fp(or)g(a)f Fm(Brute)i(F)m(or)n(c)n(e)f(Se)n (ar)n(ch)p Fp(.)324 1851 y(This)f(metho)q(d)g(is)h(m)o(uc)o(h)e(easier)j(to)f (implem)o(en)o(t)e(than)h(a)h(selectiv)o(e)h(searc)o(h.)k(Ho)o(w)o(ev)o(er,) 262 1901 y(in)g(order)i(for)f(pla)o(y)g(to)g(b)q(e)h(of)e(a)h(reasonable)h (standard)g(a)f(relativ)o(ely)f(deep)i(searc)o(h)h(is)262 1951 y(necessary)m(.)34 b(The)20 b(problem)d(here)j(is)f(that)g(the)h(n)o(um)o(b)q (er)e(of)g(no)q(des)i(in)o(v)o(olv)o(ed)e(in)g(a)h(full)262 2001 y(width)11 b(searc)o(h)i(gro)o(ws)e(exp)q(onen)o(tially)g(with)g(depth.) 18 b(In)12 b(a)f(tree)i(of)e(uniform)f(width)h(38,)g(the)262 2051 y(searc)o(h)j(tree)h(will)d(con)o(tain)h(o)o(v)o(er)h(3)f(billion)f(no)q (des)i(after)g(just)g(6)f(plies.)18 b(T)m(o)13 b(cut)h(do)o(wn)g(this)262 2100 y(exp)q(onen)o(tial)c(explosion,)g(v)n(arious,)g(often)h(complicated)e 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y(con)o(v)o(en)o(tion)d(where)j(eac)o(h)f(subtree)h(returns)g(its)e(v)n (alue)f(negated.)20 b(This)14 b(allo)o(ws)f(eac)o(h)i(side)262 506 y(to)g(maxim)o(ise)e(its)i(score)h(at)g(eac)o(h)f(lev)o(el)g(of)g(the)h (tree,)g(simplifying)c(the)k(implemen)o(tation)262 556 y(of)d(the)h (algorithm.)i Fh(\013)d Fp(and)h Fh(\014)i Fp(are)f(initially)c(set)k(to)f Ff(\0001)f Fp(and)h(+)p Ff(1)g Fp(resp)q(ectiv)o(ely)m(.)557 1447 y(Figure)g(3.1:)j(An)d(example)f(Negamax)f(Searc)o(h)j(tree.)324 1542 y(In)e(the)h(\014gure,)f(no)q(des)h(C)g(and)f(D)g(are)g(searc)o(hed)i (and)e(ev)n(aluated,)g(resulting)g(in)g(scores)262 1592 y(of)g Ff(\000)p Fp(5)i(and)f Ff(\000)p Fp(2)h(resp)q(ectiv)o(ely)m(.)21 b(Using)14 b(negamax)f(a)h(score)i(of)e(+2)h(is)f(bac)o(k)o(ed)h(up)g(to)f (no)q(de)262 1642 y(B.)j(This)g(v)n(alue)g(then)i(replaces)f(the)h Fh(\013)e Fp(v)n(alue)g(at)g(ply)g(1)g(b)q(ecause)j(it)d(is)g(larger)h(than)f Fh(\013)p Fp(.)262 1691 y(No)q(de)d(F)f(is)h(then)g(searc)o(hed,)h(whic)o(h)f (pro)q(duces)h(a)e(v)n(alue)g(of)g(+1.)18 b(This)c(v)n(alue)f(is)g(not)h (large)262 1741 y(enough)f(to)f(a\013ect)i(the)g Fh(\013)e Fp(v)n(alue)g(at)h(ply)f(1)h(ab)q(o)o(v)o(e.)k(Hence,)e(there)f(is)f(no)f (reason)i(to)e(searc)o(h)262 1791 y(no)q(de)18 b(G)g(since)h(the)g(resulting) f(v)n(alue)g(of)g(no)q(de)g(E)h(can)f(only)g(b)q(e)h Ff(\024)g(\000)p Fp(1)f(\(negamaxed\).)262 1841 y(Therefore,)h(no)q(de)f(G)f(is)g(said)g(to)h (b)q(e)g(cut)g(o\013)f(or)h(pruned)g(from)e(the)i(searc)o(h)h(tree.)30 b(The)262 1891 y(negamax)12 b(approac)o(h)i(has)g(the)h(e\013ect)g(of)f (making)d(all)i(cut)i(o\013s,)e Fh(\014)k Fp(cut)e(o\013s.)j(The)d(pseudo)262 1940 y(co)q(de)f(for)g(the)g Fh(\013\014)i Fp(algorithm)c(can)i(b)q(e)g (found)g(in)f(\014gure)i(3.2.)324 2026 y(The)10 b(normal)f(full)g(width)h (minim)o(ax)d(pro)q(cedure,)12 b(applied)e(to)g(a)g(tree)h(of)f(uniform)e (width)262 2075 y(W)15 b(and)h(depth)g(d,)g(w)o(ould)g(ha)o(v)o(e)f(to)h (searc)o(h)h Fh(W)1020 2060 y Fe(d)1055 2075 y Fp(terminal)e(no)q(des.)25 b(The)16 b Fh(\013\014)i Fp(algorithm)262 2125 y(under)13 b(optimal)e (conditions)h(can)i(prune)g(a)e(tree)j(to)e(the)g(exten)o(t)h(that)f(only)g (the)g(follo)o(wing)262 2175 y(terminal)f(no)q(des)i(need)h(to)f(b)q(e)g (examined)f([13)o(]:)324 2248 y Ff(\017)20 b Fh(W)410 2233 y Fk(\()p Fe(d)p Fk(+1\))p Fe(=)p Fk(2)540 2248 y Fp(+)10 b Fh(W)627 2233 y Fk(\()p Fe(d)p Fd(\000)p Fk(1\))p Fe(=)p Fk(2)757 2248 y Ff(\000)g Fp(1)k(at)f(o)q(dd)h(depths.)324 2326 y Ff(\017)20 b Fp(2)9 b Ff(\001)g Fh(W)461 2311 y Fe(d=)p Fk(2)523 2326 y Ff(\000)h Fp(1)j(at)h(ev)o(en)h(depths.)262 2399 y(This)g(is)h(kno)o(wn)f (as)h(the)h(minim)o(al)12 b(searc)o(h)17 b(tree.)25 b(T)m(o)16 b(ac)o(hiev)o(e)g(this)g(result,)g(most)f(mo)o(v)o(es)262 2449 y(m)o(ust)10 b(b)q(e)h(searc)o(hed)i(in)e(a)g(descending)h(order)g(of)f (merit.)16 b(Of)11 b(course)i(the)e(true)h(merit)e(of)h(an)o(y)957 2574 y(23)p eop %%Page: 24 26 24 25 bop 262 503 a Fl(F)l(unction)11 b Fp(AlphaBeta\(P)j(:)g Fl(p)q(osition)p Fp(;)c Fh(\013)p Fp(,)j Fh(\014)k Fp(:)h Fl(in)o(teger)p Fp(\))11 b Fl(returns)j(in)o(teger)262 603 y(v)m(ar)321 653 y Fp(m)82 b(:)18 b Fl(mo)o(v)o(e)321 702 y Fp(score,)321 752 y(b)q(est)44 b(:)18 b Fl(in)o(teger)262 852 y(b)q(egin)321 952 y(if)12 b Fp(\(T)m(erminal\(P\)\))446 b(/*)13 b Fm(Is)i(p)n(osition)g(P)g (terminal)f(?)19 b Fp(*/)380 1001 y Fl(return)11 b Fp(\(Ev)n(aluate\(P)m(,)i Fh(\013)p Fp(,)g Fh(\014)r Fp(\)\))189 b(/*)13 b Fm(R)n(eturn)i(sc)n(or)n(e)g (at)f(le)n(af)h(no)n(des)f Fp(*/)321 1051 y Fl(endif)321 1151 y Fp(GenerateMo)o(v)o(es\(P\))408 b(/*)13 b Fm(Gener)n(ate)i(al)r(l)f(moves)i (in)e(p)n(osition)h(P)f Fp(*/)321 1201 y(b)q(est)h(:=)e Ff(\0001)524 b Fp(/*)13 b Fm(b)n(est)i(move)g(sc)n(or)n(e)f(not)i(yet)e(known)h Fp(*/)321 1250 y Fl(for)g(eac)o(h)g(mo)o(v)o(e)e Fp(m)f Fl(do)380 1300 y Fp(/*)h Fm(Se)n(ar)n(ch)i(move)g(m)g(using)g(ne)n(gamax)h(c)n (onvention)g(\(p)n(ar)n(ameters)e(r)n(everse)n(d\))f Fp(*/)380 1350 y(score)i(:=)e Ff(\000)p Fp(AlphaBeta\()p Fh(P)810 1356 y Fe(m)842 1350 y Fp(,)h Ff(\000)p Fh(\014)r Fp(,)g Ff(\000)p Fl(max)p Fp(\()p Fh(\013)p Fp(,)g(b)q(est\)\))380 1400 y Fl(if)e Fp(\(score)k Fh(>)e Fp(b)q(est\))439 1450 y(b)q(est)h(:=)e(score)391 b(/*)13 b Fm(Stor)n(e)i(b)n(est)f(sc)n(or)n(e)h(found)f Fp(*/)439 1499 y Fl(if)e Fp(\(b)q(est)k Ff(\025)11 b Fh(\014)r Fp(\))498 1549 y Fl(return)g Fp(\(b)q(est\))315 b(/*)13 b Fh(\014)18 b Fm(cut)d(o\013)g(:)k(r)n(eturn)14 b(b)n(est)h(sc)n(or)n(e)e Fp(*/)439 1599 y Fl(endif)380 1649 y(endif)321 1699 y(endfor)321 1798 y(return)e Fp(\(b)q(est\))492 b(/*)13 b Fm(R)n(eturn)i(sc)n(or)n(e)g(of) f(b)n(est)h(move)g(found)g Fp(*/)262 1898 y Fl(end)d Fp(AlphaBeta)262 2047 y(The)i Fl(max)p Fp(\()p Fh(\013)p Fp(,)f(b)q(est\))i(op)q(eration)f (represen)o(ts)j(the)d('fail)e(soft')h(condition)h(whic)o(h)f(allo)o(ws)g (the)262 2097 y(searc)o(h)i(at)e(eac)o(h)i(lev)o(el)e(to)h(return)h(the)g(b)q (est)g(v)n(alue)e(found,)g(ev)o(en)h(if)f(this)h(is)g(less)h(than)f Fh(\013)p Fp(.)552 2280 y(Figure)g(3.2:)j(Pseudo)d(co)q(de)h(for)f(the)g Fh(\013\014)i Fp(Algorithm.)957 2574 y(24)p eop %%Page: 25 27 25 26 bop 262 307 a Fp(mo)o(v)o(e)12 b(is)j(not)f(kno)o(wn)g(b)q(efore)i(it)e (is)g(searc)o(hed.)22 b(Therefore,)16 b(heuristics)g(m)o(ust)d(b)q(e)i(used)h (to)262 357 y(ac)o(hiev)o(e)d(this)h(ordering.)k(In)13 b(practice)i(the)f Fh(\013\014)i Fp(algorithm)11 b(searc)o(hes)16 b(a)d(tree)i(3)e(to)g(6)h (times)262 407 y(larger)j(than)h(the)h(minim)o(al)14 b(tree)19 b(b)q(ecause)h(of)d(sub{optimal)e(ordering.)30 b(Ho)o(w)o(ev)o(er,)19 b(the)262 457 y(enormous)14 b(sa)o(vings)h(pro)q(duced)i(b)o(y)e(using)g(the) h Fh(\013\014)i Fp(algorithm)13 b(are)j(suc)o(h)g(that)f(it)g(b)q(egins)262 506 y(to)e(mak)o(e)g(full)f(width)i(searc)o(hing)g(a)g(plausible)f (alternativ)o(e)h(to)f(selectiv)o(e)i(searc)o(hing.)262 656 y Fu(3.1.2)55 b(Aspiration)18 b Fs(\013\014)k Fu(Searc)n(h)262 768 y Fp(The)16 b(basic)g Fh(\013\014)j Fp(searc)o(h)e(is)f(carried)h(out)f (with)g(initial)e Fh(\013\014)19 b Fp(v)n(alues)d(set)h(to)f Ff(\0001)g Fp(and)g(+)p Ff(1)262 818 y Fp(resp)q(ectiv)o(ely)m(.)22 b(The)15 b(aspiration)f Fh(\013\014)j Fp(searc)o(h)f(mak)o(es)e(assumptions)g (ab)q(out)h(the)h(exp)q(ected)262 868 y(v)n(alue)d(of)i(the)g(searc)o(h)h (tree.)21 b(The)15 b Fh(\013\014)i Fp(b)q(ounds)e(are)g(therefore)h (initially)c(set)k(to)e(a)h(narro)o(w)262 917 y(windo)o(w)c(cen)o(tered)j (around)d(the)i(exp)q(ected)h(searc)o(h)f(tree)g(v)n(alue,)e Ff(\006)i Fp(a)e(pa)o(wn,)h(for)f(example.)324 1003 y(Unlik)o(e)j(the)i (basic)f Fh(\013\014)i Fp(searc)o(h)f(whic)o(h)f(alw)o(a)o(ys)f(returns)i (the)g(true)g(score)g(of)e(the)i(tree,)262 1053 y(an)d(aspiration)g Fh(\013\014)j Fp(searc)o(h)f(can)g(pro)q(duce)g(3)e(p)q(ossible)h(outcomes:) 312 1126 y(1.)20 b Fl(A)f(true)e(score)p Fp(:)22 b(The)16 b(true)h(v)n(alue)f (of)f(the)i(tree)g(lies)f(inside)g(the)h(searc)o(h)g(windo)o(w)365 1176 y(and)d(w)o(as)g(therefore)h(found)f(b)o(y)f(the)i(searc)o(h.)312 1254 y(2.)20 b Fl(A)c(fail)f(lo)o(w)p Fp(:)i(The)d(true)h(v)n(alue)e(of)g (the)i(tree)g(is)f(smaller)e(than)i(the)g Fh(\013)g Fp(b)q(ound.)312 1332 y(3.)20 b Fl(A)d(fail)d(high)p Fp(:)j(The)e(true)g(v)n(alue)e(of)h(the)h (tree)g(is)f(larger)h(than,)e(or)i(equal)e(to,)h(the)h Fh(\014)365 1382 y Fp(b)q(ound.)262 1455 y(In)i(case)i(1,)f(the)g(searc)o(h)h(has)f(b)q (een)h(successful)g(b)q(ecause)g(the)g(b)q(est)f(mo)o(v)o(e)f(and)g(its)h (true)262 1505 y(v)n(alue)12 b(has)g(b)q(een)i(found.)k(In)12 b(cases)i(2)f(and)f(3)h(the)g(searc)o(h)h(has)f(failed)f(to)g(\014nd)h(a)g (true)g(v)n(alue)262 1554 y(for)k(the)h(tree)g(b)q(ecause)h(of)e Fh(\013\014)j Fp(cut)e(o\013s.)29 b(Ho)o(w)o(ev)o(er,)18 b(the)g(direction)f (of)g(the)h(tree's)h(true)262 1604 y(v)n(alue)c(relativ)o(e)g(to)h(the)g Fh(\013\014)i Fp(b)q(ounds)f(is)e(no)o(w)h(kno)o(wn.)23 b(When)16 b(the)h(searc)o(h)g(fails)d(lo)o(w)h(the)262 1654 y(true)f(v)n(alue)e(is)h (kno)o(wn)g(to)g(lie)f(in)h(the)h(range)f(\()p Ff(\0001)p Fp(,)p Fh(\013)p Fp(\),)f(and)h(when)h(it)f(fails)f(high,)g(the)i(true)262 1704 y(v)n(alue)g(will)h(lie)g(in)g(the)h(range)g(\()p Fh(\014)r Fp(,+)p Ff(1)p Fp(\).)23 b(Using)16 b(the)g(appropriate)g(new)g(searc)o(h)g (windo)o(w)262 1754 y(the)e(tree)h(m)o(ust)e(b)q(e)i(re-searc)o(hed)h(to)d (\014nd)h(the)h(true)g(score.)324 1839 y(This)k(approac)o(h)h(can)g(pro)q (duce)g(a)g(noticeably)f(faster)h(searc)o(h)h(than)e(the)i(basic)e Fh(\013\014)262 1889 y Fp(algorithm)c(if)i(the)h(initial)e(windo)o(w)h(is)g (w)o(ell)h(c)o(hosen.)30 b(It)18 b(can,)h(ho)o(w)o(ev)o(er,)f(also)f(pro)q (duce)262 1939 y(a)e(slo)o(w)o(er)g(searc)o(h)i(if)d(the)i(v)n(alue)f(of)g (the)h(tree)h(lies)e(outside)h(the)g(initial)d(windo)o(w,)h(as)i(a)f(re-)262 1988 y(searc)o(h)h(will)e(b)q(e)i(necessary)m(.)25 b(In)15 b(c)o(hess,)i(material)d(is)h(rarely)h(w)o(on)f(or)g(lost.)23 b(Therefore,)17 b(a)262 2038 y(windo)o(w)10 b(of)h(a)g(couple)h(of)e(pa)o (wns)i(width)f(will)f(only)g(fail)g(o)q(ccasionally)g(to)i(\014nd)f(a)g(true) h(score)262 2088 y(at)j(the)i(\014rst)f(attempt,)f(making)f(this)i(tec)o (hnique)g(generally)g(faster)g(than)g(the)g(basic)g Fh(\013\014)262 2138 y Fp(algorithm.)262 2287 y Fu(3.1.3)55 b(Principle)17 b(V)-5 b(ariation)19 b Fs(\013\014)i Fu(Searc)n(h)262 2399 y Fp(The)16 b(aspiration)g Fh(\013\014)i Fp(searc)o(h)g(is)e(e\013ectiv)o(e)i (b)q(ecause)f(the)g(reduced)h Fh(\013\014)h Fp(windo)o(w)c(cuts)j(o\013)262 2449 y(n)o(umerous)13 b(subtrees)k(on)d(the)h(assumption)e(that)i(something)e (b)q(etter)j(exists.)k(If)14 b(w)o(e)h(to)q(ok)957 2574 y(25)p eop %%Page: 26 28 26 27 bop 262 307 a Fp(this)13 b(reduced)j(windo)o(w)d(idea)h(to)g(its)f (limits)f(w)o(e)i(w)o(ould)f(ha)o(v)o(e)h(a)f(minima)o(l)e(windo)o(w.)324 392 y(A)17 b(minim)o(al)c(windo)o(w)k(uses)h Fh(\013)f Fp(and)f Fh(\014)k Fp(v)n(alues)d(set)h(so)f(close)g(together)h(that)g(no)e(tree)262 442 y(v)n(alue)8 b(can)i(b)q(e)g(enclosed)h(within)e(the)h(windo)o(w.)16 b(Therefore,)11 b(the)f Fh(\013\014)i Fp(searc)o(h)e(will)e(de\014nitely)262 492 y(fail)13 b(lo)o(w)h(or)h(high)f(dep)q(ending)h(on)g(where)h(the)g(true)f (score)h(lies)f(relativ)o(e)g(to)g(the)g(minim)o(al)262 542 y(windo)o(w,)10 b(thereb)o(y)i(iden)o(tifying)d(in)i(whic)o(h)f(direction)i (the)f(true)h(score)g(lies.)17 b(The)11 b Fl(P)p Fp(rinciple)262 592 y Fl(V)p Fp(ariation)i Fh(\013\014)18 b Fl(S)p Fp(earc)o(h)d(\()p Fl(PVS)p Fp(\))g(uses)h(this)f(idea)g(b)o(y)g(\014rst)h(doing)e(a)h(basic)g Fh(\013\014)j Fp(searc)o(h)e(to)262 641 y(\014nd)e(the)i(true)f(v)n(alue)f (of)g(the)i(principle)e(v)n(ariation.)19 b(All)14 b(subsequen)o(t)i(searc)o (hes)h(are)e(then)262 691 y(done)d(with)g(a)g(minima)o(l)d(windo)o(w)j(cen)o (tered)i(on)e(the)h(curren)o(t)h(v)n(alue)e(of)f(the)i(principle)g(line.)262 741 y(This)h(w)o(orks)g(on)g(the)h(idea)f(that)h(it)f(is)g(m)o(uc)o(h)f (easier)i(to)f(sho)o(w)g(that)h(a)f(subtree)i(is)e(inferior)262 791 y(than)h(determine)g(its)g(true)h(v)n(alue.)22 b(Therefore,)16 b(when)g(a)f(minim)o(al)d(windo)o(w)i(searc)o(h)j(fails)262 841 y(lo)o(w,)i(the)g(mo)o(v)o(e)f(is)h(discarded)h(as)f(b)q(eing)g(w)o(orse) h(than)f(the)h(mo)o(v)o(e)e(already)h(found.)33 b(If)262 891 y(ho)o(w)o(ev)o(er,)18 b(it)g(fails)f(high,)h(it)f(m)o(ust)g(b)q(e)i (re-searc)o(hed)h(with)e(a)g(windo)o(w)f(wide)h(enough)g(to)262 940 y(encompass)13 b(the)i(true)f(score.)324 1026 y(Figure)g(3.3)f(sho)o(ws)i (the)g(pseudo)g(co)q(de)g(for)e(the)i(PVS)g(algorithm.)h(The)f(pseudo)g(co)q (de)262 1075 y(includes)h(Reinefeld's)g(depth)h Ff(\024)g Fp(2)f(enhancemen)o (t)h([46)o(].)25 b(This)16 b(enhancemen)o(t)g(uses)i(the)262 1125 y(fact)12 b(that)h(the)g('fail-soft')d(max)h(op)q(eration)i(allo)o(ws)f (true)h(scores)i(rather)e(than)g Fh(\014)i Fp(v)n(alues)e(to)262 1175 y(b)q(e)f(returned)i(from)d(the)i(last)f(2)g(plies)g(of)f(the)i(tree.)19 b(Hence,)14 b(at)e(the)g(b)q(ottom)f(2)h(plies)g(of)g(the)262 1225 y(tree,)i(re-searc)o(hes)j(are)d(unnecessary)m(.)957 2574 y(26)p eop %%Page: 27 29 27 28 bop 262 342 a Fl(F)l(unction)11 b Fp(PVS\(P)k(:)e Fl(p)q(osition)p Fp(;)d Fh(\013)p Fp(,)j Fh(\014)r Fp(,)h(depth)h(:)j Fl(in)o(teger)p Fp(\))11 b Fl(returns)j(in)o(teger)262 442 y(v)m(ar)321 491 y Fp(m)82 b(:)18 b Fl(mo)o(v)o(e)321 541 y Fp(score,)321 591 y(b)q(est)44 b(:)18 b Fl(in)o(teger)262 691 y(b)q(egin)321 790 y(if)12 b Fp(\(depth)j(=)f(0\))380 840 y Fl(return)d Fp(\(Ev)n(aluate\(P) m(,)i Fh(\013)p Fp(,)g Fh(\014)r Fp(\)\))189 b(/*)13 b Fm(Evaluate)i(le)n(af) g(no)n(de)f Fp(*/)321 890 y Fl(endif)321 990 y Fp(GenerateMo)o(v)o(es\(P\)) 408 b(/*)13 b Fm(Gener)n(ate)i(al)r(l)f(moves)i(in)e(p)n(osition)h(P)f Fp(*/)321 1039 y(/*)f Fm(Se)n(ar)n(ch)i(principle)f(variation)h(to)g(next)g (depth)h(using)f(ne)n(gamax)h(c)n(onvention)f Fp(*/)321 1089 y(b)q(est)g(:=)e Ff(\000)p Fp(PVS\()p Fh(P)624 1095 y Fk(1)643 1089 y Fp(,)h Ff(\000)p Fh(\014)r Fp(,)g Ff(\000)p Fh(\013)p Fp(,)f(depth)p Ff(\000)p Fp(1\))321 1139 y Fl(if)f Fp(\(b)q(est)j Ff(\025)g Fh(\014)r Fp(\))380 1189 y Fl(return)c Fp(\(b)q(est\))433 b(/*)13 b Fh(\014)k Fm(cut)e(o\013)g(:)k(r)n(eturn)14 b(b)n(est)h(sc)n(or)n (e)e Fp(*/)321 1239 y Fl(endif)321 1289 y(for)i(eac)o(h)g(mo)o(v)o(e)e Fp(m)f Fl(do)380 1338 y Fh(\013)h Fp(:=)h Fl(max)p Fp(\(b)q(est,)h Fh(\013)p Fp(\))339 b(/*)13 b Fm(A)o(l)r(low)h(fail)g(soft)f Fp(*/)380 1388 y(/*)g Fm(Se)n(ar)n(ch)i(move)g(m)g(to)g(next)g(depth)h(using) f(ne)n(gamax)h(c)n(onvention)f Fp(*/)380 1438 y(score)g(:=)e Ff(\000)p Fp(PVS\()p Fh(P)698 1444 y Fe(m)730 1438 y Fp(,)h Ff(\000)p Fh(\013)9 b Ff(\000)h Fp(1,)j Ff(\000)p Fh(\013)p Fp(,)g(depth)p Ff(\000)p Fp(1\))380 1488 y Fl(if)f Fp(\(score)k Fh(>)e Fp(b)q(est\))439 1538 y(/*)f Fm(R)n(e-se)n(ar)n(ch)i(only)g(if)f(sc)n (or)n(e)h(is)f(within)h Fh(\013\014)i Fm(window)d(and)i(not)f(a)g(true)f Fp(*/)439 1587 y(/*)f Fm(sc)n(or)n(e)i(r)n(eturne)n(d)f(fr)n(om)g(de)n(ep)n (est)h(2)g(levels)g(\(R)n(einefeld's)f(enhanc)n(ement\))h Fp(*/)439 1637 y Fl(if)d Fp(\(\()p Fh(\013)g(<)i Fp(score\))h Fl(and)e Fp(\(score)j Fh(<)11 b(\014)r Fp(\))k Fl(and)e Fp(\(depth)i Fh(>)f Fp(2\)\))498 1687 y(b)q(est)h(:=)e Ff(\000)p Fp(PVS\()p Fh(P)801 1693 y Fe(m)833 1687 y Fh(;)7 b Ff(\000)p Fh(\014)r(;)g Ff(\000)p Fp(score,)15 b(depth)p Ff(\000)p Fp(1\))439 1737 y Fl(else)498 1787 y Fp(b)q(est)g(:=)e(score)439 1836 y Fl(endif)439 1886 y(if)f Fp(\(b)q(est)k Ff(\025)11 b Fh(\014)r Fp(\))498 1936 y Fl(return)g Fp(\(b)q(est\))315 b(/*)13 b Fh(\014)k Fm(cut)e(o\013)g(:) k(r)n(eturn)14 b(b)n(est)h(sc)n(or)n(e)e Fp(*/)439 1986 y Fl(endif)380 2036 y(endif)321 2086 y(endfor)321 2185 y(return)e Fp(\(b)q(est\))492 b(/*)13 b Fm(R)n(eturn)i(sc)n(or)n(e)g(of)f(b)n(est)h(move)g(found)g Fp(*/)262 2285 y Fl(end)d Fp(PVS)537 2467 y(Figure)i(3.3:)j(Pseudo)d(co)q(de) h(for)f(the)g(PVS)g(Algorithm.)957 2574 y(27)p eop %%Page: 28 30 28 29 bop 262 307 a Fu(3.1.4)55 b(Iterativ)n(e)17 b(Deep)r(ening)262 419 y Fp(Iterativ)o(e)11 b(deep)q(ening)h([4)o(])f(is)g(a)g(metho)q(d)f(of)h (impro)o(ving)d(mo)o(v)o(e)h(ordering,)j(thereb)o(y)g(increas-)262 469 y(ing)h Fh(\013\014)j Fp(cut)e(o\013s.)19 b(It)14 b(also)f(enables)h(the) h(exp)q(ected)h(principle)e(v)n(ariation)e(to)i(b)q(e)g(primed.)324 554 y(Iterativ)o(e)e(deep)q(ening)h(is)f(ac)o(hiev)o(ed)g(b)o(y)g(p)q (erforming)e(a)i(series)h(of)e(searc)o(hes)j(to)e(progres-)262 604 y(siv)o(ely)e(greater)h(depths)h(e.g.)17 b(1)10 b(ply)m(,)g(2)g(ply)m(,)g (3)g(ply)g(etc.)18 b(After)12 b(eac)o(h)f(searc)o(h)h(the)f(1)f(ply)g(mo)o(v) o(e)262 654 y(list)j(can)h(b)q(e)h(re-ordered)g(to)f(increase)h(the)g (e\016ciency)f(of)g(the)g(subsequen)o(t)i(iterations.)324 739 y(It)h(migh)o(t)e(b)q(e)j(though)o(t)f(that)h(doing)e(an)h(iterativ)o(e)g (searc)o(h)i(to)e(4)g(ply)g(w)o(ould)f(b)q(e)i(less)262 789 y(e\016cien)o(t)c(than)g(a)g(direct)h(4)e(ply)h(searc)o(h,)h(whic)o(h)f (after)g(all)f(will)f(b)q(e)j(done)f(an)o(yw)o(a)o(y)f(as)h(part)262 839 y(of)d(an)h(iterativ)o(e)g(searc)o(h.)19 b(Ho)o(w)o(ev)o(er,)12 b(there)i(exists)f(n)o(umerous)e(tec)o(hniques)j(for)d(impro)o(ving)262 889 y(the)16 b(sp)q(eed)i(of)e(eac)o(h)h(subsequen)o(t)h(iteration)e(b)o(y)g (making)e(b)q(est)k(use)f(of)f(the)h(information)262 938 y(gained)d(so)h (far.)20 b(These)c(tec)o(hniques)h(include)e(refutation)f(tables,)h(transp)q (osition)g(tables,)262 988 y(the)e(history)h(heuristic)g(etc.)19 b(These)14 b(tec)o(hniques)h(will)d(b)q(e)i(explained)f(in)g(detail)g(later.) k(An)262 1038 y(iterativ)o(e)h(PVS)g(com)o(bined)f(with)h(some)g(of)f(the)i (tec)o(hniques)h(men)o(tioned)d(can)h(pro)q(duce)262 1088 y(trees)d(v)o(ery)f (close)h(to)e(the)i(minim)o(al)10 b(tree)15 b([40)o(].)324 1173 y(An)j(iterativ)o(e)f(deep)q(ening)i Fh(\013\014)h Fp(searc)o(h)e(also)f (has)h(another)g(imp)q(ortan)o(t)e(b)q(ene\014t;)k(the)262 1223 y(b)q(est)f(mo)o(v)o(e)e(found)h(so)g(far)h(is)f(alw)o(a)o(ys)f(kno)o (wn.)32 b(As)18 b(all)g(mo)o(v)o(es)f(are)i(searc)o(hed)h(at)e(eac)o(h)262 1273 y(iteration,)d(this)g(mo)o(v)o(e)f(is)i(lik)o(ely)e(to)i(b)q(e)g (reasonable.)24 b(Therefore,)16 b(if)f(the)i(a)o(v)n(ailable)c(time)262 1323 y(expires,)h(the)g(b)q(est)h(mo)o(v)o(e)d(found)i(so)g(far)f(could)h(b)q (e)g(pla)o(y)o(ed)f(with)h(con\014dence.)20 b(In)13 b(a)h(non{)262 1372 y(iterativ)o(e)h(searc)o(h,)i(ho)o(w)o(ev)o(er,)f(if)f(the)h(time)f (expires,)i(the)f(mo)o(v)o(e)e(selected)k(as)e(b)q(est)g(w)o(ould)262 1422 y(dep)q(end)f(on)f(what)h(mo)o(v)o(es)e(had)h(b)q(een)h(searc)o(hed)h (so)f(far.)k(If)14 b(only)g(p)q(o)q(or)g(mo)o(v)o(es)f(had)h(b)q(een)262 1472 y(searc)o(hed,)j(only)e(a)h(p)q(o)q(or)g(mo)o(v)o(e)e(could)h(b)q(e)i(c) o(hosen.)25 b(This)15 b(is)h(an)g(imp)q(ortan)o(t)e(b)q(ene\014t)j(for)262 1522 y(comp)q(etitiv)o(e)12 b(c)o(hess)k(programs)c(b)q(ecause)k(they)e(m)o (ust)f(con)o(trol)h(their)g(o)o(wn)g(time)e(usage.)262 1673 y Fu(3.1.5)55 b(Mo)n(v)n(e)19 b(Ordering)262 1785 y Fp(As)g(stressed)i (earlier,)e(the)g(order)h(in)e(whic)o(h)g(mo)o(v)o(es)g(are)h(examined)e(is)h (critical)h(to)f(the)262 1835 y(e\016ciency)e(of)f Fh(\013\014)r Fp(.)23 b(The)16 b(mo)o(v)o(es)e(from)g(eac)o(h)i(no)q(de)g(can)g(b)q(e)g (ordered)h(using)e(a)g(v)n(ariet)o(y)g(of)262 1885 y(heuristics:)324 1968 y Ff(\017)20 b Fp(An)f(iterativ)o(e)f(searc)o(h)h(is)f(a)g(go)q(o)q(d)g (basis)g(for)g(impro)o(ving)d(mo)o(v)o(e)i(ordering)h(as)g(the)365 2018 y(mo)o(v)o(es)12 b(at)g(the)h(ro)q(ot)g(of)f(the)h(tree)h(are)f (directly)g(ordered)g(b)o(y)g(a)f(searc)o(h)i(to)e(a)h(depth)g(1)365 2067 y(ply)f(less)h(than)f(the)h(curren)o(t)h(searc)o(h)g(depth.)k(As)13 b(the)g(subtree)h(b)q(elo)o(w)e(mo)o(v)o(es)f(at)h(the)365 2117 y(\014rst)17 b(ply)d(is)i(usually)e(larger)i(than)f(subtrees)j(at)d (greater)h(depths,)h(mo)o(v)o(e)d(ordering)365 2167 y(at)g(ply)f(1)h(is)g (lik)o(ely)e(to)i(ha)o(v)o(e)g(the)g(greatest)h(e\013ect)h(on)e(o)o(v)o (erall)e(tree)j(size.)324 2250 y Ff(\017)20 b Fp(Storing)11 b(mo)o(v)o(es)f(in)g(a)h(transp)q(osition)g(table)g(represen)o(ts)j(p)q (erhaps)e(the)g(b)q(est)g(metho)q(d)365 2300 y(of)k(ordering)h(mo)o(v)o(es)e (in)h(an)g(iterativ)o(e)h Fh(\013\014)i Fp(searc)o(h)e([18)o(].)26 b(This)16 b(is)h(b)q(ecause)h(mo)o(v)o(es)365 2350 y(found)c(to)g(b)q(e)h(b)q (est)h(at)e(iteration)g(n)g(are)h(v)o(ery)f(lik)o(ely)f(to)i(remain)d(b)q (est)k(at)e(iteration)365 2399 y(n+1.)28 b(Therefore)18 b(mo)o(v)o(es)e (stored)i(in)e(the)i(transp)q(osition)f(table)g(should)g(b)q(e)g(tried)365 2449 y(\014rst)e(if)e(the)i(no)q(de)f(is)g(re-visited.)957 2574 y(28)p eop %%Page: 29 31 29 30 bop 324 307 a Ff(\017)20 b Fp(Capture)d(mo)o(v)o(es)d(are)i(w)o(orth)f (searc)o(hing)h(b)q(efore)h(other)f(less)g(dynamic)e(mo)o(v)o(es)g(b)q(e-)365 357 y(cause)h(they)f(are)h(more)d(lik)o(ely)h(to)h(refute)g(the)h(curren)o(t) g(line)e(of)h(pla)o(y)f(and)g(therefore)365 407 y(cause)i(a)e(cut)h(o\013.)k (Capturing)13 b(the)h(piece)g(just)f(mo)o(v)o(ed)f(is)h(generally)g(v)o(ery)h (e\013ectiv)o(e)365 457 y(at)g(refuting)g(a)f(giv)o(en)h(line)f(of)g(pla)o(y) g([4].)324 539 y Ff(\017)20 b Fp(A)12 b(mo)o(v)o(e)e(that)i(causes)h(a)e(cut) i(o\013)e(at)h(a)f(giv)o(en)h(depth)g(should)g(b)q(e)g(tried)g(early)g(as)f (part)365 589 y(of)16 b(another)g(v)n(ariation)f(at)h(the)g(same)g(depth.)25 b(This)16 b(tec)o(hnique)h(is)f(kno)o(wn)g(as)g(the)365 638 y Fm(Kil)r(ler)d Fp(heuristic)h([4].)324 721 y Ff(\017)20 b Fp(The)14 b Fm(History)f Fp(heuristic)h(pro)o(vides)f(a)g(metho)q(d)g(of)g ("recording)g(eac)o(h)h(mo)o(v)o(es)e(abilit)o(y)365 770 y(to)17 b(cause)g(a)f(refutation")h([50)o(].)25 b(This)16 b(information)e(can)j(then) g(b)q(e)g(used)g(to)g(order)365 820 y(mo)o(v)o(es)c(according)h(to)g(the)g (lik)o(eliho)q(o)q(d)e(of)h(them)h(causing)f(a)h(refutation.)324 902 y Ff(\017)20 b Fp(Metho)q(ds)c(whic)o(h)f(use)g(the)h(ev)n(aluation)d (function)i(to)f(score)i(and)f(order)h(mo)o(v)o(es)d(are)365 952 y(quite)g(accurate,)h(but)f(exp)q(ensiv)o(e;)h(prohibitiv)o(ely)e(so)h (at)f(the)i(deep)q(est)h(lev)o(els)e(of)f(the)365 1002 y(tree.)262 1083 y(The)g(ob)r(jectiv)o(e)g(of)f(mo)o(v)o(e)g(ordering)h(is)f(therefore)j (to)d(searc)o(h)i(mo)o(v)o(es)e(in)g(a)h(b)q(est)h(\014rst)f(order.)262 1133 y(Therefore)21 b(\014nding)f(go)q(o)q(d)g Fh(\013)g Fp(v)n(alues)h(quic) o(kly)e(and)h(causing)h(early)f Fh(\014)j Fp(cut)e(o\013s.)38 b(The)262 1183 y(time)13 b(sp)q(en)o(t)j(ordering)f(mo)o(v)o(es)f(m)o(ust)g (b)q(e)h(small)e(or)i(the)h(pro)q(cess)g(will)e(b)q(e)h(self{defeating.)262 1233 y(Therefore)f(the)g(\014rst)h(\014v)o(e)f(metho)q(ds)f(are)h(most)e (common)f(in)i(con)o(temp)q(orary)g(brute)h(force)262 1283 y(c)o(hess)h(programs.)262 1434 y Fu(3.1.6)55 b(Null)18 b(Mo)n(v)n(es)262 1546 y Fp(In)d(c)o(hess,)j(unlik)o(e)d(some)g(other)i(games,)e(the)h(option)g (of)f(not)h(pla)o(ying)e(a)i(mo)o(v)o(e)e(do)q(es)j(not)262 1596 y(exist.)h(Ho)o(w)o(ev)o(er,)13 b(this)f(option)g(can)h(b)q(e)h(used)g (to)e(go)q(o)q(d)h(e\013ect)h(as)f(part)g(of)f(the)h(searc)o(h)h(tree)262 1645 y(in)f(order)i(to)e(detect)j(tactical)d(mo)o(v)o(es.)324 1731 y(The)k(idea)f(is)h(that)g(b)o(y)f(giving)f(up)i(the)h(righ)o(t)e(to)g (mo)o(v)o(e,)g(it)g(allo)o(ws)g(the)h(opp)q(onen)o(t)g(a)262 1781 y(second)i(consecutiv)o(e)h(mo)o(v)o(e.)29 b(If)18 b(this)g(second)i(mo) o(v)o(e)c(do)q(es)k(not)e(accomplish)f(an)o(ything)262 1830 y(b)q(ene\014cial,)i(then)g(it)f(can)g(b)q(e)h(assumed)f(that)h(the)g (\014rst)g(mo)o(v)o(e)d(did)i(not)g(represen)o(t)j(an)o(y)262 1880 y(threat.)d(In)c(this)g(w)o(a)o(y)f(mo)o(v)o(es)g(whic)o(h)h(represen)o (t)i(a)d(threat)i(can)f(b)q(e)h(iden)o(ti\014ed.)324 1965 y(This)d(metho)q(d) f(assumes)h(that)g(it)g(is)f(alw)o(a)o(ys)g(b)q(etter)j(to)e(mak)o(e)e(a)i (mo)o(v)o(e,)e(than)i(no)g(mo)o(v)o(e)262 2015 y(at)f(all)g(\(a)g Fm(nul)r(l)i(move)p Fp(\).)18 b(In)12 b(fact)g(in)f(c)o(hess,)i(a)f (situation)f(kno)o(wn)g(as)h("zugzw)o(ang")f(can)h(exist)262 2065 y(where)k(all)e(a)o(v)n(ailable)f(mo)o(v)o(es)h(lead)h(to)g(a)f(loss)i (of)e(some)h(sort;)g(whereas)i(if)d(no)h(mo)o(v)o(e)f(w)o(ere)262 2115 y(made,)c(the)h(loss)h(could)f(b)q(e)h(a)o(v)o(oided.)k(An)11 b(algorithm)e(using)i(the)h(n)o(ull)e(mo)o(v)o(e)g(to)h(determine)262 2165 y(threats)k(could)g(therefore)h(o)o(v)o(erlo)q(ok)e(mo)o(v)o(es)f(whic)o (h)i(lea)o(v)o(e)f(the)i(opp)q(onen)o(t)f(in)f(zugzw)o(ang.)262 2214 y(Ho)o(w)o(ev)o(er,)e(zugzw)o(ang)g(is)f(v)o(ery)h(rare)h(and)e(do)q(es) i(not)f(cause)g(a)g(signi\014can)o(t)f(problem)g(for)g(the)262 2264 y(tec)o(hnique.)324 2350 y(Don)j(Beal)h(has)g(done)f(a)h(lot)f(of)g(exp) q(erimen)o(tation)g(in)o(to)g(the)h(use)h(of)e(n)o(ull)f(mo)o(v)o(es)h(in)g (a)262 2399 y(normal)g Fh(\013\014)20 b Fp(minim)o(ax)14 b(searc)o(h.)28 b(In)17 b(his)g(pap)q(er)h("Exp)q(erimen)o(ts)f(with)f(the)i(Null)e(Mo)o(v)o (e")262 2449 y([5)o(],)i(he)g(prop)q(oses)h(an)f(algorithmic)d(approac)o(h)j (to)f(selectiv)o(e)i(searc)o(hing)g(based)f(on)g(n)o(ull)957 2574 y(29)p eop %%Page: 30 32 30 31 bop 262 653 a Fl(F)l(unction)11 b Fp(Quiescence\(P)17 b(:)c Fl(p)q(osition)p Fp(;)d Fh(\013)p Fp(,)k Fh(\014)i Fp(:)i Fl(in)o(teger)p Fp(\))11 b Fl(returns)j(in)o(teger)262 752 y(v)m(ar)321 802 y Fp(m)82 b(:)18 b Fl(mo)o(v)o(e)321 852 y Fp(score,)321 902 y(b)q(est)44 b(:)18 b Fl(in)o(teger)262 1001 y(b)q(egin)321 1101 y Fp(/*)13 b Fm(Calculate)h(nul)r(l)h(move)g(sc)n(or)n (e.)k(Note)c(:)j(Evaluate)e(may)f(itself)f(b)n(e)h(a)g(se)n(ar)n(ch)e Fp(*/)321 1151 y(b)q(est)i(:=)c Ff(\000)p Fp(Ev)n(aluate\(P)m(,)i Ff(\000)p Fh(\014)r Fp(,)h Ff(\000)p Fh(\013)p Fp(\))321 1250 y(GenerateMo)o(v)o(es\(P\))321 1300 y Fl(for)h(eac)o(h)g(mo)o(v)o(e)e Fp(m)f Fl(do)380 1350 y(if)g Fp(\(b)q(est)j Ff(\025)d Fh(\014)r Fp(\))439 1400 y Fl(return)f Fp(\(b)q(est\))374 b(/*)13 b Fh(\014)18 b Fm(cut)d(o\013)g(:)k(r)n(eturn)14 b(b)n(est)h(sc)n(or)n(e)e Fp(*/)380 1450 y Fl(endif)380 1499 y Fp(/*)g Fm(Se)n(ar)n(ch)i(move)g(m)g(to) g(next)g(depth)h(using)f(ne)n(gamax)h(c)n(onvention)f Fp(*/)380 1549 y(score)g(:=)e Ff(\000)p Fp(Quiescence\()p Fh(P)812 1555 y Fe(m)847 1549 y Fp(,)g Ff(\000)p Fh(\014)r Fp(,)h Ff(\000)p Fp(b)q(est\))380 1599 y Fl(if)e Fp(\(score)k Fh(>)e Fp(b)q(est\))439 1649 y(b)q(est)h(:=)e(score)391 b(/*)13 b Fm(Stor)n(e)i(b)n(est)f(sc)n(or)n (e)h(found)f Fp(*/)380 1699 y Fl(endif)321 1749 y(endfor)321 1848 y(return)d Fp(\(b)q(est\))492 b(/*)13 b Fm(R)n(eturn)i(sc)n(or)n(e)g(of) f(b)n(est)h(move)g(found)g Fp(*/)262 1948 y Fl(end)d Fp(Quiescence)338 2130 y(Figure)i(3.4:)j(Pseudo)e(co)q(de)g(for)e(a)h(Quiescence)i(searc)o(h)f (based)g(on)e(Null)g(Mo)o(v)o(es.)957 2574 y(30)p eop %%Page: 31 33 31 32 bop 262 307 a Fp(mo)o(v)o(es.)15 b(In)c(particular)g(he)g(de\014nes)h (a)e(n)o(ull)g(mo)o(v)o(e)f(quiescence)k(searc)o(h)f(whic)o(h)f(is)f(capable) h(of)262 357 y("selecting)h(mo)o(v)o(es)e(suc)o(h)i(as)g(c)o(hec)o(ks,)h(mo)o (v)o(es)d(out)i(of)f(c)o(hec)o(k,)h(attac)o(ks)g(on)f(pieces,)i(defences,)262 407 y(blo)q(c)o(ks)j(and)h(other)g(t)o(yp)q(es)h(of)e(sharp)h(tactical)g(mo)o (v)o(es)e(that)i(c)o(hess)h(pla)o(y)o(ers)f(concen)o(trate)262 457 y(on".)g(This)d(is)g(ac)o(hiev)o(ed)g(with)f(no)h(more)f(c)o(hess)i(kno)o (wledge)f(than)g(material)e(balance.)324 542 y(Beal)i(uses)g(the)h(score)g (returned)g(from)d(a)h(quiescence)j(searc)o(h)f(follo)o(wing)c(a)j(n)o(ull)e (mo)o(v)o(e)262 592 y(as)f(a)f(b)q(ound)i(to)e(guide)h(the)h(searc)o(h)g(and) f(enable)g(forw)o(ard)g(pruning)g(of)f(inadequate)h(mo)o(v)o(es.)262 641 y(Beal)j(sho)o(ws)h(that)f(suc)o(h)h(a)f(quiescence)j(searc)o(h)e(is)g (capable)f(of)g(a)g(p)q(erformance)g(on)g(Rein-)262 691 y(\014eld's)f(300)h (tactical)f(p)q(ositions)h([47)o(],)f(equiv)n(alen)o(t)g(to)h(that)g(of)f (the)i(c)o(hess)g(mac)o(hine)e(Belle,)262 741 y(while)g(using)h(only)f(1)p Fh(=)p Fp(15th)g(of)g(the)h(e\013ort)h(!)324 826 y(V)m(ery)e(recen)o(tly)m(,) g(Hamlen)e([25)o(])i(extended)h(this)f(idea)g(b)o(y)f(applying)g(a)g(full)g (width)h(2)f(ply)262 876 y(searc)o(h,)19 b(in)f(addition)f(to)h(the)h(normal) d(quiescence)k(searc)o(h,)g(after)e(a)g(n)o(ull)f(mo)o(v)o(e.)29 b(This)262 926 y(allo)o(w)o(ed)17 b(the)i(algorithm)d(to)i(additionally)f (detect)j(tactical)e(plo)o(ys)g(suc)o(h)i(as)e(forks)h(and)262 976 y(sk)o(ew)o(ers.)24 b(Other)17 b(programs,)d(notably)h(Kaissa)h([1)o(],)f (ha)o(v)o(e)g(used)i(the)f(n)o(ull)e(mo)o(v)o(e)g(idea)i(to)262 1026 y(pro)o(vide)e(faster)g(cut)h(o\013s,)f(without)g(using)g(it)g (algorithmical)o(ly)d(to)j(select)h(mo)o(v)o(es)e(as)i(Beal)262 1075 y(and)e(Hamlen)g(ha)o(v)o(e.)324 1161 y(Beal's)g(n)o(ull)f(mo)o(v)o(e)g (quiescence)j(searc)o(h)g(can)e(b)q(e)h(seen)h(in)d(\014gure)i(3.4.)j(It)c (is)g(imp)q(ortan)o(t)262 1210 y(to)20 b(realise)h(that)g(Ev)n(aluate)f(ma)o (y)f(itself)h(b)q(e)i(a)e(searc)o(h)i(of)e(some)g(kind.)38 b(In)21 b(fact)g(Beal)262 1260 y(adv)o(o)q(cates)d(the)g(use)h(of)e(a)h(2nd)f (lev)o(el)h(n)o(ull)e(mo)o(v)o(e)g(quiescence)k(searc)o(h)f(supp)q(orted)g(b) o(y)f(a)262 1310 y(1st)e(lev)o(el)g(quiescence)i(searc)o(h,)f(in)f(place)g (of)g(Ev)n(aluate,)f(using)h(material)e(balance)i(as)h(its)262 1360 y(ev)n(aluation.)262 1512 y Fu(3.1.7)55 b(Razoring)262 1624 y Fp(Razoring)13 b(is)i(a)g(tec)o(hnique)h(devised)f(b)o(y)g(Birmingham) c(and)k(Ken)o(t)h([11)o(].)k(The)c(tec)o(hnique)262 1673 y(uses)i(the)g (assumption)e(that)h(a)g(pla)o(y)o(er)g(who)g(has)h(the)g(mo)o(v)o(e)d(can)j (alw)o(a)o(ys)e(main)o(tain)f(or)262 1723 y(impro)o(v)o(e)d(his)h(p)q (osition)h(b)o(y)f(pla)o(ying)g(a)g(mo)o(v)o(e.)324 1808 y(The)k(tec)o (hnique)i(w)o(orks)e(b)o(y)g(using)g(a)g(static)g(ev)n(aluation)f(v)n(alue)h (at)g(in)o(terior)g(as)g(w)o(ell)262 1858 y(as)i(terminal)f(no)q(des.)35 b(This)19 b(v)n(alue)g(is)g(compared)g(to)g(the)h(curren)o(t)h Fh(\013)e Fp(v)n(alue)g(with)g(the)262 1908 y(assumption)10 b(that)h(the)h(opp)q(onen)o(t)g(can)g(alw)o(a)o(ys)e(main)o(tain)f(or)i (impro)o(v)o(e)f(his)h(p)q(osition)g(with)262 1958 y(a)g(mo)o(v)o(e.)16 b(Therefore,)d(the)f(static)h(score)g(is)f(treated)h(as)f(an)f(upp)q(er)i(b)q (ound)f(on)g(the)g(p)q(ossible)262 2008 y(scores)j(resulting)f(from)e(the)j (opp)q(onen)o(ts)g(a)o(v)n(ailable)d(mo)o(v)o(es.)17 b(Hence,)e(if)e(this)h (static)g(v)n(alue)262 2058 y(is)f(no)h(greater)h(than)f(the)h Fh(\013)e Fp(v)n(alue,)g(it)h(is)g(assumed)f(that)h(the)h(subtree)h(cannot)e (a\013ect)h(the)262 2107 y Fh(\013)g Fp(v)n(alue)h(at)g(this)g(lev)o(el)g (and)g(can)g(therefore)i(b)q(e)e(cut)h(o\013.)25 b(Note)16 b(that)h(this)f(tec)o(hnique)h(is)262 2157 y(only)c(applied)g(from)f(the)j(p) q(oin)o(t)e(of)g(view)h(of)f(the)i(pla)o(y)o(er)e(who)h(has)g(just)g(mo)o(v)o (ed.)324 2242 y(Figure)h(3.5)e(illustrates)i(the)g(razoring)g(tec)o(hnique)g (in)f(action.)20 b(The)15 b(n)o(um)o(b)q(ers)g(to)f(the)262 2292 y(left)k(of)g(eac)o(h)h(no)q(de)g(represen)o(t)i(the)e(static)g(v)n (alues,)h(while)e(the)h(n)o(um)o(b)q(ers)f(to)h(the)g(righ)o(t)262 2342 y(represen)o(t)e(bac)o(k)o(ed)f(up)f(negamax)f(v)n(alues.)22 b(No)q(de)15 b(B)h(is)f(examined)f(\014rst)i(giving)e(a)h(static)262 2392 y(v)n(alue)e(of)h(+7.)21 b(No)q(des)15 b(C)g(and)f(D)g(are)h(then)g (searc)o(hed,)h(resulting)f(in)f(v)n(alues)g(of)g Ff(\000)p Fp(15)h(and)262 2442 y Ff(\000)p Fp(4)i(resp)q(ectiv)o(ely)m(.)31 b(A)18 b(v)n(alue)f(of)h(+4)f(using)h(negamax)e(is)i(subsequen)o(tly)h(bac)o (k)o(ed)f(up)g(to)957 2574 y(31)p eop %%Page: 32 34 32 33 bop 697 1103 a Fp(Figure)14 b(3.5:)j(Razoring)c(in)h(action.)262 1236 y(no)q(de)g(B.)g(The)h Fh(\013)f Fp(v)n(alue)f(at)h(this)h(lev)o(el)e (is)i(then)f(made)f(equal)h(to)g(+4.)19 b(The)c(mo)o(v)o(e)e(leading)262 1286 y(to)h(no)q(de)h(E)g(is)g(no)o(w)f(examined)g(and)g(giv)o(en)h(a)f (static)h(v)n(alue)f(of)g(+1.)21 b(Using)14 b(the)i(razoring)262 1335 y(tec)o(hnique,)e(this)g(v)n(alue)f(represen)o(ts)k(an)d(upp)q(er)g(b)q (ound,)g(b)q(ecause)i(the)e(opp)q(onen)o(ts)h(mo)o(v)o(es)262 1385 y(leading)g(to)h(no)q(des)g(F)g(and)g(G)g(are)g(assumed)g(to)g(main)o (tain)d(or)j(impro)o(v)o(e)e(the)j(opp)q(onen)o(ts)262 1435 y(score)g(thereb)o(y)g(decreasing)h(the)e(score)i(at)e(this)g(lev)o(el.)25 b(As)17 b(the)f(upp)q(er)i(b)q(ound)e(of)g(+1)g(is)262 1485 y(already)d(less)h(than)f(the)h(curren)o(t)h Fh(\013)d Fp(v)n(alue)h(at)g (ply)g(1,)g(no)q(des)h(F)f(and)g(G)g(cannot)h(a\013ect)g(the)262 1535 y(searc)o(h)h(result)f(and)g(can)g(therefore)h(b)q(e)g(cut)f(o\013)g(b)o (y)g(razoring.)324 1620 y(The)19 b(razoring)h(tec)o(hnique)g(can)f(b)q(e)h (extended)h(b)o(y)e(using)g(the)h(assumption)e(that)h(a)262 1670 y(pla)o(y)o(er)f(can)g(impro)o(v)o(e)f(his)h(curren)o(t)i(p)q(osition)e (b)o(y)g(pla)o(ying)e(his)j(mo)o(v)o(e,)e(y)o(our)h(mo)o(v)o(e,)g(his)262 1720 y(mo)o(v)o(e.)29 b(This)18 b(extension)g(of)g(the)h(idea)f(is)g(kno)o (wn)f(as)i(deep)g(razoring.)30 b(It)18 b(causes)i(ev)o(en)262 1769 y(more)12 b(razor)j(cut)f(o\013s,)g(but)g(at)g(a)f(m)o(uc)o(h)g(greater) i(risk)f(of)f(cutting)h(out)g(a)g(vital)e(mo)o(v)o(e.)324 1855 y(Birmingham)h(and)j(Ken)o(t)i(also)e(prop)q(osed)h(a)f(further)i(enhancemen) o(t)f(where)h(b)o(y)e(the)262 1904 y(assumption)f(is)h(made)f(that)i(there)g (alw)o(a)o(ys)f(exists)h(a)f(mo)o(v)o(e)f(whic)o(h)h(not)g(only)g(impro)o(v)o (es)262 1954 y(a)e(pla)o(y)o(ers)h(p)q(osition,)e(but)i(impro)o(v)o(es)e(it)i (b)o(y)f(at)h(least)f(3)p Fh(=)p Fp(10ths)h(of)f(a)g(pa)o(wn,)g(for)g (example.)262 2004 y(This)e('enhancemen)o(t')f(further)i(increases)h(razored) f(cut)g(o\013s,)f(but)g(at)g(the)h(cost)g(of)e(missing)262 2054 y(p)q(ossibly)i(more)g(vital)g(mo)o(v)o(es.)324 2139 y(I)20 b(b)q(eliev)o(e)g(the)h(tec)o(hnique)g(w)o(ould)e(b)q(e)i(b)q(etter)g (enhanced)h(b)o(y)d(taking)h(an)f(opp)q(osite)262 2189 y(view)14 b(to)g(the)h(enhancemen)o(t)g(ab)q(o)o(v)o(e.)20 b(F)m(or)14 b(example,)f(assume)h(that)h(there)g(alw)o(a)o(ys)f(exists)262 2239 y(a)g(mo)o(v)o(e)g(that)h(will)e(not)i(deteriorate)h(the)g(p)q(osition)e (b)o(y)h(more)f(than)h(a)g(threshold,)g(of)g(sa)o(y)262 2289 y(half)i(a)h(pa)o(wn.)31 b(Di\013eren)o(t)19 b(thresholds)h(could)e(b)q(e)h (applied)f(at)g(eac)o(h)h(lev)o(el)f(of)g(the)h(tree,)262 2338 y(p)q(erhaps)14 b(w)o(eigh)o(ted)f(so)g(that)g(as)g(the)h(searc)o(h)g (progresses)h(more)d(deeply)h(do)o(wn)g(the)g(searc)o(h)262 2388 y(tree,)i(more)e(cut)i(o\013s)f(are)h(made.)i(This)e(enhancemen)o(t)f(w) o(ould)g(decrease)i(the)f(n)o(um)o(b)q(er)e(of)262 2438 y(cut)h(o\013s,)g (but)g(impro)o(v)o(e)e(the)i(lik)o(eliho)q(o)q(d)f(of)g(including)g(go)q(o)q (d)g(mo)o(v)o(es)g(in)g(the)i(searc)o(h)g(tree,)957 2574 y(32)p eop %%Page: 33 35 33 34 bop 262 307 a Fp(particularly)13 b(at)g(shallo)o(w)o(er)h(depths)h (where)g(missing)d(suc)o(h)i(mo)o(v)o(es)f(can)h(b)q(e)g(fatal.)324 392 y(I)j(b)q(eliev)o(e)g(the)h(assumption)d(made)h(b)o(y)h(the)h(Razoring)e (tec)o(hnique)h(is)g(m)o(uc)o(h)f(w)o(eak)o(er)262 442 y(than)f(that)h(of)f (the)i(Null)e(mo)o(v)o(e)f(tec)o(hnique,)i(whic)o(h)g(only)f(assumes)h(that)f (it)h(is)f(b)q(etter)j(to)262 492 y(mak)o(e)12 b(a)i(mo)o(v)o(e,)d(than)j(no) g(mo)o(v)o(e)e(at)i(all.)262 665 y Fr(3.2)69 b(Ev)l(aluation)262 791 y Fp(This)11 b(section)h(describ)q(es)i(a)d(n)o(um)o(b)q(er)g(of)g(tec)o (hniques)i(for)e(heuristic)i(p)q(ositional)d(ev)n(aluation)262 841 y(of)j(c)o(hess)j(p)q(ositions.)k(Most)15 b(of)e(these)j(tec)o(hniques)g (are)f(b)q(est)h(used)f(in)f(com)o(bination)e(with)262 891 y(eac)o(h)i(other.)324 976 y(The)g(imp)q(ortance)g(of)f(the)i(ev)n(aluation)d (function)i(cannot)h(b)q(e)f(to)q(o)g(highly)f(stressed)k(as)262 1026 y(it)12 b(is)h(this)g(that)g(giv)o(es)g(a)g(program)e(its)i(distinctiv)o (e)g(st)o(yle.)18 b(Ac)o(hieving)13 b(a)g(go)q(o)q(d)f(p)q(osition)h(is)262 1076 y(often)g(a)h(prelude)h(to)e(a)h(winning)f(tactical)g(com)o(bination.) 365 1159 y("T)m(actics)h(\015o)o(w)g(from)e(a)h(go)q(o)q(d)h(p)q(osition")970 1225 y Fm(R)n(ob)n(ert)g(J.)h(Fischer.)262 1377 y Fu(3.2.1)55 b(Piece)17 b(Square)i(T)-5 b(ables)262 1489 y Fp(Piece)12 b(Square)f (\(Pc/Sq\))h(tables)f(are)g(used)h(to)f(hold)f(v)n(alues)h(for)f(pieces)j(o)q (ccup)o(ying)d(squares)262 1539 y(on)h(the)h(b)q(oard.)18 b(F)m(or)11 b(example,)f(a)i(knigh)o(t)f(square)h(table)g(w)o(ould)f(con)o(tain)g(a)h (score)h(for)e(eac)o(h)262 1588 y(square)16 b(indicating)e(the)i(merits)e(of) h(ha)o(ving)f(a)h(knigh)o(t)f(on)h(that)h(square.)23 b(T)m(ables)15 b(can)g(b)q(e)262 1638 y(used)g(for)g(eac)o(h)g(t)o(yp)q(e)h(of)e(piece)i (and)e(can)h(b)q(e)h(pre-loaded)f(b)q(efore)g(the)h(searc)o(h)g(b)q(egins,)f (b)o(y)262 1688 y(doing)i(some)h(preliminary)f(p)q(ositional)g(analysis.)32 b(Using)19 b(suc)o(h)h(tables,)f(it)g(b)q(ecomes)g(a)262 1738 y(simple)c(matter)i(to)g(p)q(erform)f(a)h(p)q(ositional)f(ev)n(aluation)g(at) h(a)f(giv)o(en)h(no)q(de.)28 b(Giv)o(en)17 b(the)262 1788 y(lo)q(cation)e(of) h(eac)o(h)i(piece)f(on)g(the)g(b)q(oard,)g(a)f(v)n(alue)g(can)h(b)q(e)g(lo)q (ok)o(ed)f(up)h(in)f(the)i(relev)n(an)o(t)262 1837 y(table)13 b(and)f(added)i(to)f(the)h(p)q(ositional)d(total)i(for)f(the)i(appropriate)f (side,)g(white)h(or)f(blac)o(k.)262 1887 y(Finally)c(the)i(di\013erence)i(b)q (et)o(w)o(een)f(the)f(t)o(w)o(o)g(totals)f(is)h(calculated)g(giving)e(an)i(o) o(v)o(erall)e(v)n(alue)262 1937 y(for)k(the)i(p)q(osition.)324 2022 y(The)e(main)e(adv)n(an)o(tage)i(of)f(using)h(these)i(tables)e(is)g(sp)q (eed.)20 b(The)13 b(w)o(orlds)g(fastest)h(c)o(hess)262 2072 y(mac)o(hines,)c(Hitec)o(h)j(and)e(Deep)i(Though)o(t,)e(mak)o(e)g(extensiv)o (e)h(use)h(of)e(Pc/Sq)h(tables.)18 b(Ho)o(w-)262 2122 y(ev)o(er,)13 b(b)q(ecause)h(these)g(tables)f(are)g(generally)g(pre-loaded)f(b)q(efore)i (the)f(searc)o(h)h(b)q(egins)f(and)262 2172 y(applied)h(n)h(ply)g(further)h (do)o(wn)e(the)i(tree)g(at)f(leaf)g(no)q(des,)g(man)o(y)f(p)q(ositional)f (asp)q(ects)k(are)262 2222 y(no)10 b(longer)h(applicable.)16 b(The)11 b(tables)h(also)e(do)g(not)h(re\015ect)i(up)e(to)g(date)g(piece)h (in)o(teractions.)324 2307 y(These)20 b(problems)e(are)h(exasp)q(erated)i(b)o (y)d(deep)i(searc)o(hing.)33 b(It)19 b(is)g(therefore)h(ironic)262 2357 y(that)14 b(the)h(tables)g(are)g(used)h(for)e(the)i(express)g(purp)q (ose)g(of)e(deep)h(searc)o(hing)h(due)f(to)f(their)262 2406 y(e\016ciency)m(.)22 b(It)15 b(is)g(in)o(teresting)h(that)f(the)h(Hitec)o(h)f (team)f(at)h(CMU)h(are)f(no)o(w)g(\014nding)g(that)957 2574 y(33)p eop %%Page: 34 36 34 35 bop 262 307 a Fp(as)14 b(their)h(program)e(impro)o(v)o(es,)g(more)h (kno)o(wledge)g(m)o(ust)g(b)q(e)h(migrated)e(from)g(the)i(Pc/Sq)262 357 y(tables)f(to)f(the)i(leaf)e(no)q(de)h(static)h(ev)n(aluation)d(pro)q (cess)k([7)o(].)262 508 y Fu(3.2.2)55 b(Static)18 b(Ev)m(aluation)262 620 y Fp(In)11 b(most)g(programs,)g(a)g(static)h(ev)n(aluation)f(is)g(p)q (erformed)h(at)g(the)g(leaf)f(no)q(des)i(of)e(the)i(main)262 670 y(searc)o(h.)32 b(In)18 b(full)g(width)g(searc)o(hes,)j(a)d(quiescence)i (searc)o(h)g(is)e(usually)f(also)h(applied)g(at)262 720 y(these)f(leaf)e(no)q (des,)i(th)o(us)g(creating)f(new)g(leaf)g(no)q(des)g(at)g(a)g(deep)q(er)i (lev)o(el)d(whic)o(h)h(are)h(not)262 770 y(usually)c(p)q(ositionally)f(ev)n (aluated)h(for)h(e\016ciency)g(reasons.)324 855 y(The)19 b(static)g(ev)n (aluation)e(pro)q(cess)j(in)o(v)o(olv)o(es)e(computing)f(the)i(existence)h (of)e(v)n(arious)262 905 y(p)q(ositional)11 b(factors.)17 b(Dep)q(ending)c (on)f(the)h(degree)h(to)e(whic)o(h)h(these)h(factors)e(exist,)h(appro-)262 955 y(priate)h(v)n(alues)g(are)h(calculated.)k(Finally)13 b(the)i(v)n(alues)f (are)g(w)o(eigh)o(ted)h(according)f(to)g(their)262 1004 y(relativ)o(e)f(imp)q (ortance.)324 1090 y(In)20 b(c)o(hess,)j(determining)c(the)i(factors)g(whic)o (h)f(con)o(tribute)h(to)f(a)g(go)q(o)q(d)g(p)q(osition)g(is)262 1139 y(v)o(ery)c(di\016cult.)25 b(Standard)17 b(criteria)g(ha)o(v)o(e)f(b)q (een)i(dev)o(elop)q(ed)f(o)o(v)o(er)f(the)h(y)o(ears)g(b)o(y)g(whic)o(h)262 1189 y(a)f(program)g(can)h(judge)g(a)f(p)q(osition.)27 b(Using)17 b(suc)o(h)g(criteria)h(curren)o(t)g(programs)e(pla)o(y)g(a)262 1239 y(reasonable)d(game.)k(Ho)o(w)o(ev)o(er,)c(it)h(is)f(still)f(clear)i (from)e(their)i(p)q(ositional)e(pla)o(y)m(,)g(that)h(some)262 1289 y(subtle)j(factors)g(are)h(still)e(not)h(b)q(eing)f(included.)25 b(I)16 b(will)e(try)i(to)g(unco)o(v)o(er)h(some)e(of)g(these)262 1339 y(in)h(the)h(next)g(c)o(hapter.)27 b(The)17 b(most)e(di\016cult)h(task)h (remains)e(determining)h(the)h(relativ)o(e)262 1389 y(imp)q(ortance)c(of)g (eac)o(h)i(factor)f(or)f(criterion.)19 b(An)14 b(attempt)g(w)o(as)f(made)g (to)h(determine)g(the)262 1438 y(relativ)o(e)f(imp)q(ortance)g(of)h(a)f(n)o (um)o(b)q(er)g(of)h(ev)n(aluation)e(criteria)i(in)g([51)o(].)k(I)13 b(think)h(the)g(basic)262 1488 y(idea)9 b(of)h(this)g(researc)o(h)i(is)e(an)g (excellen)o(t)h(one,)g(ho)o(w)o(ev)o(er,)f(I)h(feel)f(the)h(sp)q(eci\014c)g (order)g(in)f(whic)o(h)262 1538 y(the)k(ev)n(aluation)e(criteria)j(w)o(ere)g (tested,)g(in\015uenced)g(the)f(result)h(of)e(the)h(exp)q(erimen)o(ts.)324 1623 y(Sev)o(eral)e(attempts)g(ha)o(v)o(e)g(b)q(een)i(made)d(to)h(generate)h (a)f('b)q(est)h(\014t')f(ev)n(aluation)f(function)262 1673 y([27)o(,)i(39].)19 b(Most)c(of)f(these)h(studies)h(are)f(based)g(on)f(an)g (analysis)g(of)g(grandmaster)f(mo)o(v)o(es.)262 1723 y(The)g(ob)r(jectiv)o(e) h(is)f(to)g(\014nd)h(a)f(function)g(whic)o(h)g(selects)i(grandmaster)e(mo)o (v)o(es)f(as)h(often)h(as)262 1773 y(p)q(ossible.)j(Suc)o(h)11 b(attempts)f(ha)o(v)o(e)h(hit)f(serious)h(problems)f(b)q(ecause,)j(as)e(I)f (see)i(it,)f(5)f(problem)262 1823 y(areas)k(exist:)312 1904 y(1.)20 b(A)c(b)q(est)h(\014t)f(can)g(only)e(b)q(e)j(attempted)e(for)h(the)g (kno)o(wn)f(functions.)24 b(If)15 b(a)g(program)365 1954 y(do)q(es)d(not)e (kno)o(w)g(ab)q(out)h(a)f(particular)h(asp)q(ect)h(of)e(c)o(hess,)i(for)e (example)g(w)o(eak)g(pa)o(wns,)365 2003 y(it)j(cannot)g(include)g(suc)o(h)g (considerations)h(in)e(its)h(ev)n(aluation)e(pro)q(cess.)20 b(Therefore,)365 2053 y(p)q(ossibly)14 b(in)o(tro)q(ducing)f(side)i (e\013ects)h(in)o(to)d(existing)g(functions.)312 2135 y(2.)20 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(b)q(ene\014t)i(from)c(more)i(in)o(v)o(olv)o(emen)o(t)e(b)o(y)i(strong)h(c)o (hess)h(pla)o(y-)262 490 y(ers.)324 575 y(In)f(practice,)i(static)f(ev)n (aluation)e(functions)h(tend)i(to)e(b)q(e)h(primitiv)o(e,)d(particularly)i (in)262 625 y(brute)j(force)g(programs,)f(to)g(enable)h(deep)h(searc)o(hing.) 26 b(Pc/Sq)17 b(tables)g(are)g(used)g(where)262 675 y(p)q(ossible)11 b(to)g(impro)o(v)o(e)f(e\016ciency)m(.)17 b(Information)9 b(whic)o(h)i (cannot)h(b)q(e)g(stored)g(in)f(the)h(tables,)262 725 y(suc)o(h)k(as)g (pinned)g(piece)h(information,)c(m)o(ust)i(b)q(e)h(calculated.)24 b(The)16 b(ev)n(aluation)f(pro)q(cess)262 774 y(can)j(b)q(e)h(supp)q(orted)h (b)o(y)e(sp)q(eci\014c)i(hash)e(tables)h(e.g.)31 b(pa)o(wn)18 b(structure)j(hashing.)31 b(This)262 824 y(enables)15 b(m)o(uc)o(h)f(faster)i (ev)n(aluation)e(b)q(ecause)j(calculations)d(do)h(not)g(ha)o(v)o(e)g(to)g(b)q (e)h(re-done)262 874 y(when)d(p)q(ositions)g(with)g(iden)o(tical)g(pa)o(wn)g 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y(It)f(should)h(b)q(e)g (realised)g(that)f(static)h(ev)n(aluation)e(is)h(not)h(adequate)g(in)f (dynamic)e(tac-)262 1358 y(tical)18 b(situations.)33 b(Suc)o(h)20 b(tactical)f(problems)f(are)h(b)q(etter)i(resolv)o(ed)f(b)o(y)e(some)h(kind)f (of)262 1408 y(quiescence)i(searc)o(h.)32 b(I)18 b(b)q(eliev)o(e)h(it)f(is)g (the)h(job)f(of)f(the)i(static)g(ev)n(aluation)e(function)h(to)262 1457 y(realise)13 b(when)g(a)g(p)q(osition)f(is)h(unsuitable)f(for)h(static)g (ev)n(aluation)f(and)g(inform)f(the)i(searc)o(h)262 1507 y(pro)q(cess,)i(so)f (it)f(can)h(attempt)f(to)h(resolv)o(e)h(the)f(tactical)g(uncertain)o(t)o(y)m (.)262 1659 y Fu(3.2.3)55 b(Incremen)n(tal)16 b(Ev)m(aluation)262 1771 y Fp(Static)e(ev)n(aluation)f(at)i(leaf)e(no)q(des)j(is)e(exp)q(ensiv)o (e)i(in)e(terms)g(of)g(time;)f(and)h(Pc/Sq)h(tables)262 1821 y(do)e(not)h(re\015ect)h(the)g(true)g(merits)e(of)g(a)g(p)q(osition,)g(esp)q (ecially)h(as)g(the)h(searc)o(h)f(deep)q(ens.)21 b(A)262 1870 y(third)12 b(option)g(is)h(a)o(v)n(ailable,)d(that)j(of)g(incremen)o(tally)e (up)q(dating)h(the)i(p)q(ositional)d(totals)i(as)262 1920 y(mo)o(v)o(es)f (are)i(made.)j(The)e(p)q(ositional)d(totals)i(could)f(b)q(e)i(up)q(dated)f (as)g(follo)o(ws:)312 2003 y(1.)20 b(Calculate)9 b(the)h(p)q(ositional)e(v)n (alue,)h(for)g(the)h(piece)g(just)g(mo)o(v)o(ed,)e(on)h(its)g(from{square.) 312 2086 y(2.)20 b(Decremen)o(t)15 b(this)e(v)n(alue)h(from)e(the)i(p)q (ositional)f(total)g(for)h(the)g(relev)n(an)o(t)g(side.)312 2169 y(3.)20 b(Calculate)14 b(the)g(p)q(ositional)e(v)n(alue,)h(for)h(the)g (piece)h(just)f(mo)o(v)o(ed,)d(on)j(its)g(to{square.)312 2252 y(4.)20 b(Incremen)o(t)14 b(this)g(new)h(v)n(alue)e(to)h(the)g(p)q(ositional) f(total)g(for)g(the)i(relev)n(an)o(t)f(side.)262 2335 y(This)e(pro)q(cess)i (is)e(quite)g(simple)f(and)h(therefore)i(fast,)e(but)h(do)q(es)g(not)f(tak)o (e)g(accoun)o(t)h(of)f(the)262 2385 y(e\013ects)j(mo)o(ving)10 b(a)j(piece)i(ma)o(y)c(ha)o(v)o(e)i(on)g(the)h(p)q(ositional)e(v)n(alue)g(of) h(the)h(pieces)g(around)f(it.)262 2435 y(F)m(or)g(example,)f(mo)o(ving)f(a)j (piece)h(ma)o(y)c(rev)o(eal)j(or)g(blo)q(c)o(k)g(a)f(n)o(um)o(b)q(er)g(of)h (p)q(ossible)g(attac)o(ks.)957 2574 y(35)p eop %%Page: 36 38 36 37 bop 262 307 a Fp(Therefore,)13 b(if)g(the)g(pro)q(cess)i(is)e(to)f(b)q (e)i(truly)f(incremen)o(tal)f(it)g(m)o(ust)g(tak)o(e)h(accoun)o(t)h(of)e(suc) o(h)262 357 y(factors.)18 b(Ho)o(w)o(ev)o(er,)12 b(suc)o(h)i(a)e(detailed)h (incremen)o(tal)f(ev)n(aluation)f(will)g(b)q(e)j(costly)f(in)f(terms)262 407 y(of)h(time,)f(p)q(erhaps)j(prohibitiv)o(ely)d(so.)324 492 y(In)i(practice)h(incremen)o(tal)e(ev)n(aluation)f(is)i(used)h(in)e (conjunction)h(with)g(a)f(static)h(ev)n(al-)262 542 y(uation)i(at)h(the)h (horizon)f(no)q(des)i(of)d(the)i(main)e(searc)o(h.)29 b(Incremen)o(tal)17 b(ev)n(aluations)f(can)262 592 y(also)e(b)q(e)h(useful)h(during)e(a)h (quiescence)i(searc)o(h)f(where)g(there)h(is)e(not)f(enough)i(time)d(for)i(a) 262 641 y(full)f(static)i(ev)n(aluation.)23 b(This)16 b(is)g(b)q(ecause)h(a)f (quiescence)i(searc)o(h)f(also,)e(usually)g(o)q(ccurs)262 691 y(at)e(the)i(horizon)e(no)q(des)i(of)e(the)i(main)d(searc)o(h.)324 777 y(The)20 b(Pc/Sq)h(tables)f(explained)g(earlier)g(can)g(also)g(b)q (ene\014t)h(from)e(an)h(incremen)o(tal)262 826 y(approac)o(h,)13 b(to)h(close)g(the)h(gap)e(b)q(et)o(w)o(een)i(kno)o(wledge)f(storage)g(and)g (application.)262 976 y Fu(3.2.4)55 b(Phases)19 b(of)g(Pla)n(y)262 1088 y Fp(The)14 b(game)e(of)i(c)o(hess)h(consists)g(of)e(3)h(main)d(game)i (phases:)324 1163 y Ff(\017)20 b Fp(The)15 b(Op)q(ening.)324 1242 y Ff(\017)20 b Fp(The)15 b(Middle)e(game.)324 1321 y Ff(\017)20 b Fp(The)15 b(Endgame.)262 1396 y(Di\013eren)o(t)22 b(ev)n(aluation)f (criteria)h(are)g(applicable)f(at)h(di\013eren)o(t)h(phases)g(of)e(the)i (game.)262 1446 y(Therefore,)f(it)e(is)g(imp)q(ortan)o(t)f(for)g(a)h(c)o 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y(endgame.)j(If)11 b(this)g(pro)q(cess)j(is)d(not)g(p)q(erformed)g (gradually)m(,)f(the)i(program)e(ma)o(y)f(\014nd)j(itself)262 1930 y(in)f(an)h(endgame)g(with)g(its)g(king)f(misplaced,)g(and)h(a)g(sudden) h(realisation)f(that)g(things)g(are)262 1980 y(not)f(as)h(go)q(o)q(d)f(as)h (predicted)h(b)o(y)f(the)g(ev)n(aluation)f(function)g(at)h(the)g(previous)g (game)e(phase.)324 2065 y(Assume,)15 b(for)g(example,)e(w)o(e)j(ha)o(v)o(e)f (8)f(game)g(phases,)i(then)g(new)g(ev)n(aluation)d(criteria)262 2115 y(could)g(b)q(e)g(in)o(tro)q(duced)h(gen)o(tly)m(,)e(or)i(existing)f (criteria)g(could)g(b)q(e)h(scaled)g(according)f(to)g(the)262 2165 y(phase.)324 2250 y(The)h(game)e(phase)j(is)e(a)h(factor)f(of)g(the)i (material)d(remaining)f(on)j(the)g(b)q(oard)g(and)f(can)262 2300 y(therefore)f(b)q(e)f(easily)f(calculated,)h(although)f(deciding)h(when) g(one)g(phase)g(should)g(end)g(and)262 2350 y(another)i(should)g(start)h(is)f (more)g(di\016cult.)k(This)c(recognition)g(of)g(the)h(game)e(phase)i(m)o(ust) 262 2399 y(also)e(include)h(realising)f(when)i(p)q(ositional)d(factors)j(can) f(b)q(e)h(ignored)e(and)h(the)h(opp)q(onen)o(ts)262 2449 y(king)f(can)h(b)q (e)g(driv)o(en)g(to)g(c)o(hec)o(kmate.)957 2574 y(36)p eop %%Page: 37 39 37 38 bop 324 307 a Fp(The)14 b(game)f(phase)i(can)f(also)f(b)q(e)i(used)g (to)f(encourage)h(the)f(program)f(to)h(trade)g(pieces)262 357 y(when)g(ahead)g(in)f(material.)262 509 y Fu(3.2.5)55 b(Planning)262 621 y Fp(Planning)19 b(pla)o(ys)h(an)g(imp)q(ortan)o(t)f(role)i(in)f(h)o (uman)e(c)o(hess.)40 b(It)21 b(could)f(b)q(e)h(said)f(that)h(a)262 670 y(program)d(is)i(con)o(tin)o(ually)f(planning)f(to)i(maximi)o(se)e(its)i (ev)n(aluation)f(function's)h(score.)262 720 y(Ho)o(w)o(ev)o(er,)c(this)g (often)g(leads)g(to)g(aimless)e(pla)o(y)m(,)h(w)o(aiting)f(for)i(the)g(opp)q (onen)o(t)h(to)e(mak)o(e)g(a)262 770 y(mistak)o(e.)324 855 y(A)20 b(plan)f(could)h(b)q(e)g(conceiv)o(ed)h(at)e(the)i(ro)q(ot)f(of)f(the) h(tree)h(b)o(y)f(an)g(analysis)f(of)g(the)262 905 y(p)q(osition.)29 b(Sp)q(eci\014c)19 b(goals)d(can)j(b)q(e)f(iden)o(ti\014ed,)g(suc)o(h)h(as)f (a)f(king)g(side)h(pa)o(wn)g(rush,)h(for)262 955 y(example.)d(The)f(relev)n (an)o(t)f(Pc/Sq)g(tables)g(and)g(static)h(ev)n(aluation)d(criteria)i(can)h(b) q(e)f(giv)o(en)262 1005 y(w)o(eigh)o(tings)c(to)h(encourage)h(ac)o(hiev)o (emen)o(t)f(of)f(these)j(goals.)j(F)m(or)11 b(example,)f(increasing)h(the)262 1055 y(b)q(on)o(us)k(for)g(pushing)h(pa)o(wns)f(on)h(the)g(king)e(side.)23 b(The)16 b(subsequen)o(t)i(searc)o(h)e(w)o(ould)f(then)262 1104 y(b)q(e)h(biased)f(to)o(w)o(ards)h(selecting)g(mo)o(v)o(es)e(whic)o(h)h (ac)o(hiev)o(e)h(these)h('sub{goals'.)k(T)m(o)15 b(further)262 1154 y(encourage)20 b(the)g(use)g(of)e(a)h(consisten)o(t)i(plan,)e(the)h (principle)f(v)n(ariation)f(from)f(the)j(last)262 1204 y(searc)o(h)15 b(can)g(b)q(e)g(used)h(to)e(direct)h(the)h(curren)o(t)g(searc)o(h.)21 b(Deviations)14 b(only)f(b)q(eing)i(allo)o(w)o(ed)262 1254 y(when)f(they)g(are)h(clearly)e(sup)q(erior.)324 1339 y(Chess)k(programs)e (generally)h(ha)o(v)o(e)f(no)h(problem)f(in)g(\014nding)h(the)h(correct)g(mo) o(v)o(es)e(of)262 1389 y(com)o(binations)i(leading)i(to)g(a)h(gain)e(in)i (material.)33 b(Ho)o(w)o(ev)o(er,)21 b(they)f(\014nd)g(it)f(far)h(more)262 1439 y(di\016cult)13 b(to)g(create)j(p)q(ositions)d(where)i(suc)o(h)g(com)o (binations)d(exist.)262 1611 y Fr(3.3)69 b(Learning)262 1738 y Fp(The)14 b(Learning)g(pro)q(cess)h(can)f(b)q(e)h(split)e(in)o(to)g(5)h (main)e(categories:)324 1821 y Ff(\017)20 b Fp(Rote)14 b(Learning.)324 1904 y Ff(\017)20 b Fp(Advice)15 b(T)m(aking.)324 1987 y Ff(\017)20 b Fp(Induction.)324 2070 y Ff(\017)g Fp(Learning)14 b(b)o(y)g(Analogy)m(.)324 2153 y Ff(\017)20 b Fp(P)o(arameter)14 b(Adjustmen)o(t.)262 2236 y(The)e(\014rst)h(four)f(categories)h(are)g(directly)g(related)g(to)f (the)h(w)o(a)o(y)e(h)o(umans)g(learn.)18 b(The)12 b(\014nal)262 2286 y(category)f(is)g(deriv)o(ed)g(more)f(from)f(the)i(w)o(a)o(y)g(programs) e(mak)o(e)h(decisions)h(than)g(the)g(h)o(uman)262 2336 y(learning)i(pro)q (cess.)957 2574 y(37)p eop %%Page: 38 40 38 39 bop 262 307 a Fu(3.3.1)55 b(Rote)18 b(Learning)262 419 y Fp(This)12 b(is)h(the)g(simplest)e(form)g(of)h(mac)o(hine)g(learning.)17 b(It)12 b(in)o(v)o(olv)o(es)g(the)h(recording)g(of)f(data,)262 469 y(and)h(use)i(of)e(that)h(same)f(data)h(when)g(faced)g(with)g(exactly)g (the)g(same)f(situation)h(again.)324 554 y(Most)i(c)o(hess)h(programs)e(use)i (what)e(is)h(kno)o(wn)f(as)h(an)g("Op)q(ening)g(Bo)q(ok".)23 b(This)16 b(is)g(a)262 604 y(database)i(of)g(pre-stored)h(op)q(ening)f(lines) h(of)e(pla)o(y)g(whic)o(h)i(are)f(lo)q(ok)o(ed)g(up)g(and)g(pla)o(y)o(ed)262 654 y(automatically)12 b(while)k(the)g(t)o(w)o(o)g(pla)o(y)o(ers)g(stic)o(k)g (to)g(the)h(stored)g(op)q(ening)e(line)h(of)f(mo)o(v)o(es.)262 704 y(In)h(more)g(sophisticated)i(c)o(hess)g(programs,)e(p)q(ositions)h(and)g (mo)o(v)o(es)e(are)j(stored,)g(rather)262 754 y(than)c(lines)h(of)g(mo)o(v)o (es.)20 b(This)15 b(enables)g(a)g(transp)q(osition)g(of)f(mo)o(v)o(es)g(to)h (b)q(e)h(detected)h(and)262 803 y(allo)o(ws)11 b(mo)o(v)o(es)f(to)j(b)q(e)f (pla)o(y)o(ed)g(whenev)o(er)i(a)e('kno)o(wn')f(p)q(osition)g(is)h(reac)o (hed.)19 b(The)13 b(op)q(ening)262 853 y(b)q(o)q(ok)i(is)g(v)o(ery)g(useful)h (for)f(a)o(v)o(oiding)e(op)q(ening)i(traps,)h(sa)o(ving)e(time)g(and)h (making)e(mo)o(v)o(es)262 903 y(of)h(a)h(v)o(ery)g(high)g(standard)g(whic)o (h)g(ha)o(v)o(e)g(y)o(ears)h(of)f(theory)g(and)g(practice)h(b)q(ehind)g (them.)262 953 y(Ob)o(viously)i(this)i(tec)o(hnique)g(can)f(only)g(co)o(v)o (er)h(the)g(\014rst)g(few)f(mo)o(v)o(es)f(of)h(a)g(game,)g(an)o(y)262 1003 y(deviation)13 b(causing)g(the)i(program)d(to)i('think')e(for)i(itself.) 324 1088 y(V)m(arious)i(endgame)f(databases)i(ha)o(v)o(e)f(also)g(b)q(een)i (created)g(for)e(elemen)o(tary)f(endings)262 1138 y(suc)o(h)g(as)f(king)g (and)g(pa)o(wn)h(against)e(king.)20 b(When)14 b(database)h(p)q(ositions)f (are)h(reac)o(hed)h(the)262 1187 y(program)f(can)i(simply)e(lo)q(ok)i(up)g (the)h(correct)g(mo)o(v)o(e)e(and)h(pla)o(y)f(it.)28 b(I)17 b(b)q(eliev)o(e)g(for)g(suc)o(h)262 1237 y(simple)12 b(endings,)i(heuristics) i(can)e(b)q(e)h(dev)o(elop)q(ed)g(whic)o(h)f(will)e(allo)o(w)h(correct)j(pla) o(y)d(using)262 1287 y(searc)o(h)i(rather)f(than)g(massiv)o(e)f(storage.)324 1372 y(A)h(more)e(v)o(ersatile)i(tec)o(hnique)h(has)f(b)q(een)g(suggested)i (b)o(y)d(Da)o(vid)f(Slate)i([58)o(])f(of)g(Chess)262 1422 y(4.5)h(fame.)20 b(Slate)15 b(suggests)h(a)f(metho)q(d)f(b)o(y)h(whic)o(h)g(a)g(transp)q (osition)g(table)g(can)g(b)q(e)h(used)262 1472 y(to)d(enable)g(a)g(c)o(hess)i (program)d(to)h(learn)g(from)f(its)h(exp)q(erience.)20 b(The)14 b(idea)f(b)q(eing)g(to)h(store)262 1522 y(p)q(ositions)e(where)h(the)h (program's)c(ev)n(aluation)i(c)o(hanges)h(dramatically)m(.)h(This)f(allo)o (ws)e(the)262 1572 y(program)h(to)j(a)o(v)o(oid)e(falling)f(in)o(to)i(the)h (same)f(trap)g(again.)19 b(This)14 b(is)h(of)e(most)h(use)h(in)f(non{)262 1621 y(b)q(o)q(ok)i(op)q(ening)h(p)q(ositions)g(whic)o(h)f(ma)o(y)f(b)q(e)j (encoun)o(tered)h(in)d(another)i(game.)26 b(Fidelit)o(y)262 1671 y(Electronics)14 b(are)f(using)g(a)f(similar)f(tec)o(hnique)i(in)g(one)g (of)f(their)i(latest)f(commercial)d(c)o(hess)262 1721 y(mac)o(hines)i([21].) 262 1873 y Fu(3.3.2)55 b(Advice)18 b(T)-5 b(aking)262 1985 y Fp(Advice)16 b(taking)f(c)o(hess)i(programs)e(require)h(the)h(gap)e(b)q(et) o(w)o(een)i(the)g(programmi)o(ng)c(lev)o(el)262 2035 y(and)e(a)h(c)o(hess)i (masters)e(kno)o(wledge)g(to)f(b)q(e)i(bridged)f(b)o(y)g(some)f(high)h(lev)o (el)f(c)o(hess)j(language.)324 2120 y(Most)c(notably)g(Zobrist)g(and)g (Carlson)g([64)o(])g(dev)o(elop)q(ed)g(suc)o(h)h(a)f(t)o(yp)q(e)h(of)e (advice)h(taking)262 2170 y(program.)15 b(The)e(program)e(w)o(as)h(tutored)h (b)o(y)g(Charles)f(Kalme,)f(a)h(US)h(Senior)f(Chess)i(Mas-)262 2219 y(ter.)22 b(The)15 b('Chess)h(Language')e(used)i(w)o(as)f(relativ)o(ely) g(sophisticated,)g(but)h(still)e(required)262 2269 y(mathematical)f(w)o(eigh) o(ts)18 b(to)f(b)q(e)g(assigned)h(to)f(patterns.)29 b(Ho)o(w)o(ev)o(er,)18 b(c)o(hess)h(masters)e(do)262 2319 y(not)d(consciously)h(conceptualise)h(p)q (ositions)f(in)f(this)h(w)o(a)o(y)m(.)20 b(Therefore,)c(the)g(advice)f(that) 262 2369 y(can)f(b)q(e)g(giv)o(en)g(is)f(somewhat)g(di\016cult)g(to)h(assign) g(discrete)h(w)o(eigh)o(tings)f(to.)957 2574 y(38)p eop %%Page: 39 41 39 40 bop 324 307 a Fp(The)21 b(program)d(only)i(con)o(tained)g(50)g (patterns.)39 b(Researc)o(h)22 b(done)e(b)o(y)g(Simon)f(and)262 357 y(Gilmarti)o(n)13 b([55)o(])j(indicates)g(that)g(a)f(grandmaster)h(has)g (a)f(v)o(o)q(cabulary)g(of)h(ab)q(out)f(50,000)262 407 y(c)o(hess)i (patterns.)26 b(Therefore,)17 b(it)f(is)g(not)g(surprising)g(that)h(Zobrist)f (and)g(Carlson's)g(pro-)262 457 y(gram)c(only)h(p)q(erformed)g(at)h(the)h(no) o(vice)e(lev)o(el.)262 608 y Fu(3.3.3)55 b(Induction)262 720 y Fp(A)10 b(n)o(um)o(b)q(er)g(of)g(attempts)g(ha)o(v)o(e)g(b)q(een)i(made)d (to)h(use)i(induction)e(in)g(c)o(hess)i(programs.)j(Most)262 770 y(in)o(v)o(olv)o(ed)f(the)j(narro)o(w)f(domain)e(of)i(simple)f(endings)h (suc)o(h)h(as)g(king)e(and)h(pa)o(wn)g(against)262 820 y(king)11 b([54)o(].)17 b(Giv)o(en)12 b(a)g(relativ)o(ely)g(large)g(n)o(um)o(b)q(er)g (of)g(training)f(ev)o(en)o(ts,)j(suc)o(h)f(programs)e(are)262 870 y(able)16 b(to)g(use)i(induction)e(on)g(a)g(set)i(of)e(kno)o(wn)g (predicates)i(in)e(order)h(to)g(deriv)o(e)g(a)f(set)h(of)262 919 y(form)o(ulas.)e(The)d(programs)f(are)h(then)h(able)f(to)f(deal)h(with)g (suc)o(h)g(endings)h(with)e(80)h(to)g(90\045)262 969 y(success.)21 b(Ho)o(w)o(ev)o(er,)15 b(a)f(10)g(to)g(20\045)f(lev)o(el)i(of)e(incorrect)j (pla)o(y)m(,)d(esp)q(ecially)h(in)g(suc)o(h)h(simple)262 1019 y(endings,)e(is)h(not)g(adequate)g(in)g(tournamen)o(t)f(programs.)324 1104 y(Stev)o(en)f(Skiena)g(states)h(in)e([57)o(],)g("When)h(more)f(complex)f (endgames)h(are)i(considered,)262 1154 y(increasingly)19 b(larger)i(n)o(um)o (b)q(er)e(of)h(predicates)h(will)e(b)q(e)i(needed,)i(un)o(til)c(forms)g(of)h (con-)262 1204 y(structiv)o(e)d(induction)e(or)h(feature)h(formation)c(are)j (necessary)m(.)26 b(Systems)16 b(for)f(signi\014can)o(t)262 1254 y(constructiv)o(e)g(induction)e(simply)f(do)i(not)g(exist.".)262 1405 y Fu(3.3.4)55 b(Learning)18 b(b)n(y)g(Analogy)262 1517 y Fp(Learning)10 b(b)o(y)g(analogy)e(is)j(probably)e(the)i(most)e(p)q(o)o(w)o (erful)h(metho)q(d)g(applicable)f(to)h(pla)o(ying)262 1567 y(c)o(hess.)19 b(Unfortunately)14 b(it)f(is)h(also)f(v)o(ery)i(di\016cult)e (to)g(ac)o(hiev)o(e)i(on)e(a)h(mac)o(hine.)324 1652 y(It)h(has)f(b)q(een)i (found)e(b)o(y)h(de)g(Gro)q(ot)f([16)o(])h(that)f(grandmasters)h(notice)g (similarities)d(in)262 1702 y(piece)20 b(placemen)o(t,)f(square)h(con)o(trol) e(and)h(pressure.)36 b(These)21 b(concepts)g(are)e(kno)o(wn)g(to)262 1752 y(strong)14 b(pla)o(y)o(ers)g(in)g(the)h(form)e(of)h(patterns,)h(mo)o(v) o(es)e(and)h(goals.)19 b(No)14 b(ma)r(jor)e(w)o(ork)i(seems)262 1802 y(to)k(ha)o(v)o(e)g(b)q(een)i(done)e(in)g(this)h(imp)q(ortan)o(t)d (area.)32 b(This)19 b(seems)f(to)g(me)g(to)g(b)q(e)h(a)f(ma)r(jor)262 1851 y(omission,)11 b(if)i(kno)o(wledge)h(based)g(programs)f(are)h(to)g (succeed)i(in)d(reac)o(hing)h(master)g(lev)o(el.)262 2003 y Fu(3.3.5)55 b(P)n(arameter)17 b(Adjustmen)n(t)262 2115 y Fp(This)9 b(t)o(yp)q(e)i(of)e(learning)g(in)o(v)o(olv)o(es)g(adjusting)g(the)i(w)o (eigh)o(ts)f(applied)f(to)h(ev)n(aluation)e(criteria)262 2165 y(in)h(the)h(ligh)o(t)f(of)g(exp)q(erience.)19 b(Those)10 b(criteria)g(whic)o (h)g(lead)f(to)h(impro)o(v)o(ed)e(p)q(erformance)h(are)262 2214 y(increased,)18 b(whereas)f(those)h(criteria)f(whic)o(h)f(deteriorate)i (p)q(erformance)e(are)h(decreased)262 2264 y(or)c(discarded)i(altogether.)324 2350 y(The)22 b(most)e(notable)h(example)f(of)h(this)g(t)o(yp)q(e)h(of)f(mac) o(hine)f(learning)g(is)h(Sam)o(uel's)262 2399 y(draugh)o(ts)c(program)f([48)o (,)h(49)o(].)29 b(Ho)o(w)o(ev)o(er,)18 b(c)o(hess)h(is)e(a)g(far)g(more)g (complex)f(game)g(than)262 2449 y(draugh)o(ts.)26 b(In)17 b(1961,)e(Max)i(Eu) o(w)o(e,)g(ex{w)o(orld)f(c)o(hess)i(c)o(hampion,)d(set)j(up)e(a)h(commi)o (ttee)957 2574 y(39)p eop %%Page: 40 42 40 41 bop 262 307 a Fp([20)o(])15 b(to)h(explore)g(the)h(p)q(ossibilities)f (of)f(applying)g(Sam)o(uel's)f(tec)o(hniques)j(to)f(c)o(hess.)26 b(The)262 357 y(commi)o(ttee)16 b(concluded)j(that)f(for)f(c)o(hess)j(Sam)o (uel's)c(tec)o(hniques)j("w)o(ould)e(ha)o(v)o(e)g(to)h(deal)262 407 y(not)f(with)h(31)g(comp)q(onen)o(t)f(n)o(um)o(b)q(ers)g(but)i(with)e(31) h(millio)o(n)d(or)j(ev)o(en)h(more")e([28)o(].)30 b(In)262 457 y(other)14 b(w)o(ords)g(the)h(tec)o(hniques)g(are)f(impractical)e(for)i (c)o(hess.)324 542 y(More)h(recen)o(tly)h(Thomas)d(Nitsc)o(he)j([45)o(])e (has)h(exp)q(erimen)o(ted)g(with)g(a)f(learning)g(c)o(hess)262 592 y(program)9 b(whic)o(h)i(adjusts)h(its)f(o)o(wn)g(parameters)g(using)g (linear)g(regression.)19 b(The)11 b(program)262 641 y(is)i(capable)h(of)f (learning)h(from)e(three)j(di\013eren)o(t)g(sources:)324 725 y Ff(\017)20 b Fp(Analysing)13 b(Master)i(Games.)324 808 y Ff(\017)20 b Fp(Pla)o(ying)13 b(against)g(Human)f(Opp)q(osition.)324 891 y Ff(\017)20 b Fp(Pla)o(ying)13 b(against)g(itself.)262 974 y(Suc)o(h)18 b(tec)o(hniques)i(ha)o(v)o(e)e(not)g(b)q(een)h(generally)f (successful)i(in)e(comp)q(etitiv)o(e)f(c)o(hess)j(pro-)262 1023 y(grams.)k(I)17 b(b)q(eliev)o(e)g(the)g(reason)g(for)g(this)f(is)h(that) f(most)g(ev)n(aluation)f(functions)i(are)g(not)262 1073 y(made)e(up)j(of)e (simple)f(linear)i(features)h(as)f(used)h(b)o(y)f(Nitsc)o(he.)29 b(Therefore)18 b(making)d(this)262 1123 y(t)o(yp)q(e)f(of)f(learning)g(m)o (uc)o(h)g(more)g(di\016cult)g(to)h(apply)m(.)324 1208 y(In)9 b(conclusion,)h(I)f(think)h(the)g(amoun)o(t)d(of)i(learning)g(necessary)i (for)f(a)f(program)f(to)h(reac)o(h)262 1258 y(a)i(high)h(lev)o(el)g(of)g (abilit)o(y)e(has)j(b)q(een)g(sev)o(erely)g(under{estimated.)18 b(Simon)10 b(and)i(Chase)h([56)o(])262 1308 y(found)19 b(that)h(it)g(tak)o (es)g(a)g(pla)o(y)o(er)f(ab)q(out)h(a)g(decade)h(of)e(in)o(tense)i(pre{o)q (ccupation)g(with)262 1358 y(pla)o(ying)11 b(c)o(hess)j(to)f(b)q(ecome)g(a)g (grandmaster.)k(Humans)12 b(are)h(sup)q(erb)i(learners,)f(mac)o(hines)262 1408 y(are)19 b(clearly)h(not.)34 b(It)20 b(therefore)g(follo)o(ws)e(that)i (it)f(will)f(tak)o(e)h(success)j(in)d(most)f(of)h(the)262 1457 y(categories)e(outlined)f(in)g(this)g(section)i(together)f(with)f(at)g(least) h(a)f(decade)i(of)e(full)f(time)262 1507 y(w)o(ork,)9 b(advice)h(and)f (training)g(to)g(pro)q(duce)i(a)e(learning,)g(kno)o(wledge{based)h(c)o(hess)h (program)262 1557 y(an)o(ywhere)j(near)g(the)h(grandmaster)e(lev)o(el.)262 1730 y Fr(3.4)69 b(Time)21 b(Con)n(trol)262 1856 y Fp(Chess)11 b(clo)q(c)o(ks)g(are)g(used)h(in)e(comp)q(etitiv)o(e)g(c)o(hess)i(to)e(allo)o (w)f(fair)h(allo)q(cation)f(of)h(time)g(to)g(eac)o(h)262 1906 y(pla)o(y)o(er)j(for)h(the)h(game.)i(Both)d(pla)o(y)o(ers)g(m)o(ust)f(then)i (conform)d(to)i(a)g(set)h(of)e(time)g(con)o(trols.)262 1956 y(In)f(tournamen)o(t)g(c)o(hess)h(the)h(general)e(time)f(con)o(trol)i(is)f (40)g(mo)o(v)o(es)f(in)h(2)g(hours)h(follo)o(w)o(ed)e(b)o(y)262 2005 y(20)g(mo)o(v)o(es)g(in)h(ev)o(ery)h(subsequen)o(t)g(hour.)18 b(Some)11 b(time)g(con)o(trols)h(can)g(b)q(e)h("sudden)g(death",)262 2055 y(e.g.)k(all)c(mo)o(v)o(es)g(in)g(30)g(min)o(utes.)324 2141 y(An)o(y)j(c)o(hess)h(program)e(written)h(to)g(comp)q(ete)g(with)g(h)o (umans)f(or)h(other)g(programs)f(in)262 2190 y(tournamen)o(t)e(games)h(m)o (ust)g(therefore)i(ha)o(v)o(e)e(an)h(algorithm)d(to)i(con)o(trol)h(its)f (time)g(usage.)262 2240 y(The)g(time)f(sp)q(en)o(t)i(on)e(eac)o(h)i(mo)o(v)o (e)d(do)q(es)j(not)f(ha)o(v)o(e)f(to)h(b)q(e)h(constan)o(t,)f(in)f(fact)h(it) g(is)g(prefer-)262 2290 y(able)g(that)h(it)f(is)h(not.)20 b(It)15 b(is)g(wise)g(to)g(pla)o(y)e(ob)o(vious)h(or)h(forced)h(mo)o(v)o(es)d(quic)o (kly)h(and)h(tak)o(e)262 2340 y(longer)i(on)h(more)f(di\016cult)g(mo)o(v)o (es.)28 b(Therefore,)20 b(a)d(sophisticated)i(time)d(con)o(trol)i(algo-)262 2390 y(rithm)11 b(m)o(ust)h(detect)i(these)g(cases)h(and)d(allo)q(cate)g(its) h(time)f(appropriately)m(.)k(I)d(b)q(eliev)o(e)g(it)g(is)262 2439 y(also)g(part)h(of)f(suc)o(h)i(an)f(algorithms)d(resp)q(onsibilit)o(y)j (to)g(detect)h(when)g(the)f(horizon)g(e\013ect)957 2574 y(40)p eop %%Page: 41 43 41 42 bop 262 307 a Fp(ma)o(y)11 b(b)q(e)j(o)q(ccurring)f(and)g(allo)q(cate)g (enough)g(time)f(where)i(p)q(ossible)g(to)f(see)h(o)o(v)o(er)f(the)h(hori-) 262 357 y(zon.)k(T)m(o)13 b(ac)o(hiev)o(e)h(these)h(aims,)c(the)k(algorithm)c (m)o(ust)h(kno)o(w)i(what)f(scores)j(the)e(searc)o(h)h(is)262 407 y(calculating)10 b(at)i(eac)o(h)g(iteration)f(and)h(the)g(state)h(of)e (the)i(searc)o(h)f(at)g(a)g(giv)o(en)f(p)q(oin)o(t)g(in)g(time.)324 492 y(Time)j(con)o(trol)h(problems)f(are)i(eased)h(b)o(y)e(the)h(use)g(of)f (iterativ)o(e)g(deep)q(ening)i(b)q(ecause)262 542 y(of)c(the)j(con)o(tin)o (uous)e(a)o(v)n(ailabili)o(t)o(y)e(of)i(the)h(b)q(est)h(mo)o(v)o(e)d(found)h (so)g(far.)20 b(The)15 b(time)e(used)j(up)262 592 y(thinking)g(ab)q(out)i (the)h(curren)o(t)g(mo)o(v)o(e)d(m)o(ust)h(b)q(e)i(c)o(hec)o(k)o(ed)g (regularly)e(against)g(the)i(time)262 641 y(allo)q(cation)14 b(to)j(a)o(v)o(oid)e(the)i(p)q(ossibilities)f(of)g(o)o(v)o(er)g(using)h(time) e(or)h(ev)o(en)i(losing)d(on)h(time.)262 691 y(Unfortunately)m(,)g(it)g(is)g (not)h(enough)f(to)h(c)o(hec)o(k)g(the)g(time)f(after)g(eac)o(h)h(iteration)f (or)h(ev)o(en)262 741 y(after)f(eac)o(h)h(\014rst)g(lev)o(el)g(branc)o(h.)26 b(This)16 b(is)g(b)q(ecause)i(some)e(branc)o(hes)i(ma)o(y)c(tak)o(e)j(a)f (large)262 791 y(amoun)o(t)c(of)j(time)e(to)h(searc)o(h.)22 b(Therefore,)16 b(a)e(successful)j(time)c(con)o(trol)i(algorithm)d(m)o(ust) 262 841 y(b)q(e)g(closely)f(link)o(ed)g(to)h(the)g(actual)f(tree)i(searc)o(h) g(mec)o(hanism)c(at)j(all)e(but)i(the)h(v)o(ery)f(deep)q(est)262 891 y(lev)o(els)h(of)h(the)g(tree.)324 976 y(During)h(m)o(y)g(researc)o(h)j (I)e(ha)o(v)o(e)g(noticed)g(a)g(distinct)h(lac)o(k)e(of)h(published)g (material)e(in)262 1026 y(this)f(area.)18 b(The)13 b(articles)h(b)o(y)f(R.)f (Hy)o(att)h([30])f(and)h(H.)g(Berliner)h([7])e(are)i(the)g(only)e(articles) 262 1075 y(of)j(an)o(y)g(substance)i(in)f(this)g(area.)23 b(I)16 b(\014nd)g(this)g(rather)g(surprising)g(b)q(ecause)i(as)e(I)f(see)i(it,)262 1125 y(this)c(is)h(an)g(imp)q(ortan)o(t)e(elemen)o(t)h(of)h(an)o(y)f(strong)h (c)o(hess)i(program.)957 2574 y(41)p eop %%Page: 42 44 42 43 bop 262 654 a Fn(Chapter)34 b(4)262 897 y Fo(The)39 b(Ev)-7 b(aluation)42 b(F)-10 b(unction)262 1148 y Fp(In)11 b(this)g(c)o(hapter)h(I)f (will)f(de\014ne)i(and)f(explain)f(the)i(heuristics)g(I)g(consider)g(to)f(b)q (e)g(imp)q(ortan)o(t)262 1198 y(in)h(assessing)j(the)f(merits)e(of)h(a)g(c)o (hess)i(p)q(osition.)i(I)d(in)o(tend)f(to)g(implemen)o(t)e(these)k(ideas)e (in)262 1248 y(a)g(new)h(c)o(hess)i(program)c(called)i("HIAR)o(CS)f(5.0".)324 1333 y(I)e(hop)q(e)h(to)f(pro)q(duce)h(an)f(ev)n(aluation)f(function)h(whic)o (h)g(has)g(the)h(p)q(ositional)e(kno)o(wledge)262 1383 y(at)j(or)g(near)g (the)h(exp)q(ert)h(lev)o(el)e(\(2000)f(ELO\).)h(It)g(w)o(ould)g(normally)d (tak)o(e)k(a)e(h)o(uman)g(pla)o(y)o(er)262 1433 y(some)17 b(5)h(y)o(ears)g (of)g(in)o(tensiv)o(e)g(c)o(hess)i(exp)q(erience)g(and)e(learning)g(to)g(ac)o (hiev)o(e)g(this)g(lev)o(el.)262 1483 y(Therefore,)f(m)o(y)e(aim)f(to)i (instill)f(enough)i(kno)o(wledge)f(in)g(a)g(program)f(within)g(the)i(short) 262 1532 y(p)q(erio)q(d)12 b(of)f(time)f(a)o(v)n(ailable)g(for)h(this)h(pro)r (ject)h(is)f(daun)o(ting.)k(Ho)o(w)o(ev)o(er,)c(I)g(can)g(dra)o(w)g(on)f(m)o (y)262 1582 y(o)o(wn)j(exp)q(erience)j(of)e(tournamen)o(t)f(c)o(hess)j(and)e (the)g(exp)q(eriences)j(of)c(some)h(great)g(master)262 1632 y(pla)o(y)o(ers)e(who)f(ha)o(v)o(e)h(written)h(ab)q(out)f(c)o(hess)i (strategy)m(.)j(In)13 b(particular,)f(the)i(famous)d(b)q(o)q(oks)262 1682 y("My)j(System")h(and)g("Chess)h(Praxis")f(b)o(y)g(Aron)h(Nimzo)o(witsc) o(h)e([43)o(,)g(44])h(con)o(tain)f(some)262 1732 y(v)o(ery)h(deep)g(though)o (ts)g(on)g(p)q(ositional)e(and)i(strategic)h(pla)o(y)m(.)j(Therefore,)d(I)f (will)e(use)j(suc)o(h)262 1781 y(ideas)e(to)f(help)h(dev)o(elop)g(heuristics) h(to)f(ev)n(aluate)f(p)q(ositions.)324 1867 y(As)f(I)g(see)h(it,)e(there)i (are)f(three)h(main)d(problems)g(facing)h(the)i(dev)o(elopmen)o(t)d(of)i(a)f ('go)q(o)q(d')262 1916 y(ev)n(aluation)h(function:)324 1999 y Ff(\017)20 b Fp(Determining)13 b Fl(whic)o(h)f Fp(criteria)i(are)h(imp)q (ortan)o(t.)324 2083 y Ff(\017)20 b Fp(Deciding)14 b Fl(when)f Fp(the)h(criteria)h(are)f(imp)q(ortan)o(t.)324 2166 y Ff(\017)20 b Fp(Deciding)14 b Fl(what)f Fp(the)i(relativ)o(e)e(merits)h(of)f(eac)o(h)h (criterion)h(should)e(b)q(e.)262 2249 y(It)h(is)g(vital)e(to)i(get)h(all)d (three)k(of)d(these)j(asp)q(ects)f('righ)o(t'.)i(F)m(or)d(example,)e(a)i (program)f(ma)o(y)262 2298 y(kno)o(w)i(that)g(bishops)h(are)g(strong)g(in)f (some)g(p)q(ositions.)22 b(Ho)o(w)o(ev)o(er,)16 b(if)f(it)g(do)q(es)i(not)e (kno)o(w)262 2348 y(with)10 b(accuracy)j(when)f(those)g(p)q(ositions)f(o)q (ccur,)h(it)f(cannot)h(apply)e(its)h(ev)n(aluation)f(criteria)262 2398 y(e\013ectiv)o(ely)m(.)20 b(There)c(are)f(no)f(p)q(erfect)j(answ)o(ers,) e(often)g(ev)n(aluation)e(criteria)i(ma)o(y)e(con)o(tra-)262 2448 y(dict)j(eac)o(h)g(other)h(b)q(ecause)h(of)e(an)f(inevitable)h(in)o (teraction)g(and)g(o)o(v)o(erlap)g(b)q(et)o(w)o(een)h(eac)o(h)957 2574 y(42)p eop %%Page: 43 45 43 44 bop 262 307 a Fp(t)o(yp)q(e)15 b(of)g(c)o(hess)i(kno)o(wledge)e (represen)o(ted.)25 b(Therefore,)17 b(eac)o(h)f(criterion)g(is)f(not)g(indep) q(en-)262 357 y(den)o(t)i(in)f(its)h(o)o(wn)f(righ)o(t,)g(but)h(m)o(ust)f(b)q (e)h(considered)h(with)e(all)g(other)h(relev)n(an)o(t)g(criteria.)262 407 y(Hence,)e(the)h(relativ)o(e)e(w)o(eigh)o(ting)g(for)g(eac)o(h)h(asp)q (ect)h(of)f(ev)n(aluation)e(is)h(imp)q(ortan)o(t.)19 b(Ho)o(w-)262 457 y(ev)o(er,)f(the)g(criteria)f(can)h(only)e(b)q(e)i(considered)g(correct)h (in)e(a)g(statistical)g(sense,)i(not)e(an)262 506 y(absolute)c(sense.)324 592 y(These)k(three)f(main)e(problem)g(areas)i(m)o(ust)e(b)q(e)i(considered)h (when)f(dev)o(eloping)f(eac)o(h)262 641 y(heuristic.)36 b(Dev)o(eloping)19 b(an)h(ev)n(aluation)e(function)i(is)f(a)h(v)o(ery)g(iterativ)o(e)g(pro)q (cess.)38 b(In)262 691 y(the)16 b(ligh)o(t)e(of)h(seeing)h(a)f(program)f(pla) o(y)h(the)h(game,)e(the)i(heuristics)h(will)d(b)q(e)i(con)o(tin)o(ually)262 741 y(ev)o(olv)o(ed.)22 b(This)15 b(\014ts)h(in)f(w)o(ell)g(with)g(the)h (equiv)n(alen)o(t)e(h)o(uman)g(pro)q(cess)j(where)g(kno)o(wledge)262 791 y(is)e(con)o(tin)o(ually)f(in)i(a)f(state)i(of)e(ev)o(olution,)g (although)g(this)g(is)h(an)g(automatic)d(pro)q(cess)18 b(in)262 841 y(the)c(case)h(of)e(a)h(h)o(uman)e(pla)o(y)o(er.)324 926 y(The)f(ev)n(aluation)f(function)h(will)e(deal)i(with)f(the)i(op)q(ening,)f (middle)e(game)h(and)g(general)262 976 y(endgame)15 b(to)i(allo)o(w)e(a)i (program)e(to)i(pla)o(y)f(the)h(en)o(tire)h(game.)26 b(Kno)o(wledge)17 b(for)f(sp)q(eci\014c)262 1026 y(endgames,)j(suc)o(h)h(as)g(bishop)f(v)o (ersus)h(knigh)o(t)f(endings,)h(will)e(b)q(e)i(omitted)e(b)q(ecause)j(of)262 1075 y(time)12 b(constrain)o(ts.)20 b(Ho)o(w)o(ev)o(er,)14 b(their)g(implemen)o(tation)d(is)j(just)g(a)g(matter)g(of)f(applying)g(a)262 1125 y(similar)e(approac)o(h)j(to)g(that)f(whic)o(h)h(I)g(am)e(applying)h(to) g(the)i(more)e(general)h(cases.)324 1210 y(The)f(ev)n(aluation)f(criteria)i (will)d(b)q(e)j(de\014ned)g(in)f(a)g(formal)d(manner,)i(using)h(b)q(oth)h (func-)262 1260 y(tional)8 b(and)j(algorithmi)o(c)d(descriptions)j(where)h 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b(ev)n(aluation)e(criteria)i(ha)o(v)o(e)g(an)g (a\013ect)h(on)e(b)q(oth)h(sides.)25 b(Therefore,)17 b(while)262 1744 y(w)o(eaknesses)g(are)f(discouraged)g(from)e(one)i(sides)h(p)q(oin)o(t)e (of)g(view,)h(their)g(creation)g(in)f(the)262 1794 y(opp)q(onen)o(ts)f(p)q (osition)f(is)h(activ)o(ely)f(encouraged.)957 2574 y(43)p eop %%Page: 44 46 44 45 bop 262 307 a Fr(4.1)69 b(De\014nition)21 b(1)i(:)31 b(Material)262 434 y Fp(Lik)o(e)20 b(all)f(other)i(c)o(hess)h(programs,)e(m)o (y)f(ev)n(aluation)f(function)j(will)d(hold)i(material)f(as)262 483 y(the)13 b(main)e(comp)q(onen)o(t.)16 b(Ho)o(w)o(ev)o(er,)d(unlik)o(e)f (most)g(other)h(programs)f(this)h(will)e(not)i(b)q(e)g(the)262 533 y(o)o(v)o(erriding)d(factor.)17 b(In)11 b(fact,)g(I)g(in)o(tend)g(to)g (mak)o(e)f(the)i(ev)n(aluation)d(function)i(sophisticated)262 583 y(enough)j(to)f(b)q(e)i(willing)c(to)j(giv)o(e)g(up)g(material)d(for)j (go)q(o)q(d)f(p)q(ositional)g(comp)q(ensation.)324 668 y(T)m(raditional)j(c)o 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b(of)g(the)i(other)f(pieces)i(will)c(b)q(e)i(assigned)h (relativ)o(e)e(to)h(this)g(basic)g(pa)o(wn)g(v)n(alue.)344 1150 y Fh(M)5 b(T)413 1156 y Fe(col)469 1150 y Fp(=)513 1119 y Fc(P)556 1130 y Fk(64)556 1163 y Fe(sq)q Fk(=1)734 1150 y Fl(if)13 b Fp(\(Occup)o(y\([An)o(y],col,sq\)\))793 1203 y Fl(case)h Fp(On\(sq\))h Fl(of)852 1253 y Fp(P)o(a)o(wn)136 b(:)18 b(P)o(a)o(wnV)m(alue) 852 1303 y(Knigh)o(t)110 b(:)18 b(Knigh)o(tV)m(alue)852 1353 y(Bishop)112 b(:)18 b(BishopV)m(alue)852 1403 y(Ro)q(ok)140 b(:)18 b(Ro)q(okV)m(alue)852 1452 y(Queen)122 b(:)18 b(QueenV)m(alue)852 1502 y(King)148 b(:)18 b(KingV)m(alue)793 1552 y Fl(endcase)734 1602 y(endif)344 1702 y(where)380 1751 y Fp(P)o(a)o(wnV)m(alue)152 b(=)14 b(100)380 1801 y(Knigh)o(tV)m(alue)126 b(=)14 b(325)380 1851 y(BishopV)m(alue)128 b(=)14 b(340)380 1901 y(Ro)q(okV)m(alue)156 b(=)14 b(520)380 1951 y(QueenV)m(alue)138 b(=)14 b(960)380 2000 y(KingV)m(alue)164 b(=)14 b(10000)262 2115 y(F)m(ew)20 b(pla)o(y)o(ers)g(agree)h(on)f(the)h(relativ)o(e)f(merits)f(of)h(a)g(knigh)o (t)g(and)g(bishop.)37 b(Both)20 b(are)262 2165 y(suited)c(to)g(di\013eren)o (t)h(t)o(yp)q(es)g(of)f(p)q(osition.)23 b(My)16 b(o)o(wn)g(view)g(is)g(that)g (programs)f(generally)262 2214 y(use)g(bishops)f(more)g(e\013ectiv)o(ely)h (than)f(knigh)o(ts.)20 b(This)14 b(is)g(b)q(ecause)i(programs)e(pla)o(y)f(op) q(en)262 2264 y(p)q(ositions)g(b)q(etter)j(than)e(closed)g(ones.)19 b(Bishops)c(are)f(usually)f(stronger)i(than)f(knigh)o(ts)g(in)262 2314 y(op)q(en)i(p)q(ositions)f(and)h(inferior)f(in)g(closed)i(p)q(ositions.) 23 b(Therefore)17 b(I)f(prop)q(ose)h(to)e(set)i(the)262 2364 y(knigh)o(t)c(and)g(bishop)h(v)n(alues)g(to)f(325)h(and)f(340)g(p)q(oin)o(ts) h(resp)q(ectiv)o(ely)m(.)324 2449 y(Ro)q(oks)j(are)i(particularly)e(strong)h (pieces)i(when)e(giv)o(en)g(scop)q(e)h(e.g.)30 b(on)18 b(op)q(en)h(\014les.) 957 2574 y(44)p eop %%Page: 45 47 45 46 bop 262 307 a Fp(They)12 b(are)h(generally)e(w)o(orth)h(ab)q(out)g(a)g (knigh)o(t)g(and)g(t)o(w)o(o)f(pa)o(wns.)18 b(I)12 b(will)f(use)h(a)g(ro)q (ok)g(v)n(alue)262 357 y(of)h(520)g(p)q(oin)o(ts.)324 442 y(The)h(queen)g(is) f(the)i(most)d(p)q(o)o(w)o(erful)h(piece)h(on)g(the)g(b)q(oard.)k(Its)c(scop) q(e)g(and)g(con)o(tribu-)262 492 y(tion)e(to)h(tactical)g(c)o(hess)h(mak)o (es)e(it)h(ideal)f(for)h(c)o(hess)h(programs.)j(T)m(o)12 b(re\015ect)j(this,) e(I)f(in)o(tend)262 542 y(to)h(use)i(a)f(queen)g(v)n(alue)g(of)f(960)g(p)q (oin)o(ts.)324 627 y(The)e(king)g(is)g(ob)o(viously)e(the)j(most)e(imp)q (ortan)o(t)f(piece.)18 b(It's)12 b(capture)g(will)d(nev)o(er)k(o)q(ccur)262 677 y(in)j(an)h(actual)f(game.)25 b(Ho)o(w)o(ev)o(er,)18 b(it)e(remains)g (useful)h(to)g(assign)g(a)f(v)n(alue)g(to)h(re\015ect)i(its)262 727 y(ultimate)12 b(imp)q(ortance.)17 b(I)d(will)e(use)j(a)e(v)n(alue)h(of)f (10000)f(p)q(oin)o(ts.)324 812 y(It)k(m)o(ust)g(b)q(e)h(remem)o(b)q(ered)f (these)i(v)n(alues)e(only)g(represen)o(t)j(the)e(basic)g(piece)g(v)n(alues.) 262 862 y(When)9 b(p)q(ositions)g(particularly)g(suited)h(to)f(certain)h(t)o (yp)q(es)g(of)f(pieces)h(o)q(ccur,)h(the)f(p)q(ositional)262 912 y(v)n(alue)15 b(of)h(the)g(relev)n(an)o(t)h(piece)g(will)e(increase)i(to) f(re\015ect)i(its)e(added)h(imp)q(ortance)e(in)h(the)262 961 y(curren)o(t)f(p)q(osition.)324 1047 y(A)22 b(total)f(material)e(v)n(alue)j (will)e(b)q(e)i(main)o(tained)e(incremen)o(tally)g(throughout)i(the)262 1096 y(searc)o(h,)c(for)f(reasons)h(of)f(e\016ciency)m(.)28 b(This)18 b(allo)o(ws)e(the)h(curren)o(t)i(material)c(v)n(alue)i(to)g(b)q(e) 262 1146 y(almost)12 b(instan)o(tly)h(a)o(v)n(ailable)e(at)j(all)f(no)q(des)h (of)g(the)g(tree,)h(in)o(terior)f(and)f(leaf.)p 641 1240 673 5 v 641 1904 5 665 v 646 1323 a Fg(0Z0ZrskZ)646 1406 y(Zpo0Zpop)646 1489 y(0ZpZ0Z0Z)646 1572 y(o0Z0l0Z0)646 1655 y(0Z0ZPZnZ)646 1738 y(Z0M0L0Z0)646 1821 y(POPZ0OPO)646 1904 y(Z0ZRS0J0)p 1310 1904 V 641 1908 673 5 v 266 2027 a Fp(Figure)h(4.1:)j Fl(Fidelit)o(y)c(68030) i(v)h(HIAR)o(CS)g(4.1)p Fp(,)d(1989)g(Olympiad,)e(White)j(to)g(Pla)o(y)m(.) 324 2145 y(In)g(\014gure)g(4.1,)f(the)h(Material)f(totals)h(for)f(white)h (and)g(blac)o(k)f(are)i(as)f(follo)o(ws:)344 2242 y Fh(M)5 b(T)413 2248 y Fe(W)t(hite)533 2242 y Fp(=)14 b(13025)344 2292 y Fh(M)5 b(T)413 2298 y Fe(B)q(lack)533 2292 y Fp(=)14 b(13025)957 2574 y(45)p eop %%Page: 46 48 46 47 bop 262 307 a Fr(4.2)69 b(De\014nition)21 b(2)i(:)31 b(Game)22 b(Phase)262 434 y Fp(As)14 b(already)f(explained,)g(it)h(is)f(imp)q (ortan)o(t)f(to)i(split)f(the)i(game)d(in)o(to)h(phases,)h(so)g(that)g(the) 262 483 y(ev)n(aluation)c(criteria)j(can)f(b)q(e)h(applied)f(smo)q(othly)m(,) e(th)o(us)j(a)o(v)o(oiding)d(notorious)i(cli\013s)g(in)g(the)262 533 y(ev)n(aluation)g(surface.)324 618 y(T)m(o)e(ac)o(hiev)o(e)i(this)g(smo)q (oth)e(transition)h(b)q(et)o(w)o(een)i(di\013eren)o(t)f(ev)n(aluation)e (criteria,)i(I)f(will)262 668 y(split)i(the)h(game)f(up)h(in)o(to)f(16)g (separate)i(phases.)344 766 y(phase)g(=)f(PS)344 815 y(revPhase)i(=)e(17)f Ff(\000)h Fp(phase)344 915 y Fl(where)380 965 y Fp(PS)g(:)159 b(totalMtl)13 b(=)h Fh(M)5 b(tl)899 971 y Fe(W)t(hite)1005 965 y Fp(+)10 b Fh(M)5 b(tl)1119 971 y Fe(B)q(lack)616 1015 y Fl(if)13 b Fp(\(totalMtl)g Ff(\024)h Fp(21870\))658 1065 y(1)616 1114 y Fl(else)658 1164 y Fp(\(totalMtl)f Ff(\000)h Fp(21570\))e(/)i(300)616 1214 y Fl(endif)380 1314 y Fh(M)5 b(tl)452 1320 y Fe(W)t(hite)563 1314 y Fp(:)41 b(T)m(otal)12 b(non{pa)o(wn)i(white)g(material.)380 1413 y Fh(M)5 b(tl)452 1419 y Fe(B)q(lack)556 1413 y Fp(:)48 b(T)m(otal)12 b(non{pa)o(wn)i(blac)o(k) f(material.)324 1532 y(In)19 b(the)h(op)q(ening)f(p)q(osition)g(the)h(phase)g (will)e(b)q(e)i(16.)34 b(The)20 b(phase)g(then)g(decreases)262 1581 y(linearly)11 b(as)i(material)d(is)i(captured,)i(except)g(when)f(the)g (total)f(non-pa)o(wn)g(material)e(v)n(alue)262 1631 y(falls)i(b)q(elo)o(w)h (21870)f(units.)18 b(A)o(t)13 b(this)h(p)q(oin)o(t)f(the)h(phase)g(remains)e (at)h(1)h(for)f(the)h(rest)g(of)f(the)262 1681 y(game,)h(unless)i(the)g (material)e(v)n(alue)h(rises)h(again)1048 1666 y Fk(1)1066 1681 y Fp(.)23 b(As)16 b(an)g(example,)e(in)h(\014gure)h(4.1)f(the)262 1731 y(Game)d(Phase)i(is)g(calculated)g(b)o(y:)k(phase)d(=)f(\(24650)e Ff(\000)j Fp(21570\))d(/)i(300)f(=)h(10.)324 1816 y(This)i(phase)i(concept)g (will)d(not)i(b)q(e)g(used)h(to)f(decide)h(when)f(rapid)f(dev)o(elopmen)o(t)g (of)262 1866 y(pieces)f(should)f(tak)o(e)h(place.)20 b(This)14 b(will)f(b)q(e)i(left)f(to)g(sp)q(ecial)h(dev)o(elopmen)o(t)e(criteria.)20 b(The)262 1916 y(concept)15 b(will)e(ho)o(w)o(ev)o(er,)i(b)q(e)g(used)g(to)f (progressiv)o(ely)h(mo)q(dify)d(those)j(ev)n(aluation)e(criteria)262 1966 y(whic)o(h)f(are)h(a\013ected)h(b)o(y)e(material)e(status.)18 b(F)m(or)12 b(example,)f(passed)j(pa)o(wns)e(b)q(ecome)h(more)262 2015 y(imp)q(ortan)o(t)f(as)i(the)g(material)e(on)i(the)g(b)q(oard)g (diminishes.)324 2101 y(The)h(game)f(phase)i(is)f(based)h(on)f(non{pa)o(wn)g (material)e(b)q(ecause)k(in)e(c)o(hess)i(it)d(is)i(gen-)262 2150 y(erally)d(imp)q(ortan)o(t)f(to)i(trade)g(pieces)h(not)f(pa)o(wns)g (when)g(ahead)g(in)g(material.)i(Therefore,)262 2200 y(the)e(phase)h(pro)o (vides)g(a)f(metho)q(d)g(of)f(encouraging)i(the)g(program)d(to)i(trade)h (pieces)h(when)262 2250 y(ahead)i(in)f(order)i(to)f(increase)h(some)f(fa)o(v) o(ourable)f(p)q(ositional)f(criteria)j(suc)o(h)f(as)h(passed)262 2300 y(pa)o(wn)f(v)n(alues.)34 b(T)m(rading)19 b(pa)o(wns)g(will)f(not)h(b)q (e)h(encouraged)g(b)q(ecause)h(the)f(phase)g(will)262 2350 y(remain)12 b(una\013ected.)p 262 2411 573 2 v 308 2437 a Fj(1)325 2449 y Fi(b)q(ecause)e(of)h(pa)o(wn)g(promotions)957 2574 y Fp(46)p eop %%Page: 47 49 47 48 bop 262 307 a Fr(4.3)69 b(General)22 b(P)n(ositional)g(Ev)l(aluation) 262 442 y Fu(4.3.1)55 b(De\014nition)17 b(3)i(:)24 b(Mobilit)n(y)262 554 y Fp(Mobilit)o(y)8 b(is)i(the)h(degree)g(of)f(piece)h(freedom)e(in)h(a)g (giv)o(en)g(p)q(osition.)16 b(Study)10 b(has)g(sho)o(wn)h(that)262 604 y(there)k(is)g(a)f(clear)h(di\013erence)i(b)q(et)o(w)o(een)f(the)f (mobilit)o(y)c(of)j(the)h(winning)f(and)g(losing)g(sides)262 654 y(as)i(the)i(game)d(progresses.)28 b(This)17 b(is)g(to)f(b)q(e)h(exp)q (ected)i(when)e(one)g(side)g(has)g(a)g(material)262 703 y(adv)n(an)o(tage.)23 b(Ho)o(w)o(ev)o(er,)16 b(it)f(has)h(also)g(b)q(een)h(found)e(that)h(the)g (side)h(whic)o(h)e(can)h(main)o(tain)262 753 y(the)e(highest)g(mobilit)o(y)d (is)j(the)g(side)g(most)f(lik)o(ely)g(to)g(win)h(the)g(game)f([27)o(].)324 838 y(This)e(sho)o(ws)h(that)f(maximi)o(sing)d(mobilit)o(y)h(is)i(an)g (excellen)o(t)i(heuristic.)18 b(In)11 b(fact,)g(Slater)262 888 y([59)o(])e(is)g(of)g(the)i(opinion)d(that)i(mobilit)o(y)c(in)j(itself)h (is)f(a)h(su\016cien)o(t)g(measure)f(of)h(all)e(the)i(factors)262 938 y(suggested)15 b(b)o(y)f(Shannon)h([53)o(].)k(I)14 b(also)g(consider)h (mobilit)o(y)c(to)j(b)q(e)h(an)f(imp)q(ortan)o(t)f(factor,)262 988 y(although)f(I)i(do)g(think)g(man)o(y)e(other)i(heuristics)h(are)f(also)g 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y(and)i(clearly)h(sho)o(ws)h(mobilit)o(y)c(should)j(b)q(e)h(one)f(of)g(the)g (ma)r(jor)f(terms)h(in)f(an)o(y)h(ev)n(aluation)262 1472 y(function.)324 1557 y(Normally)m(,)c(mobilit)o(y)g(is)j(tak)o(en)h(as)g(the)g(n)o(um)o(b)q (er)e(of)h(legal)g(or)g(pseudo{legal)g(mo)o(v)o(es.)k(I)262 1607 y(will)12 b(tak)o(e)i(a)f(sligh)o(tly)g(di\013eren)o(t)i(view)f(and)f (use)i(the)f(follo)o(wing)e(de\014nition)h(of)h(mobilit)o(y)o(:)344 1737 y Fh(M)5 b(B)420 1743 y Fe(col)476 1737 y Fp(=)520 1706 y Fc(P)564 1716 y Fk(64)564 1749 y Fe(sq)q Fk(=1)640 1737 y Fp(\()p Fh(A)687 1743 y Fe(col;sq)782 1737 y Fp(+)k Fh(P)850 1743 y Fe(col;sq)936 1737 y Fp(\))344 1840 y Fl(where)380 1890 y Fh(A)411 1896 y Fe(col;sq)510 1890 y Fp(:)47 b Fh(])p Fp(A)o(ttac)o(ks\([P) o(a)o(wn,Knigh)o(t,Bishop,Ro)q(ok],)o(col,sq\))380 1989 y Fh(P)407 1995 y Fe(col;sq)506 1989 y Fp(:)k Fl(if)12 b Fp(\(Occup)o(y\([P)o(a)o (wn],col,sq\)\))628 2039 y Fh(])p Fp(Mo)o(v)o(es\([P)o(a)o(wn],col,sq\))569 2089 y Fl(else)628 2139 y Fp(0)569 2188 y Fl(endif)262 2300 y Fp(The)19 b(mobilit)o(y)e(of)i(the)h(king)e(is)h(not)h(included)f(in)g (this)h(de\014nition)f(b)q(ecause)i(I)e(do)h(not)262 2350 y(consider)f(a)g (kings)g(mobilit)o(y)d(mak)o(es)i(an)o(y)g(meaningful)f(con)o(tribution)h(to) h(a)g(successful)262 2399 y(strategy)m(.)33 b(The)20 b(king)e(m)o(ust)g(b)q (e)i(protected)h(in)e(the)g(op)q(ening)g(and)g(middle)e(game.)33 b(In)262 2449 y(the)15 b(ending)h(it)f(should)g(b)q(e)h(used)g(activ)o(ely)m (.)21 b(Ho)o(w)o(ev)o(er,)16 b(its)f(mobilit)o(y)e(should)i(neither)h(b)q(e) 957 2574 y(47)p eop %%Page: 48 50 48 49 bop 262 307 a Fp(minim)o(i)o(sed)12 b(nor)h(maxim)o(ised.)i(The)f (queens)h(mobilit)o(y)10 b(is)j(also)g(not)g(included)g(although)g(a)262 357 y(sp)q(ecialised)j(queen)i(mobilit)o(y)13 b(function)j(is)g(included)g (in)g(de\014nition)g(27,)f(Queen)j(P)o(o)o(w)o(er.)262 407 y(Other)13 b(non-pa)o(wn)f(pieces)i(are)f(giv)o(en)f(a)g(b)q(on)o(us)h(for)f (eac)o(h)h(square)g(they)g(attac)o(k,)g(including)262 457 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a Fp(piece)13 b(t)o(wice)h(in)e(the)i(op)q(ening)e(b)q (efore)i(dev)o(elopmen)o(t)e(is)h(complete.)k(Where)d(the)f(undev)o(el-)262 357 y(op)q(ed)h(pieces)h(should)f(b)q(e)g(dev)o(elop)q(ed)h(to)e(is)h (de\014ned)h(b)o(y)f(other)g(ev)n(aluation)f(criteria.)324 442 y(The)e(queen)g(is)f(discouraged)h(from)e(mo)o(ving)f(b)q(efore)j(at)g (least)f(3)g(minor)f(pieces)j(\(knigh)o(ts)262 492 y(and)k(bishops\))i(are)f (dev)o(elop)q(ed.)28 b(This)17 b(is)g(an)f(attempt)h(to)g(a)o(v)o(oid)e(p)q (ositions)i(where)h(the)262 542 y(program's)11 b(queen)k(is)e(dev)o(elop)q (ed)h(to)q(o)g(early)m(,)e(allo)o(wing)f(the)j(opp)q(onen)o(t)g(to)g(gain)e (a)h(temp)q(o)262 592 y(b)o(y)d(pla)o(ying)f(a)i(dev)o(eloping)f(mo)o(v)o(e)f (attac)o(king)h(the)i(queen.)18 b(Applying)10 b(these)i(Dev)o(elopmen)o(t)262 641 y(criteria)i(to)f(the)i(p)q(osition)e(in)h(\014gure)g(4.2)f(giv)o(es:)344 738 y Fh(D)q(V)403 744 y Fe(W)t(hite)533 738 y Fp(=)h(14)9 b Ff(\000)h Fp(4)f Ff(\000)g Fp(7)g Ff(\000)h Fp(7)h(=)h Ff(\000)p Fp(4)344 788 y Fh(D)q(V)403 794 y Fe(B)q(lack)533 788 y Fp(=)i(14)9 b Ff(\000)h Fp(0)f Ff(\000)g Fp(0)g Ff(\000)h Fp(0)h(=)h(14)262 940 y Fu(4.3.3)55 b(De\014nition)17 b(5)i(:)24 b(Cen)n(tre)19 b(Con)n(trol)262 1052 y Fp(The)g(imp)q(ortance)g(of)f(con)o(trolling)g(the)i (cen)o(tre)h(of)e(the)h(b)q(oard)f(cannot)h(b)q(e)g(to)q(o)f(highly)262 1102 y(stressed.)37 b(A)19 b(clear)h(connection)g(b)q(et)o(w)o(een)h(winning) e(the)h(game)e(and)h(con)o(trolling)f(the)262 1151 y(cen)o(tre)f(has)g(b)q (een)g(established)g(in)f([27)o(].)25 b(Ho)o(w)o(ev)o(er,)16 b(this)h(will)d(come)i(as)g(no)g(surprise)i(to)262 1201 y(an)o(y)13 b(strong)h(c)o(hess)i(pla)o(y)o(ers.)324 1286 y(The)g(cen)o(tre)i(is)e(con)o (trolled)f(b)o(y)h(b)q(oth)g(o)q(ccupation)g(and)g(attac)o(k)g(of)g(cen)o (tral)g(squares.)262 1336 y(Therefore)j(m)o(y)e(cen)o(tre)j(con)o(trol)e(ev)n (aluation)f(criteria)i(m)o(ust)f(detect)i(suc)o(h)f(factors)g(and)262 1386 y(encourage)14 b(their)h(ac)o(hiev)o(emen)o(t.)p 641 1480 673 5 v 641 2144 5 665 v 646 1563 a Fg(0Z0Z0Z0Z)646 1646 y(Z0Z0Z0Z0)646 1729 y(0Z0Z0Z0Z)646 1812 y(Z0Z0Z0Z0)646 1895 y(0Z0Z0Z0Z)646 1978 y(Z0Z0Z0Z0)646 2061 y(0Z0Z0Z0Z)646 2144 y(Z0Z0Z0Z0)p 1310 2144 V 641 2148 673 5 v 687 1539 a Fl(1)58 b(1)h(1)g(1)f(1)h(1)g(1)f(1)687 1622 y(1)g(2)h(2)g(2)f(2)h(2)g(2)f(1)687 1705 y(1)g(2)h(4)g(4)f(4)h(4)g(2)f (1)687 1788 y(1)g(2)h(4)g(8)f(8)h(4)g(2)f(1)687 1871 y(1)g(2)h(4)g(8)f(8)h(4) g(2)f(1)687 1954 y(1)g(2)h(4)g(4)f(4)h(4)g(2)f(1)687 2037 y(1)g(2)h(2)g(2)f (2)h(2)g(2)f(1)687 2120 y(1)g(1)h(1)g(1)f(1)h(1)g(1)f(1)617 2246 y Fp(Figure)14 b(4.3:)j(Cen)o(tre)e(Con)o(trol)e(b)q(on)o(us)h(table.) 344 2396 y Fh(C)s(C)407 2402 y Fe(col)462 2396 y Fp(=)506 2365 y Fc(P)550 2375 y Fk(64)550 2409 y Fe(sq)q Fk(=1)633 2396 y Fh(V)657 2402 y Fe(sq)691 2396 y Ff(\001)o Fp(\()p Fh(A)749 2402 y Fe(col;sq)845 2396 y Fp(+)9 b Fh(O)918 2402 y Fe(col;sq)1013 2396 y Fp(+)g Fh(P)1081 2402 y Fe(col;sq)1167 2396 y Fp(\))957 2574 y(50)p eop %%Page: 51 53 51 52 bop 344 307 a Fl(where)380 357 y Fh(V)404 363 y Fe(sq)452 357 y Fp(:)105 b(Cen)o(tre)15 b(Con)o(trol)e(b)q(on)o(us)h(table,)f(indexed)i (b)o(y)e(sq.)19 b(See)14 b(\014gure)h(4.3.)380 457 y Fh(A)411 463 y Fe(col;sq)510 457 y Fp(:)47 b Fh(])p Fp(A)o(ttac)o(ks\([An)o (y],col,sq\))380 556 y Fh(O)412 562 y Fe(col;sq)511 556 y Fp(:)f Fl(if)12 b Fp(\(Occup)o(y\([Knigh)o(t],col,sq\)\))628 606 y(1)569 656 y Fl(else)628 706 y Fp(0)569 756 y Fl(endif)380 855 y Fh(P)407 861 y Fe(col;sq)506 855 y Fp(:)51 b Fl(if)12 b Fp(\(A)o(ttac)o(k)o(ed\([P)o (a)o(wn],col,sq\)\))628 905 y(1)569 955 y Fl(else)628 1005 y Fp(0)569 1054 y Fl(endif)262 1181 y Fp(Pieces)i(are)g(giv)o(en)f(b)q(on)o (uses)h(for)f(attac)o(king)g(cen)o(tral)g(squares.)19 b(The)14 b(b)q(on)o(us)g(is)f(dep)q(enden)o(t)262 1231 y(on)k(ho)o(w)f(close)i(the)g (square)g(is)f(to)g(the)h(cen)o(tre.)29 b(P)o(a)o(wn)17 b(attac)o(ks)h (receiv)o(e)g(an)f(additional)262 1281 y(b)q(on)o(us)f(to)h(re\015ect)h(the)g (imp)q(ortance)e(of)g(suc)o(h)h(attac)o(ks.)27 b(Occupation)17 b(of)f(the)i(cen)o(tre)g(b)o(y)262 1331 y(knigh)o(ts)12 b(is)g(of)g (particular)h(imp)q(ortance.)k(A)c(knigh)o(t)e(has)i(a)g(relativ)o(ely)f (short)h(range,)g(more)262 1380 y(than)d(an)o(y)h(other)g(piece)h(it)e(needs) i(to)f(b)q(e)g(close)g(to)g(the)g(\014eld)g(of)f(action.)17 b(A)11 b(cen)o(trally)f(placed)262 1430 y(knigh)o(t)j(is)g(b)q(est)i(able)f (to)f(exert)i(pressure)h(o)o(v)o(er)e(most)f(of)g(the)h(b)q(oard.)19 b(Therefore,)14 b(cen)o(tral)262 1480 y(o)q(ccupation)g(b)o(y)f(knigh)o(ts)h (receiv)o(es)h(a)f(sp)q(ecial)g(b)q(on)o(us.)324 1565 y(I)e(b)q(eliev)o(e)i (that)e(cen)o(tre)j(con)o(trol)d(is)h(imp)q(ortan)o(t)e(throughout)h(the)i (game,)d(although)h(its)262 1615 y(imp)q(ortance)d(should)i(diminish)d(as)j (the)g(game)e(progresses.)19 b(This)10 b(function)h(will)e(naturally)262 1665 y(pla)o(y)f(a)i(less)g(prominen)o(t)e(role)i(as)g(pieces)h(are)f(exc)o (hanged)g(b)q(ecause)i(of)d(the)h(reduced)h(n)o(um)o(b)q(er)262 1715 y(of)j(attac)o(ks)h(and)g(p)q(ossible)g(squares)i(o)q(ccupied.)22 b(Therefore,)16 b(no)f(phase)h(adjustmen)o(t)e(w)o(as)262 1765 y(felt)f(necessary)m(.)324 1850 y(Applied)e(to)g(the)h(p)q(osition)e(in)h (\014gure)g(4.2,)g(the)g(Cen)o(tre)i(Con)o(trol)d(criteria)i(will)d(pro)q (duce)262 1900 y(the)14 b(follo)o(wing)d(v)n(alues:)344 1997 y Fh(C)s(C)407 2003 y Fe(W)t(hite)533 1997 y Fp(=)j(169)344 2047 y Fh(C)s(C)407 2053 y Fe(B)q(lack)533 2047 y Fp(=)g(183)957 2574 y(51)p eop %%Page: 52 54 52 53 bop 262 307 a Fu(4.3.4)55 b(De\014nition)17 b(6)i(:)24 b(Square)19 b(Con)n(trol)262 419 y Fp(During)8 b(the)i(game)e(it)h(is)g(imp)q (ortan)o(t)f(to)h(ac)o(hiev)o(e)h(a)f(balance)g(b)q(et)o(w)o(een)i(attac)o(k) e(and)h(defence.)262 469 y(As)k(the)h(game)e(progresses)j(this)e(balance)h (ma)o(y)d(shift)i(a)g(n)o(um)o(b)q(er)g(of)f(times)h(from)e(defence)262 519 y(to)k(attac)o(k)h(and)g(visa{v)o(ersa.)28 b(Square)17 b(con)o(trol)g(can)g(pro)o(vide)g(a)g(metho)q(d)f(of)h(measuring)262 569 y(the)d(exten)o(t)h(to)f(whic)o(h)f(the)i(program)d(is)i(attac)o(king)f (or)h(defending.)324 654 y(W)m(e)i(can)h(de\014ne)h(attac)o(k)f(as)g(the)g(n) o(um)o(b)q(er)g(of)f(squares)i(attac)o(k)o(ed)f(in)f(the)i(opp)q(onen)o(ts) 262 704 y(half)12 b(of)h(the)h(b)q(oard.)k(Defence)d(can)f(b)q(e)g(de\014ned) h(as)e(the)i(n)o(um)o(b)q(er)d(of)h(squares)i(attac)o(k)o(ed)f(in)262 754 y(ones)g(o)o(wn)f(half)g(of)h(the)g(b)q(oard.)324 839 y(A)j(comparison)f (b)q(et)o(w)o(een)i(suc)o(h)g(attac)o(k)f(and)g(defence)i(for)e(b)q(oth)g(ev) o(en)o(tual)g(winners)262 889 y(and)e(losers)i(is)f(made)f(in)g([27)o(].)24 b(Analysing)15 b(the)i(results)g(obtained)f(it)f(can)i(b)q(e)f(seen)i(that) 262 938 y(throughout)c(the)h(game)f(the)h(winners)g(and)g(losers)g(main)o (tain)d(appro)o(ximately)g(the)j(same)262 988 y(n)o(um)o(b)q(er)c(of)g (squares)i(defended.)18 b(Ho)o(w)o(ev)o(er,)12 b(there)i(is)d(a)h(clear)g (di\013erence)i(in)d(the)h(attac)o(k)o(ed)262 1038 y(squares)j(b)q(et)o(w)o 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d(planning)i(phase)h(to)g(b)q(e)g(used.)33 b(A)19 b(planning)e(phase)j(could) e(use)i(this)262 1760 y(function)13 b(to)h(go)q(o)q(d)g(e\013ect)h(b)o(y)f (iden)o(tifying)f(a)g(basic)h(plan,)f(lik)o(e)h(a)f(king)g(side)i(attac)o(k.) j(The)262 1810 y(table)12 b(could)h(then)g(b)q(e)h(pre-loaded)f(with)f(v)n (alues)g(whic)o(h)h(w)o(ould)f(encourage)i(the)f(program)262 1860 y(to)g(attac)o(k)h(certain)h(squares)g(on)e(the)i(king)e(side,)h(for)f (example.)324 1945 y(Applying)g(this)h(Square)g(Con)o(trol)f(criterion)h(to)g (the)h(p)q(osition)e(in)g(\014gure)i(4.2)e(giv)o(es:)344 2042 y Fh(S)r(C)401 2048 y Fe(W)t(hite)533 2042 y Fp(=)h(74)344 2092 y Fh(S)r(C)401 2098 y Fe(B)q(lack)533 2092 y Fp(=)g(62)957 2574 y(52)p eop %%Page: 53 55 53 54 bop 262 307 a Fr(4.4)69 b(P)n(a)n(wn)23 b(Ev)l(aluation)262 434 y Fp(P)o(a)o(wns)15 b(pro)o(vide)g(the)h(basic)g(framew)o(ork)d(around)j (whic)o(h)f(the)h(game)e(will)g(dev)o(elop.)22 b(The)262 483 y(correct)15 b(handling)e(of)g(the)i(pa)o(wn)e(structure)j(is)e(vital)f(in)g (high)g(lev)o(el)h(c)o(hess.)365 599 y("P)o(a)o(wns)g(are)g(the)h(Soul)e(of)g (Chess")838 665 y Fm(Philidor)262 781 y Fp(I)i(b)q(eliev)o(e)g(this)h(is)f (the)h(one)f(area)h(whic)o(h)f(ab)q(o)o(v)o(e)g(all)f(others)i(is)g(most)e (neglected)i(in)f(c)o(hess)262 831 y(programs.)h(The)11 b(problem)g(is)g (that)h(w)o(eak)f(pa)o(wns)h(do)f(not)g(usually)g(cause)i(an)o(y)e(imm)o (ediate)262 881 y(deterioration)k(in)g(the)i(o)o(v)o(erall)d(p)q(osition.)22 b(Ho)o(w)o(ev)o(er,)16 b(o)o(v)o(er)g(a)f(longer)h(term,)e(p)q(erhaps)j(30) 262 931 y(or)12 b(40)h(plies,)f(the)i(existence)g(of)f(w)o(eak)g(pa)o(wns)f (causes)j(n)o(umerous)d(p)q(ositional)g(w)o(eaknesses)262 981 y(e.g.)17 b(w)o(eak)12 b(squares,)h(space)g(to)f(blo)q(c)o(k)n(ade,)f (isolation)f(etc.)19 b(Often)12 b(a)g(game's)f(result)h(hinges)262 1030 y(on)h(the)i(strength)g(or)f(w)o(eakness)h(of)e(the)h(underlying)g(pa)o (wn)f(structure.)324 1116 y(It)e(is)g(notable)g(in)f(a)h(recen)o(t)i([27)o (],)d(relativ)o(ely)h(large)f(study)i(of)e(ev)n(aluation)g(criteria,)i(that) 262 1165 y(there)j(w)o(as)e(no)h(sp)q(eci\014c)h(atten)o(tion)e(giv)o(en)g (to)h(pa)o(wn)f(ev)n(aluation.)k(I)c(feel)h(this)g(is)f(a)h(serious)262 1215 y(omission.)324 1300 y(My)e(pa)o(wn)g(ev)n(aluation)e(criteria)j(will)d (b)q(e)j(amongst)e(the)h(most)f(complex)g(and)h(compre-)262 1350 y(hensiv)o(e)i(of)f(the)h(whole)f(ev)n(aluation)f(function.)18 b(I)13 b(feel)h(this)g(is)f(critical)g(to)h(o)o(v)o(erall)e(success)262 1400 y(b)q(ecause)j(man)o(y)c(of)i(the)i(e\013ects)g(caused)g(b)o(y)e(bad)h (pa)o(wn)f(pla)o(y)f(cannot)i(b)q(e)g(determined)g(b)o(y)262 1450 y(searc)o(h.)19 b(Therefore,)14 b(heuristics)h(m)o(ust)e(\014ll)g(this)h (gap.)324 1535 y(I)19 b(will)f(split)h(the)h(pa)o(wn)f(ev)n(aluation)f (criteria)i(up)f(so)g(they)h(can)g(b)q(e)g(dealt)f(with)g(in)262 1585 y(su\016cien)o(t)14 b(detail.)262 1736 y Fu(4.4.1)55 b(De\014nition)17 b(7)i(:)24 b(Doubled)19 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b(b)o(y)f(\014le)g(f)f(\(1)h(to)g(8\).)957 2574 y(53)p eop %%Page: 54 56 54 55 bop 262 307 a Fp(Doubled)13 b(pa)o(wns)h(are)g(p)q(enalised,)g(the)g (size)h(of)e(the)h(p)q(enalt)o(y)g(dep)q(ends)h(on)f(the)g(\014le.)k(Dou-)262 357 y(bled)e(pa)o(wns)g(are)g(w)o(orse)h(on)f(a)g(cen)o(tre)h(\014le)f(than)g (on)g(the)h(\015ank,)f(not)g(b)q(ecause)i(they)e(are)262 407 y(considered)c(an)o(y)e(w)o(eak)o(er,)i(but)f(b)q(ecause)i(they)e(hinder)g (in)o(ter{piece)h(comm)o(unication.)i(Of-)262 457 y(ten)f(there)i(are)f(comp) q(ensations)e(for)h(doubled)g(pa)o(wns,)g(suc)o(h)h(as)f(op)q(en)h(\014les,)f (extra)h(cen)o(tre)262 506 y(con)o(trol)i(and)h(square)h(protection,)g(for)f (example.)26 b(Ho)o(w)o(ev)o(er,)18 b(these)g(asp)q(ects)h(are)f(dealt)262 556 y(with)13 b(b)o(y)h(other)g(ev)n(aluation)f(criteria.)324 641 y(This)d(criterion)g(tak)o(es)h(a)f(simplistic)e(view)i(of)g(the)g(p)q (enalties)h(asso)q(ciated)g(with)f(doubled)262 691 y(pa)o(wns)j(b)o(y)g 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b(idea)f(of)g(this)h(de\014nition)g(is)f(to)h(pic)o(k)f(up)h(as)g(man)o(y)e (cases)j(of)e(w)o(eak)262 357 y(pa)o(wns)i(as)h(p)q(ossible)h(in)e(one)h (general)g(set)h(of)e(criteria.)31 b(Therefore)19 b(isolated,)f(doubled,)262 407 y(bac)o(kw)o(ard)13 b(and)h(pa)o(wn)g(c)o(hain)f(bases)i(ma)o(y)d(all)h (b)q(e)h(p)q(enalised)g(for)g(w)o(eakness.)324 492 y(In)i("My)f(System")g ([43)o(],)g(Aron)h(Nimzo)o(witsc)o(h)f(giv)o(es)g(the)h(follo)o(wing)e(c)o (hess)j(strategy)262 542 y(for)9 b(handling)g(pa)o(wn)h(c)o(hains,)g("W)m(e)g (\014rst)g(direct)h(our)f(op)q(erations)h(against)e(the)i(base,)g(whic)o(h) 262 592 y(w)o(e)17 b(attac)o(k)g(with)f(a)h(pa)o(wn,)g(and)f(b)o(y)h(threats) h(or)f(otherwise,)h(seek)g(to)f(cut)h(o\013)e(the)i(base)262 641 y(from)13 b(its)j(asso)q(ciates)g(in)f(the)h(c)o(hain.)23 b(This)15 b(done,)h(w)o(e)g(turn)g(our)f(atten)o(tion)h(to)f(the)h(next)262 691 y(opp)q(onen)o(t,)d(namely)f(the)i(link)e(whic)o(h)h(has)h(no)o(w)f(b)q (ecome)g(the)h(new)g(base".)k(This)13 b(metho)q(d)262 741 y(of)18 b(handling)g(pa)o(wn)h(c)o(hains)h(will)e(b)q(e)i(encouraged)g(b)o(y)f(this)h (de\014nition)f(b)q(ecause)i(w)o(eak)262 791 y(pa)o(wn)11 b(bases)i(are)f (iden)o(ti\014ed)g(and)f(progressiv)o(ely)h(p)q(enalised,)g(therefore)h (encouraging)f(the)262 841 y(attac)o(king)h(side)h(to)g(build)f(up)h (pressure)i(on)e(the)g(w)o(eak)g(pa)o(wn.)344 943 y Fh(W)6 b(P)416 949 y Fe(col)471 943 y Fp(=)515 912 y Fc(P)559 922 y Fk(64)559 955 y Fe(sq)q Fk(=1)642 943 y Fh(W)g(K)722 949 y Fe(col;sq)344 1046 y Fl(where)380 1095 y Fh(W)g(K)460 1101 y Fe(col;sq)559 1095 y Fp(:)j Fl(if)k Fp(\(Occup)o(y\([P)o(a)o(wn],col,sq\))g Fl(and)g Fp(W)m(eak\(col,sq\)\))639 1145 y Fh(W)6 b(K)719 1151 y Fe(col;sq)817 1145 y Fp(=)12 b Fh(W)900 1151 y Fe(col;sq)995 1145 y Ff(\000)d Fp(10)g Ff(\001)g Fh(])p Fp(A)o(ttac)o(ks\([P)o(a)o (wn],Opp\(col\),)p Fh(sq)1625 1151 y Fe(inf)s(r)q(ont)1744 1145 y Fp(\))639 1195 y Fl(if)k Fp(\(SemiOp)q(en\(Opp\(col\),OnFile\(sq\)\)) 639 1245 y Fl(and)h Fp(Has\([Ro)q(ok,Queen],Opp\(col\)\)\))699 1295 y Fh(W)6 b(K)779 1301 y Fe(col;sq)876 1295 y Fp(=)12 b Fh(W)6 b(K)1000 1301 y Fe(col;sq)1086 1295 y Ff(\000)14 b Fp(phase/2)639 1345 y Fl(endif)639 1394 y(if)f Fp(\(A)o(ttac)o(k)o(ed\([Ro)q (ok],Opp\(col\),sq\)\))699 1444 y Fh(W)6 b(K)779 1450 y Fe(col;sq)876 1444 y Fp(=)12 b Fh(W)6 b(K)1000 1450 y Fe(col;sq)1095 1444 y Ff(\000)k Fp(4)639 1494 y Fl(endif)639 1544 y(if)j Fp(\(Occup)o(y\([An)o (y],Opp\(col\),)p Fh(sq)1170 1550 y Fe(inf)s(r)q(ont)1290 1544 y Fp(\)\))699 1594 y Fh(W)6 b(K)779 1600 y Fe(col;sq)876 1594 y Fp(=)12 b Fh(W)6 b(K)1000 1600 y Fe(col;sq)1095 1594 y Ff(\000)k Fp(8)639 1643 y Fl(endif)580 1693 y(else)639 1743 y Fh(W)c(K)719 1749 y Fe(col;sq)817 1743 y Fp(=)12 b(0)580 1793 y Fl(endif)380 1892 y Fh(W)419 1898 y Fe(col;sq)518 1892 y Fp(:)50 b(di\013)14 b(=)g Fh(])p Fp(Di\013A)o(ttac)o(ks\(Opp\(col\),sq\))580 1942 y Fl(if)f Fp(\(di\013)h Fh(>)g Fp(0\))639 1992 y Fl(if)f Fp(\(di\013)h Fh(<)g Fp(5\))699 2042 y Fh(W)738 2048 y Fe(col;sq)835 2042 y Fp(=)g([)p Ff(\000)p Fp(10)p Fh(;)7 b Ff(\000)p Fp(18)p Fh(;)g Ff(\000)p Fp(26)p Fh(;)g Ff(\000)p Fp(32])758 2092 y(Indexed)14 b(b)o(y)g(di\013)g(\(1)f(to)h(4\).)639 2142 y Fl(else)699 2191 y Fh(W)738 2197 y Fe(col;sq)835 2191 y Fp(=)e Ff(\000)p Fp(35)639 2241 y Fl(endif)580 2291 y(else)639 2341 y Fh(W)678 2347 y Fe(col;sq)776 2341 y Fp(=)g Ff(\000)p Fp(4)580 2391 y Fl(endif)957 2574 y Fp(55)p eop %%Page: 56 58 56 57 bop 262 307 a Fp(W)m(eak)10 b(pa)o(wns)h(are)g(p)q(enalised)g(for)g (the)g(sev)o(erit)o(y)g(of)g(the)g(attac)o(k)g(up)q(on)g(them.)16 b(A)11 b(p)q(enalt)o(y)g(is)262 357 y(levied)h(when)g(a)g(w)o(eak)g(pa)o(wn)g (is)g(on)g(a)g(semi-op)q(en)g(\014le)g(and)g(the)h(opp)q(onen)o(t)f(has)h (the)f(pieces)262 407 y(to)j(tak)o(e)g(adv)n(an)o(tage)g(of)g(this)g(w)o (eakness.)24 b(A)15 b(w)o(eak)h(pa)o(wn)f(whose)h(adv)n(ance)f(is)h (restricted)262 457 y(b)o(y)d(enem)o(y)g(pa)o(wn)h(attac)o(ks)g(is)g(further) h(p)q(enalised.)324 542 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Fl(else)734 1758 y Fp(0)675 1808 y Fl(endif)262 1934 y Fp(Eac)o(h)18 b(ro)q(ok)g(is)g(p)q (enalised)g(for)g(its)g(distance)h(from)d(the)j(enem)o(y)e(king.)30 b(A)18 b(ro)q(ok)g(on)g(the)262 1984 y(same)13 b(\014le)h(\(or)g(rank\))g(as) g(the)g(enem)o(y)g(king)f(w)o(ould)g(not)h(receiv)o(e)h(an)o(y)f(p)q(enalt)o (y)g(no)f(matter)262 2034 y(what)j(the)g(corresp)q(onding)h(rank)g(\(or)f (\014le\))g(distance)h(is.)25 b(An)o(y)16 b(p)q(enalties)h(giv)o(en)e(will)g (b)q(e)262 2084 y(directly)e(related)i(to)e(the)h(minim)n(um)c(rank)j(or)h (\014le)f(distance.)19 b(This)14 b(a)o(v)o(oids)e(the)i(pitfall)e(of)262 2134 y(encouraging)k(a)g(ro)q(ok)g(to)g(mak)o(e)f(w)o(eak)h(mo)o(v)o(es)f(in) h(order)h(to)f(attain)f(the)i(b)q(est)h(rank)e Fm(and)262 2183 y Fp(\014le)d(distance.)18 b(F)m(or)13 b(example,)f(in)h(\014gure)h(4.6,)e (this)h(criterion)h(w)o(ould)e Fl(not)h Fp(encourage)h(the)262 2233 y(mo)o(v)o(es)e(Rh4-h5)h(or)h(Rg3-g4,)e(ho)o(w)o(ev)o(er,)h(it)h Fl(w)o(ould)e Fp(encourage)j(the)f(mo)o(v)o(e)f(Rg3-h3.)957 2574 y(66)p eop %%Page: 67 69 67 68 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(0ZrZ0Zna)646 482 y(ZbZ0ZpZk)646 565 y(pZ0o0o0o)646 648 y(ZpZ0sPZ0)646 731 y(0Z0Z0M0S)646 814 y(ZNZBZ0S0)646 897 y(qZPL0ZPO)646 980 y(Z0Z0Z0J0)p 1310 980 V 641 984 673 5 v 275 1102 a Fp(Figure)14 b(4.6:)j(Illustration)c (of)g(the)i(Ro)q(ok{King)d(Closeness)j(Heuristic,)f(White)g(to)g(Pla)o(y)m(.) 262 1254 y Fu(4.7.2)55 b(De\014nition)17 b(22)i(:)24 b(Connected)19 b(Ro)r(oks)344 1420 y Fh(C)s(R)409 1426 y Fe(col)464 1420 y Fp(=)508 1389 y Fc(P)551 1400 y Fk(64)551 1433 y Fe(sq)q Fk(=1)675 1420 y Fl(if)13 b Fp(\(Occup)o(y\([Ro)q(ok],col,sq\))f Fl(and)h Fp(A)o(ttac)o(k)o(ed\([Ro)q(ok],col,sq\)\))734 1473 y(3)675 1523 y Fl(else)734 1573 y Fp(0)675 1623 y Fl(endif)262 1750 y Fp(Ro)q(oks)j(are)h(said)f(to)h(b)q(e)g(connected)i(if)c(they)j(defend)f (eac)o(h)g(other.)27 b(Ro)q(oks)17 b(are)g(giv)o(en)f(a)262 1799 y(b)q(on)o(us)g(for)h(b)q(eing)f(connected.)29 b(This)16 b(encourages)i(ro)q(oks)f(to)f(double)h(up)g(on)f(op)q(en)h(\014les)262 1849 y(and)12 b(w)o(eak)h(p)q(oin)o(ts.)18 b(Connected)c(ro)q(oks)f(are)g (also)g(self)f(supp)q(orting)i(whic)o(h)e(div)o(ersi\014es)i(the)262 1899 y(options)f(a)o(v)n(ailable.)957 2574 y(67)p eop %%Page: 68 70 68 69 bop 262 307 a Fu(4.7.3)55 b(De\014nition)17 b(23)i(:)24 b(Ro)r(ok)18 b(on)h(Op)r(en)f(File)344 403 y Fh(RO)408 409 y Fe(col)463 403 y Fp(=)507 372 y Fc(P)551 382 y Fk(64)551 415 y Fe(sq)q Fk(=1)675 403 y Fl(if)13 b Fp(\(Occup)o(y\([Ro)q (ok],col,sq\)\))734 456 y Fl(if)g Fp(\(Op)q(en\(OnFile\(sq\)\)\))793 506 y(14)734 556 y Fl(else)793 605 y(if)g Fp(\(SemiOp)q (en\(col,OnFile\(sq\)\)\))852 655 y(6)793 705 y Fl(else)852 755 y Fp(0)793 805 y Fl(endif)734 854 y(endif)675 904 y(else)734 954 y Fp(0)675 1004 y Fl(endif)262 1119 y Fp(A)h(\014le)h(is)g(op)q(en)g(if)e (no)i(pa)o(wns)g(of)f(an)o(y)g(colour)g(exist)h(on)g(the)g(\014le.)21 b(A)14 b(\014le)h(is)g(semi{op)q(en)e(if)262 1168 y(only)e(enem)o(y)h(pa)o (wns)h(exist)g(on)f(the)i(\014le.)j(Ro)q(oks)12 b(receiv)o(e)i(a)f(b)q(on)o (us)f(for)h(b)q(eing)f(on)h(an)f(op)q(en)262 1218 y(\014le.)18 b(Con)o(trol)13 b(of)g(the)i(op)q(en)f(\014le)g(is)g(vital)f(in)h(order)g(to) g(b)q(e)h(able)e(to)h(ev)o(en)o(tually)g(p)q(enetrate)262 1268 y(to)k(the)i(7th)e(and)h(8th)g(ranks.)33 b(Ev)o(en)19 b(if)f(the)h(opp)q (onen)o(t)g(has)g(con)o(trol)g(of)f(the)i(\014le)e(it)h(is)262 1318 y(imp)q(ortan)o(t)12 b(to)h(rew)o(ard)i(attempts)e(whic)o(h)h(c)o (hallenge)g(this)g(con)o(trol.)324 1403 y(This)d(heuristic)g(has)h(the)f (added)h(b)q(ene\014t)g(of)e(encouraging)h(the)h(program)d(to)i(op)q(en)g (\014les)262 1453 y(whic)o(h)i(it)h(can)g(con)o(trol)g(and)f(k)o(eep)i (closed)f(those)h(whic)o(h)f(w)o(ould)f(b)q(ene\014t)i(the)f(opp)q(onen)o(t.) 324 1538 y(A)k(ro)q(ok)g(is)g(also)f(rew)o(arded)j(for)d(b)q(eing)h(on)g(a)g (semi{op)q(en)f(\014le.)31 b(The)19 b(enem)o(y)e(pa)o(wn)262 1588 y(whic)o(h)12 b(mak)o(es)g(the)h(\014le)f(semi{op)q(en)g(is)h(an)f(ob)o (vious)g(w)o(eak)h(p)q(oin)o(t)f(to)g(c)o(hallenge)h(with)f(ones)262 1638 y(o)o(wn)f(pa)o(wns.)18 b(In)12 b(this)g(w)o(a)o(y)f(the)i(opp)q(onen)o (t)f(can)h(b)q(e)f(put)h(on)f(the)g(defensiv)o(e)h(and)f(attempts)262 1688 y(can)f(b)q(e)h(made)e(to)h(build)f(up)i(pressure)h(or)e(fully)f(op)q (en)i(the)g(\014le)f(at)g(an)g(opp)q(ortune)h(momen)o(t.)262 1837 y Fu(4.7.4)55 b(De\014nition)17 b(24)i(:)24 b(Ro)r(ok)18 b(on)h(Sev)n(en)n(th)f(Rank)344 1933 y Fh(RS)401 1939 y Fe(col)457 1933 y Fp(=)501 1902 y Fc(P)545 1912 y Fk(64)545 1945 y Fe(sq)q Fk(=1)675 1933 y Fl(if)13 b Fp(\(Occup)o(y\([Ro)q(ok],col,sq\))f Fl(and)h Fp(OnRank\(col,sq\))h(=)g(7\))734 1986 y Fl(if)f Fp (\(OnRank\(col,KingSq\(Opp\(col\)\)\))g Ff(\025)h Fp(7\))793 2036 y(14)734 2085 y Fl(else)793 2135 y Fp(6)734 2185 y Fl(endif)675 2235 y(else)734 2285 y Fp(0)675 2334 y Fl(endif)262 2449 y Fp(P)o(enetration)j(to)f(the)h(7th)g(rank)g(is)f(the)h(natural)f(consequence) j(and)e(goal)e(of)h(ro)q(ok)h(pla)o(y)957 2574 y(68)p eop %%Page: 69 71 69 70 bop 262 307 a Fp(on)13 b(op)q(en)i(\014les.)k(A)c(ro)q(ok)f(on)f(the)i (7th)f(rank)g(can)h(wreak)f(ha)o(v)o(o)q(c)g(on)g(the)h(enem)o(y)e(king)h (and)262 357 y(pa)o(wns.)20 b(Therefore)15 b(o)q(ccupation)g(of)f(the)h(7th)g (rank)f(b)o(y)g(a)h(ro)q(ok)f(receiv)o(es)i(a)e(b)q(on)o(us.)21 b(This)262 407 y(b)q(on)o(us)14 b(is)f(esp)q(ecially)h(large)g(if)f(the)i (enem)o(y)e(king)g(is)h(on)f(the)i(7th)e(or)h(8th)g(ranks.)262 558 y Fu(4.7.5)55 b(De\014nition)17 b(25)i(:)24 b(Ro)r(ok)18 b(V)-5 b(alue)344 649 y Fh(RV)400 655 y Fe(col)456 649 y Fp(=)12 b Fh(RC)562 655 y Fe(col)614 649 y Fp(+)e Fh(C)s(R)721 655 y Fe(col)773 649 y Fp(+)g Fh(RO)879 655 y Fe(col)931 649 y Fp(+)g Fh(RS)1030 655 y Fe(col)344 748 y Fl(where)380 798 y Fh(RC)442 804 y Fe(col)498 798 y Fp(:)23 b Fl(Ro)q(ok{King)15 b(Closeness)f(\(De\014nitio)o(n)f(21\).)380 898 y Fh(C)s(R)445 904 y Fe(col)498 898 y Fp(:)23 b Fl(Connected)15 b(Ro)q(oks)g(\(De\014nitio)o (n)e(22\).)380 997 y Fh(RO)444 1003 y Fe(col)498 997 y Fp(:)23 b Fl(Ro)q(ok)16 b(on)f(Op)q(en)g(File)g(\(De\014niti)o(on)d(23\).)380 1097 y Fh(RS)437 1103 y Fe(col)498 1097 y Fp(:)23 b Fl(Ro)q(ok)16 b(On)f(Sev)o(en)o(th)f(Rank)h(\(De\014nitio)o(n)e(24\).)262 1219 y Fp(All)g(the)h(ro)q(ok)g(ev)n(aluation)f(criteria)h(de\014ned)h(in)e (this)i(section)f(are)h(summed)d(to)i(calculate)262 1269 y(the)g(total)f(ro)q (ok)h(v)n(alue)f(for)h(a)f(giv)o(en)h(colour.)p 641 1363 673 5 v 641 2027 5 665 v 646 1446 a Fg(0ZrZ0ZkZ)646 1529 y(ZqZ0ZpZp)646 1612 y(po0LpZpZ)646 1695 y(Z0Z0Z0Z0)646 1778 y(PZ0O0Z0Z)646 1861 y(Z0Z0O0ZP)646 1944 y(0ZrZ0OPZ)646 2027 y(SRZ0Z0J0)p 1310 2027 V 641 2031 673 5 v 343 2146 a Fp(Figure)g(4.7:)j Fl(Alatorze\013)d(v)i (Capablanca)p Fp(,)d(Mosco)o(w,)h(1935,)e(Blac)o(k)i(to)f(pla)o(y)m(.)324 2261 y(Applying)g(these)i(ro)q(ok)f(ev)n(aluation)e(criteria)i(to)g(the)h(p)q (osition)e(in)g(\014gure)i(4.7)e(giv)o(es:)344 2355 y Fh(RV)400 2361 y Fe(W)t(hite)533 2355 y Fp(=)h Ff(\000)p Fp(22)9 b(+)h(6)f(+)g(6)g(+)h (0)h(=)h Ff(\000)p Fp(10)344 2405 y Fh(RV)400 2411 y Fe(B)q(lack)533 2405 y Fp(=)i Ff(\000)p Fp(10)9 b(+)h(6)f(+)g(28)g(+)h(14)h(=)g(38)957 2574 y(69)p eop %%Page: 70 72 70 71 bop 262 307 a Fr(4.8)69 b(Queen)22 b(Ev)l(aluation)262 434 y Fp(The)12 b(queen)h(is)f(the)h(most)d(p)q(o)o(w)o(erful)i(and)g(also)f (the)i(most)e(v)n(aluable)g(piece)i(apart)f(from)e(the)262 483 y(king.)16 b(The)e(queen)f(has)g(great)g(range)g(whic)o(h)g(allo)o(ws)e (it)i(to)f(mak)o(e)g(sim)o(ultaneous)f(m)o(ultiple)262 533 y(attac)o(ks)j(on)f(enem)o(y)h(pieces.)324 618 y(In)e(the)g(op)q(ening)g(a)g (queen)h(should)e(not)h(b)q(e)h(exp)q(osed)g(to)f(hostile)g(attac)o(ks)g (where)h(a)f(loss)262 668 y(of)k(temp)q(o)h(will)f(o)q(ccur.)30 b(Therefore,)19 b(lik)o(e)e(ro)q(oks)h(it)f(should)g(b)q(e)h(k)o(ept)g(bac)o (k)g(during)f(the)262 718 y(op)q(ening.)324 803 y(In)g(the)h(middle)d(game)h 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y Fp(=)506 1475 y Fc(P)550 1485 y Fk(64)550 1518 y Fe(sq)q Fk(=1)675 1506 y Fl(if)13 b Fp(\(Occup)o (y\([Queen],col,sq\)\))734 1559 y Ff(\000)p Fp(2)p Ff(\001)p Fp(KingDistance\(sq,KingSq\(Opp\(col\)\)\))675 1608 y Fl(else)734 1658 y Fp(0)675 1708 y Fl(endif)262 1835 y Fp(The)j(queen)h(is)f(p)q (enalised)h(for)f(its)g(distance)h(from)d(the)j(enem)o(y)f(king.)24 b(A)16 b(queen)h(on)f(the)262 1885 y(same)e(rank)h(\(or)h(\014le\))g(as)f (the)h(enem)o(y)f(king)f(will)g(receiv)o(e)j(no)e(p)q(enalt)o(y)h(regardless) g(of)f(the)262 1934 y(corresp)q(onding)g(\014le)g(\(or)g(rank\))f(distance.) 21 b(An)o(y)15 b(p)q(enalties)g(giv)o(en)f(will)g(b)q(e)h(directly)g(pro-)262 1984 y(p)q(ortional)d(to)i(the)h(minim)n(um)9 b(rank)14 b(or)g(\014le)g (distance.)324 2069 y(This)c(criterion)h(therefore)h(encourages)g(the)g (queen)f(to)f(k)o(eep)i(close)f(to)f(the)i(enem)o(y)d(king)262 2119 y(with)k(resp)q(ect)j(to)d(either)h(the)g(rank)g(or)f(\014le)h (distance,)g(not)f(b)q(oth.)18 b(If)c(a)f(more)f(dominating)262 2169 y(queen/king)g(p)q(osition)f(is)h(w)o(arran)o(ted,)h(the)g(king)e(safet) o(y)i(criteria)f(will)f(highligh)o(t)f(this)j(and)262 2219 y(encourage)h(its)g(ac)o(hiev)o(emen)o(t.)957 2574 y(70)p eop %%Page: 71 73 71 72 bop 262 307 a Fu(4.8.2)55 b(De\014nition)17 b(27)i(:)24 b(Queen)19 b(P)n(o)n(w)n(er)344 474 y Fh(QP)404 480 y Fe(col)459 474 y Fp(=)503 443 y Fc(P)547 453 y Fk(64)547 486 y Fe(sq)q Fk(=1)675 474 y Fl(if)13 b Fp(\(A)o(ttac)o(k)o(ed\([Queen],col,sq\))675 527 y Fl(and)i(not)e Fp(A)o(ttac)o(k)o(ed\([P)o(a)o(wn,Knigh)o(t,Bishop,Ro)q (ok],Opp\(col\),)o(sq\)\))734 577 y(1)675 626 y Fl(else)734 676 y Fp(0)675 726 y Fl(endif)262 853 y Fp(As)h(explained)f(in)h(the)g (mobilit)o(y)d(de\014nition,)i(a)h(straigh)o(t)f(forw)o(ard)h(measure)g(of)f (a)g(queens)262 903 y(mobilit)o(y)e(is)k(not)g(adequate.)22 b(It)15 b(is)g(often)g(the)g(queens)h(placemen)o(t)f(rather)h(than)f(its)f (mo-)262 952 y(bilit)o(y)d(whic)o(h)i(is)g(imp)q(ortan)o(t.)j(I)d(feel)g(a)f (queens)j(real)e(mobilit)o(y)c(is)k(the)h(n)o(um)o(b)q(er)e(of)g(squares)262 1002 y(it)i(can)i(actually)e(mo)o(v)o(e)g(to)h(without)f(b)q(eing)i(captured) g(b)o(y)f(lo)o(w)o(er)g(v)n(alued)f(enem)o(y)h(pieces.)262 1052 y(Therefore,)c(the)f(queen)h(is)f(encouraged)h(to)e(maximi)o(se)f(its)i (mobilit)o(y)d(to)i(accessible)i(squares)262 1102 y(only)m(.)16 b(This)d(means)f(attac)o(ks)i(on)e(squares)j(whic)o(h)d(are)i(undefended)g (or)f(only)g(defended)h(b)o(y)262 1152 y(the)g(enem)o(y)f(queen)i(or)f(king)f (are)h(w)o(orth)o(while.)324 1237 y(I)f(feel)h(this)f(criterion)h(pro)o (vides)g(a)f(m)o(uc)o(h)g(b)q(etter)i(ev)n(aluation)d(of)h(a)g(queen's)h (degree)h(of)262 1287 y(freedom)e(in)g(a)h(giv)o(en)f(p)q(osition)g(than)h (the)h(more)d(traditional)h(mobilit)o(y)e(functions.)262 1438 y Fu(4.8.3)55 b(De\014nition)17 b(28)i(:)24 b(Queen)19 b(V)-5 b(alue)344 1600 y Fh(QV)401 1606 y Fe(col)457 1600 y Fp(=)12 b Fh(QC)564 1606 y Fe(col)616 1600 y Fp(+)e Fh(QP)718 1606 y Fe(col)344 1700 y Fl(where)380 1750 y Fh(QC)443 1756 y Fe(col)498 1750 y Fp(:)23 b Fl(Queen{King)14 b(Closeness)g(\(De\014niti)o(on)e(26\).)380 1849 y Fh(QP)440 1855 y Fe(col)498 1849 y Fp(:)23 b Fl(Queen)15 b(P)o(o)o(w)o(er)f(\(De\014niti)o(on)f(27\).)262 1976 y Fp(All)f(the)i(queen) g(ev)n(aluation)e(criteria)i(de\014ned)g(in)f(this)h(section)g(are)f(summed)f (in)h(order)h(to)262 2026 y(calculate)f(the)i(total)e(queen)i(v)n(alue)e(for) h(a)f(giv)o(en)h(colour.)324 2111 y(Applying)e(these)j(queen)f(ev)n(aluation) e(criteria)h(to)h(the)g(p)q(osition)e(in)h(\014gure)h(4.7)e(giv)o(es:)344 2208 y Fh(QV)401 2214 y Fe(W)t(hite)533 2208 y Fp(=)i Ff(\000)p Fp(4)c(+)f(10)i(=)h(6)344 2258 y Fh(QV)401 2264 y Fe(B)q(lack)533 2258 y Fp(=)i Ff(\000)p Fp(10)9 b(+)h(13)h(=)h(3)957 2574 y(71)p eop %%Page: 72 74 72 73 bop 262 307 a Fr(4.9)69 b(King)23 b(Ev)l(aluation)262 434 y Fp(The)15 b(king)g(is)g(the)h(most)f(imp)q(ortan)o(t)e(piece)k(on)e (the)h(b)q(oard.)22 b(Its)16 b(loss)g(means)e(the)i(end)g(of)262 483 y(the)e(game.)324 569 y(In)e(the)i(op)q(ening,)e(the)h(king)f(m)o(ust)g (seek)i(a)e(sa)o(v)o(e)h(ha)o(v)o(en)g(protected)h(b)o(y)f(its)f(o)o(wn)h(pa) o(wns)262 618 y(and)g(pieces.)20 b(This)13 b(is)h(generally)g(b)q(est)h (accomplished)e(b)o(y)g(castling.)324 704 y(In)j(the)h(middle)e(game,)g(the)i (king)e(m)o(ust)h(still)f(b)q(e)i(protected)h(against)e(attac)o(k.)26 b(This)262 753 y(protection)16 b(will)e(in)o(v)o(olv)o(e)g(a)h(strong)h(pa)o (wn)f(structure)j(in)d(fron)o(t)h(of)e(the)j(king)d(with)i(piece)262 803 y(co)o(v)o(er)e(for)f(an)o(y)h(w)o(eak)g(p)q(oin)o(ts.)324 889 y(In)j(the)h(endgame,)g(unlik)o(e)e(other)j(stages)f(of)f(the)h(game,)f (the)h(king)e(is)i(a)f(strong)h(at-)262 938 y(tac)o(king)g(piece.)33 b(A)19 b(king)f(can)h(supp)q(ort)g(its)g(o)o(wn)f(pieces)i(and)f(pa)o(wns)g (or)f(p)q(enetrate)j(a)262 988 y(w)o(eak)16 b(enem)o(y)f(pa)o(wn)h(structure) j(to)d(win)f(material.)24 b(Late)16 b(activ)n(ation)f(of)h(a)g(king)f(in)h (the)262 1038 y(endgame)e(could)h(b)q(e)g(disastrous.)23 b(Therefore,)16 b(the)g(king)e(m)o(ust)h(b)q(e)g(suitably)g(p)q(ositioned)262 1088 y(to)e(tak)o(e)h(adv)n(an)o(tage)f(of)g(an)o(y)h(w)o(eaknesses)i(in)d (the)i(opp)q(osing)e(forces.)262 1239 y Fu(4.9.1)55 b(De\014nition)17 b(29)i(:)24 b(King)19 b(On)g(Op)r(en)f(Files)344 1371 y Fh(K)s(O)414 1377 y Fe(col)470 1371 y Fp(=)513 1339 y Fc(P)557 1350 y Fk(64)557 1383 y Fe(sq)q Fk(=1)640 1371 y Fh(K)s(F)705 1377 y Fe(col;sq)344 1473 y Fl(where)380 1523 y Fh(K)s(F)445 1529 y Fe(col;sq)544 1523 y Fp(:)36 b Fl(if)13 b Fp(\(Occup)o(y\([King],col,sq\))g Fl(and)g Fp(Has\([Ro)q(ok,Queen],Opp\(col\)\)\))651 1573 y Fl(if)g Fp(\(Op)q(en\(OnFile\(sq\)\)\))710 1623 y Fh(K)s(F)775 1629 y Fe(col;sq)873 1623 y Fp(=)e Ff(\000)p Fp(2)f Ff(\001)e Fh(phase)651 1673 y Fl(else)710 1722 y(if)13 b Fp(\(SemiOp)q (en\(Opp\(col\),OnFile\(sq\)\))710 1772 y Fl(or)h Fp(SemiOp)q (en\(col,OnFile\(sq\)\)\))769 1822 y Fh(K)s(F)834 1828 y Fe(col;sq)932 1822 y Fp(=)d Ff(\000)p Fh(phase)710 1872 y Fl(else)769 1922 y Fh(K)s(F)834 1928 y Fe(col;sq)932 1922 y Fp(=)g(0)710 1971 y Fl(endif)651 2021 y(endif)651 2071 y(if)i Fp(\(OnFile\(sq\))h(=)h(2)e Fl(or)h Fp(3)f Fl(or)h Fp(4)f Fl(or)g Fp(8\))710 2121 y Fl(if)g Fp(\(Op)q(en\(OnFile\(sq\))p Ff(\000)p Fp(1\)\))769 2171 y Fh(K)s(F)834 2177 y Fe(col;sq)932 2171 y Fp(=)e Ff(\000)p Fh(phase)710 2221 y Fl(else)769 2270 y(if)i Fp(\(SemiOp)q(en\(Opp\(col\),OnFile\(sq\))p Ff(\000)p Fp(1\)\))828 2320 y Fh(K)s(F)893 2326 y Fe(col;sq)991 2320 y Fp(=)e Ff(\000)p Fh(phase=)p Fp(2)769 2370 y Fl(endif)710 2420 y(endif)957 2574 y Fp(72)p eop %%Page: 73 75 73 74 bop 651 307 a Fl(else)710 357 y(if)13 b Fp(\(Op)q (en\(OnFile\(sq\)+1\)\))769 407 y Fh(K)s(F)834 413 y Fe(col;sq)932 407 y Fp(=)e Ff(\000)p Fh(phase)710 457 y Fl(else)769 506 y(if)i Fp(\(SemiOp)q(en\(Opp\(col\),OnFile\(sq\)+1\)\))828 556 y Fh(K)s(F)893 562 y Fe(col;sq)991 556 y Fp(=)e Ff(\000)p Fh(phase=)p Fp(2)769 606 y Fl(endif)710 656 y(endif)651 706 y(endif)592 756 y(else)651 805 y Fh(K)s(F)716 811 y Fe(col;sq)813 805 y Fp(=)h(0)592 855 y Fl(endif)262 982 y Fp(The)k(king)f(is)g(p)q(enalised)h(for)g(b)q(eing)g(on) f(either)i(an)e(op)q(en)h(or)g(semi{op)q(en)f(\014le.)24 b(It)16 b(is)f(also)262 1032 y(p)q(enalised)e(for)f(b)q(eing)h(adjacen)o(t)g(to)g(an) g(op)q(en)g(or)g(semi{op)q(en)f(\014le)h(under)h(t)o(w)o(o)e(conditions:)312 1150 y(1.)20 b(The)d(king)e(is)g Fl(not)g Fp(on)h(either)h(the)f('A')f(or)h ('H')f(\014les)h(and)g(the)g(op)q(en)h(\014le)f(is)f(on)h(the)365 1200 y(adjacen)o(t)e(\014le)g(nearest)i(the)e(edge)h(of)e(the)h(b)q(oard.)312 1283 y(2.)20 b(The)15 b(king)e(is)g(on)h(either)h(the)f('A')f(or)h('H')f (\014les)i(and)e(the)i(op)q(en)f(\014le)g(is)g(adjacen)o(t.)262 1401 y(Note)g(these)h(p)q(enalties)g(are)f(only)f(imp)q(osed)g(if)g(the)i (opp)q(onen)o(t)f(has)g(the)g(necessary)i(pieces)262 1451 y(to)d(tak)o(e)h (adv)n(an)o(tage)f(of)g(the)i(w)o(eakness.)262 1603 y Fu(4.9.2)55 b(De\014nition)17 b(30)i(:)24 b(W)-5 b(eak)19 b(Squares)f(around)h(King)262 1715 y Fp(Con)o(trol)10 b(m)o(ust)h(b)q(e)h(held)g(o)o(v)o(er)g(the)g(w)o (eak)f(squares)i(around)f(the)g(king.)k(By)c(w)o(eak)g(squares)h(I)262 1765 y(mean)e(those)j(squares)g(not)f(co)o(v)o(ered)h(b)o(y)f(friendly)g(pa)o (wns)g(whic)o(h)g(are)g(therefore,)h(p)q(ossible)262 1815 y(pa)o(wn)e(holes.) 18 b(These)d(pa)o(wn)d(holes)i(are)f(ideal)g(w)o(eak)g(p)q(oin)o(ts)g(for)f (the)i(opp)q(onen)o(t)g(to)f(attac)o(k)262 1864 y(and)g(o)q(ccup)o(y)m(.)344 1985 y Fh(W)6 b(S)414 1991 y Fe(col)470 1985 y Fp(=)12 b Fh(W)6 b(K)594 1992 y Fe(col;C)r(entr)q(alP)t(oint)p Fk(\()p Fe(K)r(ing)q(S)r(q)q Fk(\()p Fe(col)p Fk(\)\))344 2085 y Fl(where)380 2140 y Fh(W)g(K)460 2146 y Fe(col;csq)574 2140 y Fp(:)616 2108 y Fc(P)660 2119 y Fk(64)660 2152 y Fe(sq)q Fk(=1)746 2140 y Fl(if)12 b Fp (\(Distance\(sq,csq\))k Ff(\024)e Fp(1)f Fl(and)746 2193 y(not)g Fp(\(A)o(ttac)o(k)o(ed\([P)o(a)o(wn],col,sq\))f Fl(or)i Fp(Occup)o(y\([P)o(a) o(wn],col,sq\)\)\))805 2242 y Fh(C)s(O)870 2248 y Fe(col;sq)964 2242 y Fp(+)c Fh(O)q(C)1069 2248 y Fe(col;sq)1163 2242 y Fp(+)g Fh(F)c(B)1269 2248 y Fe(col;sq)1363 2242 y Fp(+)k Fh(E)r(B)1469 2248 y Fe(col;sq)746 2292 y Fl(else)805 2342 y Fp(0)746 2392 y Fl(endif)957 2574 y Fp(73)p eop %%Page: 74 76 74 75 bop 380 307 a Fh(C)s(O)445 313 y Fe(col;sq)544 307 y Fp(:)60 b Fl(if)13 b Fp(\(Con)o(trol\(sq\))g(=)i(col\))675 357 y Ff(\000)p Fp(1)616 407 y Fl(else)675 457 y Ff(\000)p Fp(4)616 506 y Fl(endif)380 606 y Fh(O)q(C)443 612 y Fe(col;sq)542 606 y Fp(:)62 b Fl(if)13 b Fp(\(Occup)o(y\([An)o(y],Opp\(col\),sq\)\))675 656 y Ff(\000)p Fp(8)616 706 y Fl(else)675 756 y Fp(0)616 805 y Fl(endif)380 905 y Fh(F)6 b(B)444 911 y Fe(col;sq)543 905 y Fp(:)61 b Fl(if)13 b Fp(\(A)o(ttac)o(k)o(ed\([Bishop],col,sq\)\))675 955 y(6)616 1005 y Fl(else)675 1054 y(if)g Fp(\(Occup)o (y\([Bishop],col,sq\)\))746 1104 y(16)675 1154 y Fl(else)746 1204 y Fp(0)675 1254 y Fl(endif)616 1303 y(endif)380 1403 y Fh(E)r(B)444 1409 y Fe(col;sq)544 1403 y Fp(:)60 b Fl(if)13 b Fp(\(A)o(ttac)o(k)o(ed\([Bishop,Queen],Opp\(col\),sq\)\))675 1453 y Ff(\000)p Fp(6)616 1503 y Fl(else)675 1553 y Fp(0)616 1602 y Fl(endif)262 1721 y Fp(Squares)i(on)f(or)h(adjacen)o(t)f(to)h(the)g (cen)o(tral)g(p)q(oin)o(t)f(of)f(the)j(king's)d(defensiv)o(e)i(p)q(osition)f (are)262 1771 y(p)q(enalised)e(for)f(b)q(eing)h(w)o(eak)g(if)f(they)h(are)h (not)e(o)q(ccupied)i(or)f(attac)o(k)o(ed)g(b)o(y)g(friendly)f(pa)o(wns.)262 1820 y(Squares)k(are)h(quite)f(hea)o(vily)e(p)q(enalised)j(for)e(not)h(b)q (eing)g(con)o(trolled)g(b)o(y)f(friendly)h(pieces.)262 1870 y(Additionally)m(,)9 b(an)k(o)q(ccupied)g(w)o(eak)g(square)g(is)g(hea)o(vily) e(p)q(enalised.)18 b(A)13 b(b)q(on)o(us)g(is)f(receiv)o(ed)262 1920 y(if)f(a)i(friendly)f(bishop)h(attac)o(ks)g(the)g(w)o(eak)g(square)g(or) g(o)q(ccupies)h(the)f(actual)g(square)g(itself.)262 1970 y(A)i(p)q(enalt)o(y) h(is)f(levied)h(if)f(the)h(opp)q(onen)o(t)g(has)f(a)h(bishop)f(or)h(queen)g (whic)o(h)g(can)g(in\014ltrate)262 2020 y(the)e(w)o(eak)g(square.)324 2105 y(These)19 b(criteria)f(will)f(encourage)i(the)f(program)e(to)i(force)h (w)o(eak)f(squares)h(near)f(the)262 2155 y(opp)q(onen)o(ts)12 b(king)f(and)g(realise)h(whic)o(h)f(of)g(its)h(pieces)g(are)g(therefore)h (made)e(more)f(v)n(aluable.)262 2205 y(It)16 b(will)e(also)i(encourage)h (vital)e(o)q(ccupation)h(and)g(blo)q(c)o(k)n(ade)g(of)f(these)j(w)o(eak)e(p)q (oin)o(ts.)25 b(Of)262 2254 y(course,)20 b(the)f(program)e(will)g(b)q(e)i (discouraged)g(from)e(allo)o(wing)f(suc)o(h)k(w)o(eak)e(squares)i(to)262 2304 y(dev)o(elop)14 b(near)i(its)e(o)o(wn)h(king.)20 b(Ev)o(en)15 b(if)f(it)g(is)h(forced)g(to)g(accept)h(some)e(w)o(eak)g(squares,)i(it)262 2354 y(will)9 b(activ)o(ely)i(seek)i(to)e(exc)o(hange)h(the)g(opp)q(onen)o (ts)g(most)e(dangerous)i(pieces)g(with)f(resp)q(ect)262 2404 y(to)i(those)i(w)o(eaknesses.)957 2574 y(74)p eop %%Page: 75 77 75 76 bop 262 307 a Fu(4.9.3)55 b(De\014nition)17 b(31)i(:)24 b(Mating)19 b(Net)262 419 y Fp(The)g(kings)f(p)q(osition)g(should)g(alw)o(a)o (ys)f(b)q(e)j(c)o(hec)o(k)o(ed)f(to)g(see)h(if)d(a)i(mating)d(net)j(is)g(b)q (eing)262 469 y(formed)e(around)h(it.)31 b(The)19 b(building)e(of)g(suc)o(h)j (a)e(mating)e(net)j(around)f(the)h(opp)q(onen)o(ts)262 519 y(king)d(is)i(to)f(b)q(e)h(encouraged.)30 b(It)17 b(will,)g(ho)o(w)o(ev)o (er,)h(b)q(e)g(discouraged)g(from)e(allo)o(wing)f(the)262 569 y(opp)q(onen)o(t)f(to)f(ac)o(hiev)o(e)i(similar)c(aims.)344 666 y Fh(M)5 b(N)422 672 y Fe(col)478 666 y Fp(=)12 b Fh(N)5 b(T)584 672 y Fe(col)344 766 y Fl(where)380 816 y Fh(N)g(T)442 822 y Fe(col)500 816 y Fp(:)33 b(W)m(eakSqs)13 b(=)i(0)545 865 y Fh(N)5 b(T)607 871 y Fe(col)663 865 y Fp(=)11 b(0)545 915 y Fl(for)k(eac)o(h)g(square)f Fp(sq)g Fl(do)604 965 y(if)f Fp(\(Distance\(KingSq\(col\),sq\))h(=)g(1\))663 1015 y(di\013)g(=)g Fh(])p Fp(Di\013A)o(ttac)o(ks\(Opp\(col\),sq\))663 1065 y Fl(if)f Fp(\(Con)o(trol\(sq\))h(=)g(Opp\(col\))g Fl(or)f Fp(di\013)h Fh(>)g Fp(0\))722 1114 y(W)m(eakSqs)g(=)g(W)m(eakSqs)f(+)h(1)722 1164 y Fl(if)f Fp(\()p Fh(])p Fp(A)o(ttac)o(ks\([An)o(y],Opp\(col\),sq\))h Fh(>)g Fp(1\))781 1214 y Fh(N)814 1220 y Fe(col)870 1214 y Fp(=)e Fh(N)947 1220 y Fe(col)1000 1214 y Ff(\000)e Fp(4)f Ff(\001)g Fh(dif)t(f)14 b Ff(\000)c Fp(2)722 1264 y Fl(endif)663 1314 y(endif)604 1363 y(endif)545 1413 y(endfor)545 1463 y(if)j Fp(\(KingSq\(col\))g(=)h(a8)g Fl(or)f Fp(h8)h Fl(or)f Fp(a1)g Fl(or)h Fp(h1\))604 1513 y(W)m(eakSqs)g(=)g(W)m(eakSqs)f(+)h(1)545 1563 y Fl(endif)545 1613 y Fh(N)578 1619 y Fe(col)634 1613 y Fp(=)e Fh(N)711 1619 y Fe(col)764 1613 y Ff(\000)e Fh(T)830 1619 y Fe(W)t(eak)q(S)r(q)q(s)380 1712 y Fh(T)404 1718 y Fe(c)435 1712 y Fp(:)98 b([0,)13 b(8,)g(20,)g(36,)g(56,)f(80,)h(108,)g(140,)g(180])604 1762 y(Indexed)i(b)o(y)f(w)o(eak)f(square)i(coun)o(t)f(c)g(\(0)g(to)g(8\))262 1880 y(An)o(y)f(squares)i(adjacen)o(t)f(to)g(the)g(king)f(are)h(p)q(enalised) h(for)e(lac)o(k)g(of)h(con)o(trol.)j(P)o(articularly)262 1930 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b(De\014nition)17 b(32)i(:)24 b(Chec)n(k)19 b(Threats)262 419 y Fp(The)c(kings)g(p)q(osition)f(m)o(ust)g(b) q(e)i(monitored)e(and)h(the)g(p)q(oten)o(tial)g(threats)h(of)f(an)o(y)f(c)o (hec)o(ks)262 469 y(assessed.)19 b(Chec)o(k)13 b(mo)o(v)o(es)d(can)i(b)q(e)h (v)o(ery)f(e\013ectiv)o(e;)h(the)g(v)n(alue)e(of)g(whic)o(h)h(can)g(b)q(e)h (an)o(ything)262 519 y(from)d(a)i(gain)f(in)h(temp)q(o)g(to)g(c)o(hec)o (kmate)g(itself.)17 b(Of)c(course)g(some)f(c)o(hec)o(k)h(mo)o(v)o(es)e(ma)o (y)f(also)262 569 y(b)q(e)i(inferior)f(for)h(the)g(side)g(giving)f(the)h(c)o (hec)o(k,)h(p)q(ossibly)e(resulting)h(in)g(the)g(loss)g(of)f(a)g(temp)q(o)262 618 y(or)i(w)o(orse)i(still)e(the)h(c)o(hec)o(king)h(piece.)j(A)c(w)o(ell)g (kno)o(wn)f(c)o(hess)i(sa)o(ying)e(states:)365 737 y("P)o(atzer)i(sees)h(c)o (hec)o(k;)e(P)o(atzer)h(giv)o(es)f(c)o(hec)o(k.")262 855 y(Indicating)i(that) h(it)g(is)g(not)g(alw)o(a)o(ys)g(wise)g(to)g(put)h(y)o(our)f(opp)q(onen)o(t)g (in)g(c)o(hec)o(k.)29 b(In)17 b(fact,)262 905 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2574 y Fp(76)p eop %%Page: 77 79 77 78 bop 380 357 a Fh(K)s(T)442 363 y Fe(n)479 357 y Fp(:)78 b([0,14,30,4)o(8,7)o(0,8)o(6,1)o(00,)o(110,)o(120)o(,120)o(,12)o(0,1)o(20,)o (120,)o(120)o(,120)o(,12)o(0])628 407 y(Indexed)14 b(b)o(y)g(n)o(um)o(b)q(er) f(of)h(lik)o(ely)e(c)o(hec)o(ks)j(n)f(\(0)g(to)g(15\).)262 525 y(P)o(enalties)20 b(are)h(giv)o(en)f(for)g(p)q(oten)o(tial)g(c)o(hec)o (ks)i(if)e(the)h(side)f(giving)f(c)o(hec)o(k)j(has)f(enough)262 575 y(con)o(trol)16 b(o)o(v)o(er)g(the)h(c)o(hec)o(king)g(square.)27 b(Chec)o(ks)17 b(are)g(considered)h(more)d(serious)j(if)d(there)262 625 y(are)i(no)f(safe)h(blo)q(c)o(king)e(mo)o(v)o(es)h(a)o(v)n(ailable)e(for) j(the)g(defender.)27 b(In)17 b(fact,)g(if)f(there)i(is)e(also)262 675 y(no)f(escap)q(e)i(square)f(for)f(the)h(c)o(hec)o(k)o(ed)h(king,)e(the)h (situation)f(is)g(considered)i(v)o(ery)f(serious)262 725 y(indeed.)h(The)12 b Fm(MateThr)n(e)n(at)e Fp(predicate)i(is)f(set)h(to)f(indicate)g(the)h(sev)o (erit)o(y)g(of)e(the)i(situation.)262 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2326 y Fp(:)23 b Fl(King)15 b(On)g(Op)q(en)g(Files)f(\(De\014nition)e(29\).)380 2426 y Fh(W)6 b(S)450 2432 y Fe(col)510 2426 y Fp(:)23 b Fl(W)l(eak)17 b(Squares)d(around)g(King)h(\(De\014nition)d(30\).)957 2574 y Fp(77)p eop %%Page: 78 80 78 79 bop 380 357 a Fh(M)5 b(N)458 363 y Fe(col)510 357 y Fp(:)23 b Fl(Mating)15 b(Net)g(\(De\014nitio)o(n)e(31\).)380 457 y Fh(C)s(T)437 463 y Fe(col)510 457 y Fp(:)23 b Fl(Chec)o(k)16 b(Threats)f(\(De\014niti)o(on)d(32\).)380 556 y Fh(K)s(T)442 562 y Fe(col)510 556 y Fp(:)23 b Fl(King)15 b(T)l(able)g(\(De\014niti)o(on)d (33\).)262 683 y Fp(All)i(the)i(king)f(ev)n(aluation)f(criteria)i(de\014ned)g (in)f(this)h(section)g(are)g(summed)e(in)h(order)h(to)262 733 y(calculate)11 b(the)h(total)f(king)g(v)n(alue)g(for)g(a)g(giv)o(en)g (colour.)17 b(The)12 b(v)n(alues)g(are)g(further)g(adjusted)262 783 y(b)o(y)i(the)h(game)e(phase)i(to)f(tak)o(e)h(accoun)o(t)g(of)f(a)g (kings)g(more)g(activ)o(e)g(role)h(as)f(the)i(endgame)262 832 y(approac)o(hes.)25 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Ff(\000)g Fp(2\))h Ff(\001)e Fp(11)p Fh(=)p Fp(16)g Ff(\000)i Fp(1)h(=)h Ff(\000)p Fp(42)344 2128 y Fh(K)s(V)406 2134 y Fe(B)q(lack)533 2128 y Fp(=)i(\()p Ff(\000)p Fp(5)c Ff(\000)f Fp(43)g Ff(\000)g Fp(36)g Ff(\000)h Fp(34\))f Ff(\001)f Fp(11)p Fh(=)p Fp(16)g(+)i(0)h(=)h Ff(\000)p Fp(81)957 2574 y(78)p eop %%Page: 79 81 79 80 bop 262 307 a Fr(4.10)69 b(Static)22 b(T)-6 b(actical)21 b(Ev)l(aluation)262 434 y Fp(The)11 b(follo)o(wing)d(criteria)k(attempt)e(to) h(ev)n(aluate)g(tactical)f(asp)q(ects)j(statically)d(from)f(within)262 483 y(the)h(ev)n(aluation)f(function)h(itself.)17 b(The)11 b(ob)r(jectiv)o(e)g(of)e(these)j(criteria)f(is)f(to)g(deriv)o(e)h(an)f(accu-) 262 533 y(rate)g(v)n(alue)g(where)h(p)q(ossible,)f(and)g(where)h(uncertain)o (t)o(y)g(exists)g(to)f(giv)o(e)f(an)h(estimate)g(of)f(the)262 583 y(lik)o(ely)j(v)n(alue)h(and)h(recommend)e(a)i(deep)q(er)h(searc)o(h)g (to)f(resolv)o(e)g(the)h(tactical)e(uncertain)o(t)o(y)m(.)262 633 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1281 y(either)f(sev)o(erely)h(diminished)d(or)i(completely)f(lost.) 344 1378 y Fh(P)6 b(N)410 1384 y Fe(col)465 1378 y Fp(=)12 b Fh(P)6 b(S)567 1384 y Fe(col)344 1478 y Fl(where)380 1527 y Fh(P)g(S)438 1533 y Fe(col)495 1527 y Fp(:)14 b Fh(P)6 b(S)579 1533 y Fe(col)635 1527 y Fp(=)12 b(0)521 1577 y Fl(for)j(eac)o(h)h(square)d Fp(sq)h Fl(do)580 1627 y(for)h(eac)o(h)h(square)d Fp(sq1)h Fl(do)639 1677 y(for)h(eac)o(h)h(square)d Fp(sq2)h Fl(do)699 1727 y(if)e Fp(\(Pin\(col,sq,sq1,sq2\)\))758 1777 y Fl(if)g Fp(\(V)m(alue\(sq2\))i Fh(>)g Fp(V)m(alue\(sq\))758 1826 y Fl(or)h(not)e Fp(A)o(ttac)o(k)o(ed\([An)o(y],Opp\(col\),sq2\)\))817 1876 y Fh(P)6 b(S)875 1882 y Fe(col)932 1876 y Fp(=)14 b(V)m(alue\(sq2\))g(+) g(V)m(alue\(sq1\))g Ff(\000)g Fp(V)m(alue\(sq\))g(+)g(10)817 1926 y Fl(if)e Fp(\(A)o(ttac)o(k)o(ed\([An)o(y)j Fh(<)f Fp (On\(sq1\)],col,sq1\))817 1976 y Fl(or)h(not)e Fp(A)o(ttac)o(k)o(ed\([An)o (y],Opp\(col\),sq1\))817 2026 y Fl(or)g Fp(\()p Fh(])p Fp(Di\013A)o(ttac)o (ks\(col,sq1\))h 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(a)f(tactically)g(dynamic)f(threat,)i(then)g(a)262 506 y(tactical)11 b(coun)o(t)h(indicating)f(the)h(uncertain)o(t)o(y)h(of)e(the)h(static)h(ev)n (aluation)d(is)i(incremen)o(ted.)262 556 y(Basically)m(,)i(this)i(indicates)g (that)g(although)e(a)i(static)g(v)n(alue)f(is)h(calculated,)g(the)g(tactical) 262 606 y(uncertain)o(t)o(y)f(should)g(b)q(e)h(resolv)o(ed)g(b)o(y)f (extending)h(the)g(searc)o(h)h(un)o(til)d(a)h(more)f(quiescen)o(t)262 656 y(p)q(osition)f(is)g(reac)o(hed.)20 b(See)15 b(c)o(hapter)f(5)g(for)g (more)e(details.)324 741 y(The)21 b(ev)n(aluation)e(function)h(do)q(es)h(not) g(kno)o(w)f(whether)i(a)e(deep)q(er)i(searc)o(h)g(will)d(b)q(e)262 791 y(successful)c(in)e(\014nding)g(a)g(quiescen)o(t)i(p)q(osition)e(or)g(ev) o(en)i(has)e(enough)h(time)e(to)i(undertak)o(e)262 841 y(suc)o(h)g(a)g(task.) 19 b(Therefore,)c(a)e(v)n(alue)h(indicating)f(its)h(liking)e(for)i(the)g (tactical)g(uncertain)o(t)o(y)262 891 y(is)f(included)h(in)g(the)g(o)o(v)o (erall)f(static)h(v)n(alue.)p 641 984 673 5 v 641 1648 5 665 v 646 1067 a Fg(0Z0Z0Zrs)646 1150 y(oQZ0Z0Z0)646 1233 y(0ZRZbj0Z)646 1316 y(Z0ZqZ0Z0)646 1399 y(0Z0O0m0Z)646 1482 y(Z0Z0ZNZ0)646 1565 y(PZ0Z0OPO)646 1648 y(Z0Z0S0J0)p 1310 1648 V 641 1652 673 5 v 384 1771 a Fp(Figure)g(4.9:)j Fl(Dy)o(atlo)o(v)d(v)i(Shashin)p Fp(,)11 b(Leningrad,)i(1962,)g(Blac)o(k)g(to)h(pla)o(y)m(.)324 1889 y(Applying)e(the)i(Pinned)f(Pieces)i(ev)n(aluation)d(criteria)i(to)f (the)h(ab)q(o)o(v)o(e)f(p)q(osition)f(giv)o(es:)344 1987 y Fh(P)6 b(N)410 1993 y Fe(W)t(hite)533 1987 y Fp(=)14 b(22)344 2037 y Fh(P)6 b(N)410 2043 y Fe(B)q(lack)533 2037 y Fp(=)14 b(15)957 2574 y(80)p eop %%Page: 81 83 81 82 bop 262 307 a Fu(4.10.2)55 b(De\014nition)17 b(36)i(:)25 b(A)n(ttac)n(k)n(ed)19 b(Pieces)344 438 y Fh(AP)402 444 y Fe(col)457 438 y Fp(=)501 407 y Fc(P)545 417 y Fk(64)545 451 y Fe(sq)q Fk(=1)628 438 y Fh(AT)683 444 y Fe(col;sq)344 541 y Fl(where)380 591 y Fh(AT)435 597 y Fe(col;sq)535 591 y Fp(:)69 b Fl(if)13 b 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1045 y Fe(col)1206 1039 y Fp(+)j(1)734 1089 y Fl(endif)675 1139 y(else)734 1189 y(if)k Fp(\(Con)o(trol\(sq\))h(=)g(Opp\(col\))g Fl(or)f Fh(])p Fp(Di\013A)o(ttac)o(ks\(Opp\(col\),sq\))i Fh(>)f Fp(0\))793 1239 y Fh(AT)848 1245 y Fe(col;sq)946 1239 y Fp(=)d Fh(AT)1044 1245 y Fe(col;sq)1131 1239 y Ff(\000)p Fp(V)m(alue\(sq\))734 1288 y Fl(endif)675 1338 y(endif)616 1388 y(endif)262 1506 y Fp(Pieces)k(whic)o(h)f(are)h(threatened)h(with)e(pro\014table)g(capture)h (\(en-prise\))g(b)o(y)f(the)h(opp)q(osing)262 1556 y(side)i(are)g(p)q (enalised.)28 b(This)17 b(p)q(enalt)o(y)g(is)g(levied)g(not)g(b)q(ecause)h (the)g(loss)f(of)f(the)i(piece)g(is)262 1606 y(considered)f(lik)o(ely)m(,)e (but)i(b)q(ecause)h(it)f(is)f(v)o(ery)h(lik)o(ely)e(that)i(a)f(temp)q(o)g (will)f(b)q(e)i(w)o(asted)g(in)262 1656 y(protecting)c(or)g(mo)o(ving)d(the)j (threatened)i(piece.)j(The)c(threat)f(coun)o(t)g(is)g(incremen)o(ted)g(for) 262 1705 y(ev)o(ery)h(piece)h(en-prise.)324 1791 y(T)m(rapp)q(ed)j(pieces)h (whic)o(h)f(are)g(also)f(en-prise)i(are)f(additionally)d(p)q(enalised)j(and)g (the)262 1840 y(threat)e(coun)o(t)f(is)h(further)g(incremen)o(ted.)23 b(Pieces)17 b(whic)o(h)e(are)h(under)g(pressure,)i(but)e(not)262 1890 y(en-prise)k(are)g(also)f(p)q(enalised)h(although)e(to)i(a)f(lesser)i (exten)o(t.)36 b(The)20 b(threat)g(coun)o(t)g(is)262 1940 y(used)13 b(to)f(extend)h(the)g(searc)o(h)h(in)e(p)q(ositions)g(where)h(an)f(accurate)i (static)e(ev)n(aluation)f(v)n(alue)262 1990 y(cannot)j(b)q(e)g(calculated.) 324 2075 y(Applying)f(the)h(A)o(ttac)o(k)o(ed)h(Pieces)g(criteria)f(to)g(the) g(p)q(osition)g(in)f(\014gure)h(4.9)f(giv)o(es:)344 2166 y Fh(AP)402 2172 y Fe(W)t(hite)533 2166 y Fp(=)h Ff(\000)p Fp(18)344 2215 y Fh(AP)402 2221 y Fe(B)q(lack)533 2215 y Fp(=)g Ff(\000)p Fp(9)344 2265 y Fh(T)6 b(hr)q(eat)474 2271 y Fe(W)t(hite)583 2265 y Fp(=)12 b(2)344 2315 y Fh(T)6 b(hr)q(eat)474 2321 y Fe(B)q(lack)576 2315 y Fp(=)12 b(1)262 2391 y(The)19 b(n)o(um)o(b)q(er)g(of)f (threats)i(against)f(white)g(\(2\),)h(represen)o(ts)i(a)d(degree)i(of)d (uncertain)o(t)o(y)262 2441 y(ab)q(out)13 b(the)i(tactical)e(p)q (ossibilities)h(threatened)h(against)e(the)i(white)f(pieces.)957 2574 y(81)p eop %%Page: 82 84 82 83 bop 262 307 a Fr(4.11)69 b(Planning)262 434 y Fp(Before)18 b(eac)o(h)g(searc)o(h)h(b)q(egins)e(an)h(analysis)f(of)f(the)j(p)q(osition)d (will)g(b)q(e)j(done.)29 b(This)17 b(will)262 483 y(enable)11 b(v)n(arious)g(piece)h(square)g(tables)g(to)f(b)q(e)h(loaded)f(with)g(v)n (alues)g(whic)o(h)g(can)g(b)q(e)h(applied)262 533 y(at)h(leaf)h(no)q(des)g (using)g(lo)q(ok)f(up)h(tables.)324 618 y(Ob)o(viously)d(this)g(is)h(m)o(uc)o (h)e(faster)j(than)e(rep)q(eatedly)i(calculating)e(information)e(at)i(leaf) 262 668 y(no)q(des.)18 b(Hence,)d(in)e(an)h(implemen)o(tati)o(on,)d(all)h (leaf)h(no)q(de)h(ev)n(aluation)f(criteria)h(whic)o(h)f(are)262 718 y(essen)o(tially)18 b(static)h(should)g(b)q(e)g(incorp)q(orated)g(in)o (to)f(these)i(tables)f(and)g(remo)o(v)o(ed)e(from)262 768 y(the)d(leaf)f(ev)n (aluation)f(pro)q(cess.)20 b(Ho)o(w)o(ev)o(er,)13 b(this)h(c)o(hapter)h (represen)o(ts)h(a)d(de\014nition)g(of)g(m)o(y)262 818 y(prop)q(osed)19 b(ev)n(aluation)e(function)h(regardless)h(of)f(implemen)o(tation)d(detail.)31 b(Therefore,)262 867 y(some)19 b(criteria)i(whic)o(h)f(are)h(suited)g(to)g (piece)g(square)h(tables)e(are)h(de\014ned)h(separately)262 917 y(b)q(ecause)15 b(of)e(their)i(imp)q(ortance.)324 1003 y(T)m(o)f(com)o(bat)f(the)j(t)o(ypically)d(aimless)h(pla)o(y)g(of)g(c)o(hess) j(programs)c(I)i(will)e(include)i(some)262 1052 y(rudimen)o(tary)h(planning)h (in)h(the)h(ev)n(aluation)d(function.)31 b(P)o(art)18 b(of)g(the)g(initial)e (analysis)262 1102 y(done)h(b)q(efore)g(eac)o(h)h(searc)o(h)g(commences)d (will)h(include)h(a)f(selection)i(of)e(an)h(appropriate)262 1152 y(plan)c(for)g(the)i(curren)o(t)g(p)q(osition.)j(The)c(plans)f(whic)o(h) h(will)f(b)q(e)h(recognised)h(are:)312 1270 y(1.)20 b Fl(King)15 b(side)g(attac)o(k)g(with)g(pa)o(wns)p Fp(.)312 1352 y(2.)20 b Fl(King)15 b(side)g(attac)o(k)g(with)g(pieces)p Fp(.)312 1435 y(3.)20 b Fl(King)15 b(side)g(attac)o(k)g(with)g(pieces)f(and)i(pa)o (wns)p Fp(.)312 1517 y(4.)k Fl(Queen)15 b(side)f(attac)o(k)i(with)f(pa)o(wns) p Fp(.)312 1600 y(5.)20 b Fl(Queen)15 b(side)f(attac)o(k)i(with)f(pieces)p Fp(.)312 1683 y(6.)20 b Fl(Queen)15 b(side)f(attac)o(k)i(with)f(pieces)f(and) h(pa)o(wns)p Fp(.)312 1765 y(7.)20 b Fl(Using)14 b(pa)o(wns)i(as)g(lev)o(ers) p Fp(.)312 1848 y(8.)k Fl(Endgame,)c(king)e(and)i(pa)o(wn)f(co-ordination)o Fp(.)262 1965 y(These)e(plans)f(are)g(relativ)o(ely)g(general,)g(but)g (should)g(pro)o(vide)g(the)h(program)e(with)h(enough)262 2015 y(v)n(ariet)o(y)h(to)g(c)o(ho)q(ose)h(a)g(plan)f(relev)n(an)o(t)g(to)h(the)g (p)q(osition)f(and)h(attempt)e(to)i(co-ordinate)g(its)262 2065 y(mo)o(v)o(es)g(to)h(ac)o(hiev)o(e)h(common)c(goals.)22 b(It)16 b(is)f(not)g(the)h(ob)r(ject)h(of)d(these)j(plans)e(to)h(suggest)262 2115 y(sp)q(eci\014c)j(mo)o(v)o(es,)e(but)i(rather)g(to)e(allo)o(w)g(the)i (searc)o(h)g(to)f(b)q(e)g(guided)g(to)o(w)o(ard)g(the)g(goals)262 2165 y(iden)o(ti\014ed.)324 2250 y(T)m(o)c(enable)h(the)h(searc)o(h)g(to)f(b) q(e)h(guided,)f(the)h(appropriate)f(piece)h(square)g(tables)f(will)262 2300 y(b)q(e)20 b(up)q(dated)h(in)f(suc)o(h)h(a)f(w)o(a)o(y)g(that)g(mo)o(v)o (es)f(whic)o(h)h(con)o(tribute)h(to)f(the)h(ac)o(hiev)o(emen)o(t)262 2350 y(of)16 b(the)h(c)o(hosen)h(goals)e(will)f(b)q(e)j(encouraged.)28 b(This)16 b(will)g(hop)q(efully)g(ha)o(v)o(e)g(the)i(e\013ect)g(of)262 2399 y(pro)o(viding)12 b(a)i(common)d(purp)q(ose)k(to)e(the)i(programs)e(mo)o (v)o(es)f(rather)j(than)f(allo)o(wing)d(it)j(to)262 2449 y(pla)o(y)e (aimless,)g(although)h(solid)g(mo)o(v)o(es.)957 2574 y(82)p eop %%Page: 83 85 83 84 bop 324 307 a Fp(There)17 b(are)f(no)f(sp)q(eci\014c)i(op)q(ening)f (plans,)f(ho)o(w)o(ev)o(er,)h(the)g(ev)n(aluation)f(function)g(do)q(es)262 357 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y Fe(O)q(pp)p Fk(\()p Fe(col)p Fk(\))p Fe(;sq)1183 1495 y Ff(\000)k Fh(D)q(F)1287 1501 y Fe(col;sq)592 1545 y Fl(else)651 1594 y Fp(0)592 1644 y Fl(endif)380 1744 y Fh(AT)435 1750 y Fe(col;sq)535 1744 y Fp(:)45 b Fh(])p Fp(A)o(ttac)o (ks\([Ro)q(ok],col,sq\))12 b(+)592 1794 y(2)d Ff(\001)g Fh(])p Fp(A)o(ttac)o(ks\([P)o(a)o(wn,Knigh)o(t,Bishop],col,sq\))j(+)592 1844 y(3)d Ff(\001)g Fh(])p Fp(A)o(ttac)o(ks\([Queen],col,sq\))380 1948 y Fh(P)d(M)453 1954 y Fe(col;sq)552 1948 y Fp(:)592 1917 y Fc(P)636 1927 y Fk(64)636 1960 y Fe(sq)q Fk(2=1)769 1948 y Fl(if)13 b Fp(\(A)o(ttac)o(king\([P)o(a)o(wn],col,sq2,sq\))769 2001 y Fl(and)g Fh(])p Fp(Mo)o(v)o(es\([P)o(a)o(wn],col,sq2\))g Fh(>)h Fp(0\))828 2051 y(2)769 2100 y Fl(else)828 2150 y Fp(0)769 2200 y Fl(endif)380 2300 y Fh(D)q(F)442 2306 y Fe(col;sq)541 2300 y Fp(:)39 b Fh(])p Fp(A)o(ttac)o(ks\([Ro)q(ok],col,sq\))12 b(+)592 2350 y(2)d Ff(\001)g Fh(])p Fp(A)o(ttac)o(ks\([Knigh)o (t,Bishop,Queen],col,sq\))k(+)592 2399 y(3)c Ff(\001)g Fh(])p Fp(A)o(ttac)o(ks\([P)o(a)o(wn],col,sq\))957 2574 y(83)p eop %%Page: 84 86 84 85 bop 380 307 a Fh(AD)445 313 y Fe(col;k)q(f)551 307 y Fp(:)592 276 y Fc(P)636 286 y Fe(k)q(f)s Fk(+1)636 320 y Fe(f)s Fk(=)p Fe(k)q(f)s Fd(\000)p Fk(1)769 307 y Fl(if)13 b Fp(\(Op)q(en\(f)s(\))i Fl(or)f Fp(SemiOp)q(en\(Opp\(col\),f)s(\)\))828 360 y(3)769 410 y Fl(else)828 460 y Fp(0)769 510 y Fl(endif)324 636 y Fp(This)19 b(de\014nition)h(attempts)f(to)g(calculate)h(ho)o(w)f(m)o(uc)o(h)g(pressure)i (in)f(terms)f(of)g(the)262 686 y(attac)o(k/defence)14 b(balance)e(is)h (curren)o(tly)g(exerted)i(on)d(the)h(king)f(in)h(question.)k(The)d(higher)262 736 y(the)e(v)n(alue)g(of)g(PK,)g(the)h(more)e(pressure)j(is)f(though)o(t)f (to)g(exist.)18 b(This)12 b(de\014nition)g(will)e(form)262 786 y(the)15 b(basis)f(of)g(a)h(decision)g(as)f(to)h(whether)h(an)e(assault)h (against)f(the)h(king)f(is)g(lik)o(ely)g(to)g(b)q(e)262 836 y(w)o(orth)o(while.)324 921 y(This)i(de\014nition)g(tak)o(es)h(in)o(to)f 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2102 y Fe(col)1012 2096 y Fp(=)14 b(PieceA)o(ttac)o(k)710 2145 y Fl(endif)710 2195 y Fh(P)6 b(l)q(anW)g(ing)907 2201 y Fe(col)965 2195 y Fp(=)14 b(Wing\(KingSq\(Opp\(col\)\)\))651 2245 y Fl(else)710 2295 y(if)f Fp(\(Opp)q(ositeFlanks\))769 2345 y Fh(P)6 b(l)q(anT)g(y)q(pe)953 2351 y Fe(col)1012 2345 y Fp(=)14 b(P)o(a)o(wnA)o(ttac)o(k)769 2394 y Fh(P)6 b(l)q(anW)g(ing)966 2400 y Fe(col)1024 2394 y Fp(=)14 b(Wing\(KingSq\(Opp\(col\)\)\))710 2444 y Fl(else)957 2574 y Fp(84)p eop %%Page: 85 87 85 86 bop 769 307 a Fl(if)13 b Fp(\(phase)i Fh(>)f Fp(10\))828 357 y Fh(P)6 b(l)q(anT)g(y)q(pe)1012 363 y Fe(col)1071 357 y Fp(=)14 b(Lev)o(erP)o(a)o(wns)828 407 y Fh(P)6 b(l)q(anW)g(ing)1025 413 y Fe(col)1083 407 y Fp(=)14 b(QueenSide)h Ff([)f Fp(KingSide)769 457 y Fl(else)828 506 y Fh(P)6 b(l)q(anT)g(y)q(pe)1012 512 y Fe(col)1071 506 y Fp(=)14 b(None)769 556 y Fl(endif)710 606 y(endif)651 656 y(endif)592 706 y(endif)262 832 y Fp(This)k(de\014nition)g 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y(1)g(1)h(1)g(1)f(1)h(1)g(1)f(1)687 1590 y(1)g(1)h(1)g(1)f(1)h(1)g(1)f(1)687 1673 y(2)g(2)h(2)g(2)f(2)h(2)g(2)f (2)687 1755 y(2)g(2)h(2)g(2)f(2)h(2)g(2)f(2)687 1838 y(2)g(2)h(2)g(2)f(2)h(2) g(2)f(2)687 1921 y(2)g(2)h(2)g(2)f(2)h(2)g(2)f(2)388 2048 y Fp(Figure)14 b(4.15:)j(Initial)c(W)m(eigh)o(tings)f(for)i(Blac)o(k's)f (Square)i(Con)o(trol)e(T)m(able.)344 2195 y Fh(S)369 2201 y Fe(col;sq)469 2195 y Fp(:)111 b Fl(for)15 b(eac)o(h)h(square)d Fp(sq)h Fl(do)651 2245 y Fh(S)676 2251 y Fe(col;sq)774 2245 y Fp(=)e Fh(S)r(T)869 2251 y Fe(col;sq)965 2245 y Fp(+)d Fh(P)d(L)1067 2251 y Fe(col;sq)592 2295 y Fl(endfor)344 2394 y(where)380 2444 y Fh(S)r(T)431 2450 y Fe(col;sq)531 2444 y Fp(:)49 b(Static)14 b(w)o(eigh)o(tings)f(indexed)i(b)o(y)e(colour)h(and)g(square,)g(see)h (\014gures)957 2574 y(92)p eop %%Page: 93 95 93 94 bop 592 307 a Fp(4.14)13 b(and)h(4.15)380 407 y Fh(P)6 b(L)441 413 y Fe(col;sq)540 407 y Fp(:)40 b Fl(if)13 b Fp(\(PieceA)o(ttac)o (k)i Ff(2)f Fh(P)6 b(l)q(anT)g(y)q(pe)1107 413 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b(This)16 b('Quiescence)i(Decision')d(ma)o(y)f(also)365 907 y(cause)i(the)f(main)e(searc)o(h)j(to)e(b)q(e)i(re{en)o(tered)h(from)c(no)q (des)i(that)g(are)g(already)f(part)365 957 y(of)g(the)g(quiescence)i(searc)o (h.)262 1075 y(The)e(results)i(obtained)e(from)e(searc)o(hing)j(eac)o(h)g(no) q(de)f(is)h(then)g(passed)g(bac)o(k)f(up)g(the)h(tree)262 1125 y(where)10 b(searc)o(h)h(heuristics)g(can)f(mak)o(e)e(use)i(of)f(the)h (information)d(in)i(searc)o(hing)h(other)g(no)q(des.)262 1175 y(It)16 b(is)h(imp)q(ortan)o(t)e(to)i(realise)g(the)g(searc)o(h)h(tree)g (explored)f(b)o(y)g(suc)o(h)g(a)g(searc)o(h)h(will)d(b)q(e)i(of)262 1225 y(v)n(ariable)10 b(depth,)i(the)g(deep)q(est)h(lines)e(b)q(eing)g(those) h(of)f(most)f(in)o(terest)i(to)g(the)f(searc)o(h.)19 b(This)262 1275 y(sho)o(ws)13 b(some)f(similarities)f(to)h(the)i(w)o(a)o(y)e(h)o(umans)g (approac)o(h)h(the)h(task)f(of)f(tree)j(searc)o(hing.)324 1360 y(The)f(follo)o(wing)d(sections)k(explain)e(this)h(searc)o(h)h(pro)q(cess)h (in)e(more)f(detail.)262 1533 y Fr(5.1)69 b(Main)23 b(Searc)n(h)262 1659 y Fp(The)14 b(main)e(searc)o(h)j(will)e(use)i(the)f(alpha{b)q(eta)g(\()p Fh(\013\014)r Fp(\))g(tree)i(pruning)e(algorithm)d(on)j(nega-)262 1709 y(max)i(trees.)32 b(This)18 b(algorithm)d(has)k(man)o(y)d(deriv)n(ativ)o (es)i(and)g(enhancemen)o(ts,)h(some)e(of)262 1759 y(whic)o(h)c(w)o(ere)i (explained)f(in)f(c)o(hapter)i(3.)324 1844 y(A)o(t)j(\014rst)i(sigh)o(t,)e (the)i(principle)e(v)n(ariation)f Fh(\013\014)j Fp(searc)o(h)g(\(PVS\))f(app) q(ears)h(to)e(b)q(e)h(the)262 1894 y(b)q(est)c(algorithm)c(to)i(select)j(as)e (it)f(t)o(ypically)g(visits)g(few)o(er)i(no)q(des)g(than)e(other)i Fh(\013\014)h Fp(deriv)n(a-)262 1943 y(tiv)o(es)h([40)o(].)28 b(Ho)o(w)o(ev)o(er,)19 b(I)e(in)o(tend)g(to)h(use)g(searc)o(h)g(extensions)h (whic)o(h)e(actually)g(use)h(the)262 1993 y(v)n(alues)11 b(of)h(the)g(curren) o(t)i Fh(\013\014)g Fp(windo)o(w)d(as)h(part)h(of)e(their)h(searc)o(h)h (extension)g(decision.)18 b(This)262 2043 y(breaks)13 b(one)h(of)f(the)g(ma)r (jor)f(principles)h(of)g(the)h Fh(\013\014)h Fp(algorithm)c(:-)h(the)i(v)n (alue)f(of)f(a)h(mo)o(v)o(e)f(is)262 2093 y(indep)q(enden)o(t)j(of)e(the)i Fh(\013\014)h Fp(windo)o(w)d(used)i(to)e(searc)o(h)i(it.)324 2178 y(The)h(PV)h(searc)o(h)g(uses)h(a)d(minimal)d(windo)o(w)k(as)g(its)g (basis.)25 b(When)16 b(the)h(searc)o(h)g(of)f(a)262 2228 y(subtree)c(fails)d (high)h(\(score)i Ff(\025)f Fh(\014)r Fp(\),)h(it)e(is)g(re-searc)o(hed)j (using)d(a)g(suitably)g(adjusted)h(windo)o(w.)262 2278 y(When)16 b(the)h(v)n(alue)f(is)g(not)h(dep)q(enden)o(t)h(on)e(the)h(windo)o(w)f(used,) h(ev)o(erything)g(w)o(orks)g(\014ne.)262 2328 y(Ho)o(w)o(ev)o(er,)d(if)f(the) h(v)n(alue)g(is)g(dep)q(enden)o(t,)h(a)f(situation)f(could)h(arise)h(where)g (a)f(mo)o(v)o(e)e(found)262 2377 y(whic)o(h)h(fails)g(high,)g(is)g(re-searc)o (hed)k(with)c(an)h(enlarged)g(windo)o(w,)e(only)i(to)f(fail)g(lo)o(w.)k(This) 262 2427 y(violates)g(the)h(PVS's)h(abilit)o(y)d(to)i(searc)o(h)h(minim)o(al) 14 b(trees)20 b(for)d(all)g(mo)o(v)o(es)g(except)i(those)957 2574 y(97)p eop %%Page: 98 100 98 99 bop 262 307 a Fp(whic)o(h)12 b(constitute)h(a)f(new)g(principle)g(v)n (ariation.)k(This)c(can)g(cause)i(serious)f(problems)e(not)262 357 y(only)i(for)g(the)i(e\016ciency)f(of)g(the)g(PVS,)g(but)g(also)f(for)h (its)g(correctness.)324 442 y(I)19 b(also)f(wish)i(to)f(use)h(the)g(curren)o (t)g(searc)o(h)h(windo)o(w)d(as)h(part)h(of)e(a)h(decision)g(as)h(to)262 492 y(whether)15 b(to)e(apply)g(the)h(ev)n(aluation)f(function)g(at)h(a)f (giv)o(en)g(no)q(de)h(in)f(the)i(tree.)k(After)14 b(all,)262 542 y(if)j(the)h(de\014cit)h(b)q(et)o(w)o(een)g(the)f(required)h(score)g(\()p Ff(\025)g Fh(\013)p Fp(\))f(necessary)i(to)d(e\013ect)j(the)e(searc)o(h)262 592 y(result)e(and)f(the)h(curren)o(t)g(material)e(v)n(alue)g(is)h(so)h (large)f(that)g(ev)o(en)h(the)g(maxim)n(um)11 b(p)q(osi-)262 641 y(tional)h(v)n(alue)i(cannot)g(alter)g Fh(\013)p Fp(,)f(then)i(it)e(w)o (ould)h(constitute)h(w)o(asted)f(e\013ort)h(to)f(apply)f(the)262 691 y(ev)n(aluation)f(function.)18 b(This)c(approac)o(h)f(could)h(also)f(adv) o(ersely)i(a\013ect)g(the)f(PV)g(searc)o(h.)324 777 y(These)k(problems)e (lead)g(me)g(to)g(prefer)i(an)f(aspiration)f Fh(\013\014)j Fp(searc)o(h.)27 b(Although)17 b(this)262 826 y(searc)o(h)e(algorithm)c(ma)o (y)h(still)i(giv)o(e)f(rise)i(to)f(some)f(of)h(the)g(problems)g(already)f (explained,)262 876 y(they)i(will)e(b)q(e)j(to)f(a)f(far)h(lesser)h(exten)o (t.)23 b(The)15 b(imp)q(ortan)o(t)e(asp)q(ect)j(ab)q(out)f(this)g(algorithm) 262 926 y(as)g(far)g(as)h(searc)o(h)h(extensions)f(are)g(concerned,)i(is)d (that)h(the)g Fh(\013\014)i Fp(v)n(alues)d(of)g(the)h(curren)o(t)262 976 y(windo)o(w)10 b(constitute)j(the)f(true)g(b)q(est)h(score)f(attained)g (b)o(y)f(eac)o(h)h(side.)17 b(The)12 b(only)f(exception)262 1026 y(b)q(eing)18 b(when)h(one)g(\(or)g(b)q(oth\))g(of)f(the)i(initial)c (aspiration)i Fh(\013\014)j Fp(b)q(ounds)f(are)f(still)f(b)q(eing)262 1075 y(used.)26 b(Ev)o(en)17 b(in)f(this)h(case)g(the)g(initial)e(aspiration) g(windo)o(w)h(can)g(b)q(e)i(sa)o(v)o(ed)e(and)g(tak)o(en)262 1125 y(in)o(to)d(accoun)o(t)h(b)o(y)g(the)g(searc)o(h)h(extension)g (heuristics.)324 1210 y(In)j(the)h(past,)g(I)g(ha)o(v)o(e)f(observ)o(ed)h (man)o(y)e(commercial)e(c)o(hess)20 b(programs)d(whic)o(h)i(un-)262 1260 y(doubtedly)c(use)i(an)f(aspiration)f Fh(\013\014)j Fp(searc)o(h.)25 b(I)16 b(ha)o(v)o(e)f(also)h(noticed)g(in)f(some)g(p)q(ositions,)262 1310 y(a)e(particular)g(searc)o(h)h(to)f(depth)i Fh(n)e Fp(tak)o(es)h (considerably)f(longer)g(than)h(exp)q(ected.)19 b(This)14 b(is)262 1360 y(b)q(ecause)i(of)f(a)g(problem)f(whic)o(h)h(I)g(b)q(eliev)o(e)h(can)f (b)q(e)h(solv)o(ed)f(b)o(y)g(an)g(enhancemen)o(t)h(to)f(the)262 1410 y(aspiration)g Fh(\013\014)k Fp(algorithm.)j(The)17 b(problem)e(is)h(as) g(follo)o(ws:)21 b(A)c(searc)o(h)g(to)f(depth)h Fh(n)11 b Ff(\000)g Fp(1)262 1460 y(deriv)o(es)18 b(a)f(v)n(alue)g(for)g(the)i(b)q(est)f(mo)o(v)o (e)e(found.)29 b(This)18 b(v)n(alue)f(then)h(forms)e(the)i(basis)g(b)o(y)262 1509 y(whic)o(h)e(the)h(new)g Fh(\013\014)i Fp(windo)o(w)d(is)h(set)g(for)g (the)g(next)g(iteration.)26 b(A)17 b(searc)o(h)g(to)g(the)g(next)262 1559 y(iteration)12 b(is)h(then)h(p)q(erformed.)k(If)12 b(this)i(searc)o(h)g (disco)o(v)o(ers)g(something)e(whic)o(h)h(refutes)i(its)262 1609 y(previous)f(analysis)f(\(b)q(ecause)j(of)d(the)h(horizon)g(e\013ect\),) h(eac)o(h)g(and)e(ev)o(ery)i(mo)o(v)o(e)d(ma)o(y)g(fail)262 1659 y(lo)o(w)h(in)h(turn.)21 b(This)15 b(will)e(tak)o(e)i(some)f(time)f(to)h (o)q(ccur)i(at)f(the)g(greater)h(iteration)e(depths.)262 1709 y(After)d(all)f(this)i(rather)g(w)o(asted)g(e\013ort,)g(a)f(re-searc)o(h)i (is)e(then)h(necessary)h(with)e(an)g(adjusted)262 1758 y Fh(\013\014)16 b Fp(windo)o(w.)324 1844 y(I)g(ha)o(v)o(e)h(found)f(that)g(if)g(the)h (principle)g(mo)o(v)o(e)e(fails)g(lo)o(w)h(when)h(searc)o(hed,)h(then)g(it)e (is)262 1893 y(b)q(etter)j(to)e(abandon)h(the)g(curren)o(t)h Fh(\013\014)h Fp(windo)o(w)d(immediately)l(,)f(adjust)h(it)h(and)f(restart) 262 1943 y(the)f(iteration.)25 b(I)17 b(b)q(eliev)o(e)f(this)h(to)f(b)q(e)h (a)f(b)q(etter)i(approac)o(h)e(b)q(ecause)i(if)e(the)h(b)q(est)g(mo)o(v)o(e) 262 1993 y(is)d(refuted,)i(it)f(is)f(lik)o(ely)g(that)h(all)f(other)h(mo)o(v) o(es)f(will)f(b)q(e)j(similarly)11 b(refuted)16 b(when)g(using)262 2043 y(the)f(same)f(searc)o(h)i(windo)o(w.)k(Of)15 b(course)h(this)f(ma)o(y)e (not)i(alw)o(a)o(ys)f(b)q(e)i(the)f(case,)h(ho)o(w)o(ev)o(er,)262 2093 y(I)f(b)q(eliev)o(e)h(the)g(sa)o(vings)g(will)e(clearly)h(out)o(w)o (eigh)g(an)o(y)h(time)e(lost)h(when)h(a)o(v)o(eraged)g(o)o(v)o(er)g(a)262 2143 y(n)o(um)o(b)q(er)10 b(of)g(games.)16 b(In)11 b(summary)m(,)d(b)q(oth)j (fail)e(lo)o(ws)i(and)f(fail)g(highs)g(are)i(treated)g(similarly)262 2192 y(at)h(the)i(\014rst)f(ply)m(.)324 2278 y(T)m(o)c(summarise,)f(m)o(y)g (c)o(hosen)i(main)e(searc)o(h)j(will)d(consist)i(of)f(an)h(iterativ)o(e,)g (depth)g(\014rst,)262 2327 y(aspiration)k Fh(\013\014)k Fp(searc)o(h)e(with)f (the)h(enhancemen)o(ts)g(outlined)f(ab)q(o)o(v)o(e.)25 b(The)17 b Fh(\013\014)h Fp(windo)o(w)262 2377 y(will)d(b)q(e)i(based)h(around)f(the)g (result)h(of)e(the)i(previous)f(iteration)g(at)f(depths)i Ff(\025)f Fp(2.)27 b(The)262 2427 y(initial)11 b(iteration)j(windo)o(w)f(will)f(b)q(e)j (based)f(on)g(a)g(preliminary)d(analysis.)957 2574 y(98)p eop %%Page: 99 101 99 100 bop 262 307 a Fr(5.2)69 b(Searc)n(h)23 b(Extensions)262 434 y Fp(The)12 b(basic)g(approac)o(h)g(when)g(using)f(an)o(y)h(of)f(the)h Fh(\013\014)j Fp(deriv)n(ativ)o(es)c(is)h(to)g(searc)o(h)h(to)e(a)h(depth)262 483 y(n,)17 b(ev)n(aluate)f(the)i(leaf)e(no)q(des)i(and)f(minim)o(ax)d(the)j (results.)28 b(This)17 b(metho)q(d)f(exempli\014es)262 533 y(the)e(full)f(width)g(approac)o(h.)18 b(Ho)o(w)o(ev)o(er,)c(it)g(su\013ers)h (from)d(a)i(n)o(um)o(b)q(er)f(of)g(w)o(eaknesses:)312 652 y(1.)20 b(The)15 b(searc)o(h)g(is)e(terminated)h(at)g(a)f(\014xed)h(depth,)h (therefore,)g(the)f(ev)n(aluation)f(func-)365 701 y(tion)h(ma)o(y)e(b)q(e)j (applied)f(to)g(non)g(quiescen)o(t)i(p)q(ositions)e(leading)f(to)h(grossly)h (inaccu-)365 751 y(rate)g(results.)312 834 y(2.)20 b(This)c(approac)o(h)g (mak)o(es)e(ine\016cien)o(t)i(use)h(of)e(the)i Fh(\013\014)h Fp(algorithm)13 b(b)q(ecause)k(its)f(leaf)365 884 y(no)q(des)f(are)f (inaccurately)g(ev)n(aluated.)312 967 y(3.)20 b(Equal)14 b(e\013ort)g(is)g (applied)f(throughout)h(the)g(tree)i(with)d(resp)q(ect)j(to)e(depth.)19 b(There-)365 1017 y(fore,)c(stupid)g(unin)o(teresting)g(v)n(ariations)e(are)i (explored)g(as)g(deeply)g(as)g(in)o(teresting)365 1067 y(or)f(go)q(o)q(d)g(v) n(ariations.)312 1150 y(4.)20 b(The)15 b(horizon)e(e\013ect)j(is)e(sev)o (erely)h(exasp)q(erated)g(b)o(y)f(the)g(\014xed)h(depth)f(searc)o(h.)262 1268 y(The)e(\014rst)g(t)o(w)o(o)f(problem)g(areas)h(can)g(b)q(e)g (signi\014can)o(tly)f(eased)i(b)o(y)e(the)h(use)h(of)e(a)g(quiescence)262 1318 y(searc)o(h)j(at)f(the)h(leaf)f(\(horizon\))h(no)q(des)g(of)f(a)g(main)e (searc)o(h.)20 b(This)13 b(quiescence)i(searc)o(h)g(will)262 1368 y(b)q(e)i(a)f(form)f(of)h(selectiv)o(e)i(searc)o(h,)g(only)e(exploring)f (tactical)i(p)q(ossibilities.)25 b(See)18 b(section)262 1418 y(5.4)12 b(for)i(more)f(details.)324 1503 y(It)f(is)g(surprising)g(ho)o(w)f (man)o(y)f(commercial)f(and)j(tournamen)o(t)f(c)o(hess)j(programs)c(su\013er) 262 1553 y(from)16 b(the)i(third)g(problem)e(area.)30 b(I)18 b(b)q(eliev)o(e)g(the)g(solution)f(to)h(this)g(problem)e(lies)i(in)f(a)262 1603 y(program's)8 b(abilit)o(y)h(to)h(select)i(and)e(searc)o(h)i(in)o (teresting)f(or)f(go)q(o)q(d)g(v)n(ariations)g(more)f(deeply)m(.)324 1688 y(Harris)j([26)o(])f(prop)q(osed)i(a)e(similar)e(idea)j(of)f(exploring)g (in)o(teresting)h(v)n(ariations,)e(except)262 1738 y(he)i(suggested)i(doing)e (so)g(without)g(the)h Fh(\013\014)i Fp(algorithm.)g(Harris)e(omitted)e(sp)q (eci\014c)j(details)262 1787 y(of)i(ho)o(w)i(his)f(ideas)h(migh)o(t)d(b)q(e)k (implem)o(en)o(ted.)27 b(Levy)18 b(et)g(al)f([38)o(])g(ha)o(v)o(e)h(implem)o (en)o(ted)e(a)262 1837 y(n)o(um)o(b)q(er)e(of)g(programs)g(using)g(the)i (idea)e(of)h(in)o(terestingness,)h(ho)o(w)o(ev)o(er,)f(their)h(approac)o(h) 262 1887 y(to)10 b(classifying)g(in)o(teresting)i(mo)o(v)o(es)e(di\013ers)i (from)d(the)j(approac)o(h)f(I)g(am)e(taking.)17 b(In)11 b(partic-)262 1937 y(ular,)h(m)o(y)g(use)i(of)f(the)h(aspiration)e Fh(\013\014)k Fp(searc)o(h)e(and)g(its)f(b)q(ounds)h(in)f(m)o(y)e(searc)o(h)k(extension)262 1987 y(heuristics)g(is)e(no)o(v)o(el.)324 2072 y(I)j(de\014ne)i(an)e(in)o (teresting)h(v)n(ariation)e(as)i(one)f(whic)o(h)h(con)o(tains)f(tactical)g (mo)o(v)o(es)g(that)262 2122 y(o\013er)c(some)f(p)q(ossibilit)o(y)g(of)g (a\013ecting)h(the)h(searc)o(h)g(result,)g(e.g.)k(pro)q(ducing)12 b(a)g(score)h(whic)o(h)262 2172 y(is)h(inside)h(the)h Fh(\013\014)h Fp(searc)o(h)f(windo)o(w.)k(I)15 b(de\014ne)h(go)q(o)q(d)e(v)n(ariations)g (as)h(those)h(whic)o(h)e(w)o(ould)262 2221 y(a\013ect)g(the)h(searc)o(h)g (result)g(if)e(the)h(searc)o(h)h(w)o(ere)g(terminated)e(immediately)l(.)324 2307 y(Applying)j(these)j(de\014nitions)f(to)f(create)i(searc)o(h)g (extension)f(heuristics,)h(I)f(hop)q(e)g(to)262 2356 y(encourage)f(the)g (searc)o(h)h(to)e(explore)h(v)n(ariations)f(o\013ering)g(some)g(lik)o(eliho)q (o)q(d)f(of)h(success,)262 2406 y(and)c(ignore)h(unin)o(teresting)h(v)n (ariations)d(whic)o(h)i(o\013er)h(little)e(or)h(no)g(lik)o(eliho)q(o)q(d)e (of)i(success.)957 2574 y(99)p eop %%Page: 100 102 100 101 bop 262 307 a Fp(This)12 b(approac)o(h)g(sho)o(ws)h(some)f (similarities)e(to)i(the)h(w)o(a)o(y)f(h)o(umans)f(pla)o(y)h(the)h(game.)j (Ho)o(w-)262 357 y(ev)o(er,)j(b)q(ecause)h(these)f(heuristics)h(are)e(far)g (less)g(sophisticated)h(than)f(a)g(strong)g(h)o(uman)262 407 y(c)o(hess)f(pla)o(y)o(ers,)f(the)g(program)f(will)f(attempt)h(to)h(bridge)g (this)g(gap)g(b)o(y)f(exploring)g(man)o(y)262 457 y(more)c(v)n(ariations)h (than)h(its)f(h)o(uman)f(coun)o(ter)j(part.)k(These)c(searc)o(h)g(extension)f (heuristics)262 506 y(m)o(ust)i(therefore)i(b)q(e)g(free)g(enough)f(to)g (extend)h(man)o(y)d(in)o(teresting)j(v)n(ariations,)e(but)h(also)262 556 y(b)q(e)d(selectiv)o(e)h(enough)e(to)h(a)o(v)o(oid)e(the)i(searc)o(h)h (blo)o(wing)d(sky)i(high.)k(A)c(searc)o(h)h(whic)o(h)e(is)h(not)262 606 y(depth)i(limited)e(and)i(can)h(explore)f(in)o(teresting)h(v)n(ariations) e(deeply)m(,)h(is)g(m)o(uc)o(h)f(less)i(lik)o(ely)262 656 y(to)d(su\013er)i (from)e(the)h(horizon)g(e\013ect)h(\(problem)e(area)h(4\).)324 741 y(In)j(order)h(to)f(determine)g(what)g(is)g(an)g(in)o(teresting)h(or)f (go)q(o)q(d)f(v)n(ariation,)g(mo)o(v)o(es)g(are)262 791 y(classi\014ed)d(and) f(receiv)o(e)i('p)q(oin)o(ts')d(dep)q(ending)i(on)g(ho)o(w)f(dynamic)f(eac)o (h)i(mo)o(v)o(e)e(is.)17 b(In)o(terest)262 841 y(p)q(oin)o(ts)d(are)i(passed) g(do)o(wn)e(the)i(searc)o(h)g(tree)g(from)d(no)q(de)j(to)f(no)q(de.)21 b(Eac)o(h)16 b(ply)e(of)g(searc)o(h)262 891 y(deducts)i(16)e(p)q(oin)o(ts)g (w)o(orth)h(of)f(in)o(terest)i(from)c(the)k(v)n(ariation.)i(When)d(the)g(in)o (terest)h(falls)262 940 y(b)q(elo)o(w)f(zero,)j(the)e(no)q(de)h(will)e(b)q(e) h(considered)i(as)e(a)g(leaf)g(or)g(horizon)g(no)q(de)g(of)g(the)h(main)262 990 y(searc)o(h.)33 b(A)o(t)18 b(this)h(p)q(oin)o(t)f(a)g(quiescence)j (decision)e(is)f(made,)g(leading)g(to)g(a)g(quiescence)262 1040 y(searc)o(h)d(or)e(con)o(tin)o(uation)g(of)h(the)g(main)e(searc)o(h.)324 1125 y(All)e(in)o(teresting)h(mo)o(v)o(es)f(are)h(classi\014ed)h(under)g(t)o (w)o(o)e(categories,)i(Threats)g(and)f(Threat)262 1175 y(Execution.)262 1326 y Fu(5.2.1)55 b(Threats)262 1438 y Fp(F)m(or)18 b(threatening)i(mo)o(v)o (es)e(to)i(b)q(e)g(considered)g(in)o(teresting)g(they)g(m)o(ust)e(indicate)h (some)262 1488 y(lik)o(eliho)q(o)q(d)14 b(of)h(a\013ecting)h(the)h(searc)o(h) g(result)g(and)f(therefore)h(b)q(ecoming)e(the)i(main)d(line.)262 1538 y(Assuming)j(a)i(negamax)e(approac)o(h,)j(the)f(no)q(de)h(resulting)f (from)e(a)i(threatening)g(mo)o(v)o(e)262 1588 y(m)o(ust)12 b(meet)i(the)g(follo)o(wing)e(criteria:)344 1683 y(Est)j(+)f(Thres)h Fh(>)d(\013)h Fl(or)h Fh(\013)f Fp(=)h(Aspir)p Fh(\013)262 1783 y Fl(where)312 1904 y Fp(1.)20 b Fl(Est)p Fp(:)j(This)17 b(is)f(an)g(estimate)g(of)g(the)h(curren)o(t)h(no)q(de's)f(v)n(alue,)f (mostly)f(dominated)365 1954 y(b)o(y)f(material.)312 2036 y(2.)20 b Fl(Thres)p Fp(:)c(Represen)o(ts)e(the)e(v)n(alue)f(of)g(ha)o(ving)g(the)h (mo)o(v)o(e)e(\(a)i(temp)q(o\))e(and)i(what)g(that)365 2086 y(mo)o(v)o(e)h(migh)o(t)e(ac)o(hiev)o(e.)312 2168 y(3.)20 b Fh(\013)p Fp(:)f(This)c(is)f(the)h(curren)o(t)h(v)n(alue)e(of)g(alpha)f(at)i (this)f(no)q(de,)h(whic)o(h)f(therefore)i(repre-)365 2218 y(sen)o(ts)e (either)g(the)f(v)n(alue)f(of)g(the)h(b)q(est)h(v)n(ariation)c(found)j(for)f (this)h(side)g(elsewhere)h(in)365 2267 y(the)h(searc)o(h)g(tree)g(or)f(an)f (initial)f(aspiration)h(v)n(alue.)312 2350 y(4.)20 b Fl(Aspir)p Fh(\013)p Fp(:)15 b(This)d(is)f(the)i(initial)d(aspiration)g(v)n(alue)i(used) g(for)g(the)g(b)q(est)h(v)n(alue)e(ac)o(hiev-)365 2399 y(able)k(b)o(y)g(the)h (curren)o(t)h(side)f(to)f(mo)o(v)o(e.)21 b(A)o(t)15 b(ev)o(en)h(depths)g(b)q (elo)o(w)f(the)h(ro)q(ot,)f(this)h(is)365 2449 y(the)f(initial)d Fh(\013)h Fp(v)n(alue;)g(at)h(o)q(dd)g(depths,)g(it)g(is)f(the)i(initial)d Fh(\014)k Fp(v)n(alue.)946 2574 y(100)p eop %%Page: 101 103 101 102 bop 262 307 a Fp(The)11 b(idea)f(of)g(this)g(heuristic)i(is)e(to)h (exclude)g(mo)o(v)o(es)e(whic)o(h)i(ma)o(y)d(otherwise)k(b)q(e)f(in)o (teresting)262 357 y(if)e(they)i(are)g(unlik)o(ely)f(to)g(c)o(hange)h(the)g (curren)o(t)i Fh(\013)d Fp(v)n(alue.)16 b(This)11 b(v)n(alue)f(after)g(all,)g (represen)o(ts)262 407 y(the)g(score)i(of)e(the)g(b)q(est)i(v)n(ariation)c (that)j(the)g(side)f(to)g(mo)o(v)o(e)f(can)h(ac)o(hiev)o(e.)17 b(Of)11 b(course)g(if)f(this)262 457 y(score)15 b(happ)q(ens)g(to)g(b)q(e)g (an)f(aspiration)g(v)n(alue,)f(then)i(the)g(score)h(of)d(the)i(b)q(est)h(v)n (ariation)d(is)262 506 y(not)d(y)o(et)h(kno)o(wn,)f(it)g(w)o(ould)g (therefore)i(b)q(e)f(un)o(wise)g(to)f(assume)g(that)h(the)g(curren)o(t)h(v)n (ariation)262 556 y(cannot)i(a\013ect)g(the)h(searc)o(h)g(result.)324 641 y(The)e(e\013ect)h(of)d(this)i(heuristic)g(is)f(to)g(a)o(v)o(oid)f (extending)i(when)g(the)g(line)f(app)q(ears)h(fruit-)262 691 y(less)j(relativ)o(e)g(to)f(what)h(can)g(b)q(e)h(ac)o(hiev)o(ed)f(elsewhere)h (in)f(the)g(tree.)25 b(F)m(or)16 b(example,)e(it)i(is)262 741 y(lik)o(ely)e(to)i(b)q(e)h(w)o(orthless)g(exploring)f(a)f(v)n(ariation)g (whic)o(h)h(wins)g(a)g(pa)o(wn)g(after)g(thro)o(wing)262 791 y(a)o(w)o(a)o(y)10 b(a)h(queen,)h(when)g(another,)g(b)q(etter)h(v)n(ariation) c(is)j(already)f(kno)o(wn)f(to)i(b)q(e)g(ac)o(hiev)n(able.)324 876 y(Giv)o(en)i(that)i(the)g(ab)q(o)o(v)o(e)f(criteria)g(are)h(met,)f(the)g (follo)o(wing)e(threatening)j(mo)o(v)o(es)e(are)262 926 y(classi\014ed)e(and) g(the)g(appropriate)g(in)o(terest)h(p)q(oin)o(ts)f(added)g(to)f(the)i(curren) o(t)g(in)o(terest)g(v)n(alue)262 976 y(at)g(this)h(no)q(de.)312 1093 y(1.)20 b Fl(In-c)o(hec)o(k)15 b(with)g(one)g(legal)f(reply)365 1159 y Fp(This)c(heuristic)g(pro)o(vides)f(a)h(searc)o(h)g(extension)g(along) f(v)n(ariations)f(whic)o(h)h(are)h(highly)365 1209 y(forced.)21 b(Often)15 b(mating)d(sequences)17 b(in)o(v)o(olv)o(e)c(forced)i(c)o(hec)o (ks)h(where)f(there)h(is)e(only)365 1258 y(one)g(legal)f(resp)q(onse.)20 b Fm(R)n(e)n(c)n(eives)15 b(24)g(p)n(oints)g(of)g(inter)n(est)p Fp(.)312 1341 y(2.)20 b Fl(Double)14 b(Chec)o(k)365 1407 y Fp(This)k(heuristic)h(pro)o(vides)f(a)f(searc)o(h)j(extension)e(when)g(a)g (side)g(is)g(in-c)o(hec)o(k)g(from)365 1456 y(more)12 b(than)h(one)h(piece.)k 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Fm(R)n(e)n(c)n(eives)c (20)h(p)n(oints)g(of)365 1953 y(inter)n(est.)312 2036 y Fp(4.)k Fl(In-c)o(hec)o(k)15 b(with)g(no)g(legal)g(king)f(reply)365 2102 y Fp(This)f(heuristic)h(pro)o(vides)f(a)g(searc)o(h)h(extension)g(when)g (a)e(side)i(is)f(in-c)o(hec)o(k)g(and)g(the)365 2151 y(king)e(has)g(no)g (legal)f(escap)q(e)j(mo)o(v)o(es.)j(The)11 b(idea)g(b)q(eing)g(to)g(iden)o (tify)f(p)q(ossible)i(mating)365 2201 y(nets.)19 b Fm(R)n(e)n(c)n(eives)c(20) h(p)n(oints)f(of)f(inter)n(est.)312 2283 y Fp(5.)20 b Fl(In-c)o(hec)o(k)15 b(with)g(more)g(than)g(one)g(legal)f(reply)365 2350 y Fp(This)i(heuristic)h (is)e(common)e(to)j(a)f(n)o(um)o(b)q(er)h(of)f(top)g(programs,)g(Hitec)o(h)h (included)365 2399 y([7].)j(Ho)o(w)o(ev)o(er,)c(m)o(y)d(program)h(is)i(more)e (selectiv)o(e)j(b)q(ecause)g(this)f(heuristic)g(is)f(only)365 2449 y(applied)k(where)i(the)f(searc)o(h)h(result)f(is)g(lik)o(ely)e(to)h(b)q (e)h(a\013ected.)34 b(I)18 b(feel)h(this)f(is)h(a)946 2574 y(101)p eop %%Page: 102 104 102 103 bop 365 307 a Fp(signi\014can)o(t)21 b(adv)n(an)o(tage)e(o)o(v)o(er)i (its)g(otherwise)h(unrestricted)h(application.)37 b(It)21 b(is)365 357 y(imp)q(ortan)o(t)14 b(to)i(explore)g(in)f(c)o(hec)o(k)i(v)n(ariations)d (throughly)h(b)q(ecause)j(other)e(tactics)365 407 y(ma)o(y)c(\015o)o(w)i (from)e(a)h(c)o(hec)o(k.)19 b Fm(R)n(e)n(c)n(eives)c(16)h(p)n(oints)f(of)f (inter)n(est.)312 488 y Fp(6.)20 b Fl(P)o(a)o(wn)15 b(mo)o(v)o(es)g(to)h(the) e(7th)h(Rank)365 553 y Fp(This)22 b(heuristic)g(encourages)h(exploration)e (of)g(v)n(ariations)f(where)j(the)f(pa)o(wn)g(is)365 603 y(pushed)15 b(near)g(to)e(promotion.)j Fm(R)n(e)n(c)n(eives)f(16)g(p)n(oints)g(of)g (inter)n(est.)312 684 y Fp(7.)20 b Fl(P)o(a)o(wn)15 b(mo)o(v)o(es)g(to)h(the) e(6th)h(Rank)365 749 y Fp(This)g(is)g(a)f(subset)j(of)d(the)h(ab)q(o)o(v)o(e) g(heuristic)g(and)g(serv)o(es)i(to)d(increase)i(exploration)365 799 y(of)e(p)q(ositions)g(where)i(passed)f(pa)o(wns)g(can)g(b)q(e)g(pushed,)g (esp)q(ecially)g(in)f(or)g(near)h(the)365 849 y(endgame.)i Fm(R)n(e)n(c)n(eives)e(r)n(evPhase)g(p)n(oints)g(of)g(inter)n(est.)312 929 y Fp(8.)20 b Fl(Piece)15 b(Threats)365 995 y Fp(The)d(follo)o(wing)d (searc)o(h)k(heuristics)g(are)f(concerned)i(with)d(threats)i(on)e(pieces)i (of)e(the)365 1045 y(side)k(curren)o(tly)f(to)g(mo)o(v)o(e:)383 1125 y(\(a\))21 b Fl(More)15 b(than)g(one)g(piece)g(is)g(en-prise)457 1182 y Fm(R)n(e)n(c)n(eives)g(16)g(p)n(oints)g(of)g(inter)n(est.)381 1247 y Fp(\(b\))21 b Fl(A)16 b(pinned)d(piece)h(whic)o(h)h(is)g(en-prise)457 1304 y Fm(R)n(e)n(c)n(eives)g(16)g(p)n(oints)g(of)g(inter)n(est.)385 1368 y Fp(\(c\))22 b Fl(A)16 b(trapp)q(ed)e(piece)g(whic)o(h)h(is)g(en-prise) 457 1425 y Fm(R)n(e)n(c)n(eives)g(16)g(p)n(oints)g(of)g(inter)n(est.)365 1506 y Fp(These)22 b(heuristics)g(pro)o(vide)e(searc)o(h)h(extensions)h (along)d(v)n(ariations)g(of)h(complex)365 1556 y(dynamic)c(p)q(ossibilities.) 30 b(The)18 b(quiescence)i(searc)o(h)f(will)d(resolv)o(e)i(suc)o(h)h(p)q (ositions)365 1605 y(when)f(the)h(threatened)g(pla)o(y)o(er)e(is)h Fl(not)e Fp(to)i(mo)o(v)o(e.)27 b(Hence)19 b(these)g(heuristics)g(are)365 1655 y(only)d(applied)h(in)f(p)q(ositions)h(where)h(the)f(threatened)i(pla)o (y)o(er)e(has)g(the)g(mo)o(v)o(e.)26 b(In)365 1705 y(this)11 b(w)o(a)o(y)f(the)i(pla)o(y)o(er)e(m)o(ust)g(sho)o(w)h(the)g(existence)i(of)d (an)g(adequate)i(defensiv)o(e)f(mo)o(v)o(e)365 1755 y(or)j(the)h(ensuing)f (quiescence)i(searc)o(h)f(will)d(refute)j(the)g(v)n(ariation.)312 1836 y(9.)20 b Fl(Mate)c(threat)e(against)h(the)g(side)f(to)h(mo)o(v)o(e)365 1901 y Fp(This)10 b(heuristic)g(pro)o(vides)g(a)g(searc)o(h)g(extension)h (when)f(mate)e(is)i(directly)g(threatened)365 1951 y(against)i(the)i(side)f (to)f(mo)o(v)o(e.)k(This)d(will)e(force)j(exploration)d(of)i(v)n(ariations)e (to)i(sho)o(w)365 2001 y(whether)18 b(the)e(mate)f(threat)i(can)f(b)q(e)g (defended)h(against.)24 b Fm(R)n(e)n(c)n(eives)17 b(24)g(p)n(oints)g(of)365 2051 y(inter)n(est.)262 2165 y Fp(Searc)o(h)c(heuristics)h(8a,)e(8b,)h(8c)g (and)f(9)h(are)g(only)f(applied)g(during)h(the)g(quiescence)i(searc)o(h)262 2214 y(after)k(a)g(full)g(p)q(ositional)f(ev)n(aluation.)33 b(An)o(y)19 b(of)g(the)h(heuristics)h(1)e(through)g(6)g(can)h(b)q(e)262 2264 y(applied)14 b(in)g(either)i(the)g(main)c(or)j(quiescence)i(searc)o (hes.)23 b(More)16 b(details)f(ab)q(out)f(this)h(can)262 2314 y(b)q(e)f(found)f(in)h(sections)h(5.3)e(and)g(5.4.)18 b(Heuristics)d(1)e(to)h (5)g(are)g(m)o(utually)d(exclusiv)o(e.)324 2399 y(Eac)o(h)h(ply)f(of)g(searc) o(h)i(consumes)f(16)g(in)o(terest)h(p)q(oin)o(ts.)k(It)12 b(can)g(therefore)h (b)q(e)f(seen)i(that)262 2449 y(some)j(heuristics)j(whic)o(h)e(equal)g(or)h (exceed)h(an)e(in)o(terest)i(v)n(alue)e(of)g(16)g(ma)o(y)e(in)i(theory)946 2574 y(102)p eop %%Page: 103 105 103 104 bop 262 307 a Fp(cause)15 b(the)f(searc)o(h)h(to)f(b)q(e)h(un)o(b)q (ounded.)j(Ho)o(w)o(ev)o(er,)c(in)g(practice)h(this)f(should)g(not)f(b)q(e)i (the)262 357 y(case)f(as:)324 464 y Ff(\017)20 b Fp(It)14 b(is)g(rare)h(to)e (get)h(out)g(of)g(c)o(hec)o(k)g(with)g(a)g(c)o(hec)o(k)g(mo)o(v)o(e)f (itself.)324 541 y Ff(\017)20 b Fp(Heuristics)15 b(8a,)d(8b,)h(8c)g(and)g(9)g (are)g(only)g(applied)f(once)i(or)f(t)o(wice)h(do)o(wn)e(an)o(y)h(giv)o(en) 365 591 y(v)n(ariation.)324 669 y Ff(\017)20 b Fp(Heuristics)15 b(6)f(and)g(7)f(are)i(self)f(limiti)o(ng)d(as)j(a)g(pa)o(wn)f(can)h(only)f (mo)o(v)o(e)g(forw)o(ard.)262 776 y(F)m(or)19 b(added)i(protection)g(against) e(an)h(un)o(b)q(ounded)h(searc)o(h,)h(all)d(no)q(des)i(visited)f(in)g(the)262 826 y(main)9 b(searc)o(h)14 b(whic)o(h)e(are)g(deep)q(er)i(than)e(t)o(wice)g (the)h(iteration)e(depth,)i(ha)o(v)o(e)f(their)g(in)o(terest)262 875 y(v)n(alue)e(decreased)k(b)o(y)d(the)h(amoun)o(t)e(whic)o(h)h(the)h (curren)o(t)h(ply)e(exceeds)i(t)o(wice)f(the)g(iteration)262 925 y(depth.)262 1074 y Fu(5.2.2)55 b(Threat)18 b(Execution)262 1186 y Fp(The)d(execution)h(of)f(a)g(previous)h(threat)g(is)f(only)f(in)o (teresting)i(if)e(at)i(the)g(curren)o(t)g(no)q(de)g(it)262 1236 y(lo)q(oks)d(lik)o(ely)f(to)i(a\013ect)h(the)f(searc)o(h)h(result.)324 1322 y(F)m(or)20 b(an)o(y)g(mo)o(v)o(e)e(whic)o(h)i(constitutes)i(the)f (execution)g(of)f(a)g(threat,)i(the)f(follo)o(wing)262 1371 y(criteria)14 b(m)o(ust)f(b)q(e)h(meet)g(for)f(the)i(mo)o(v)o(e)d(to)i(b)q(e) g(further)h(considered)g(as)f(in)o(teresting:)344 1457 y(Est)h Ff(\000)f Fp(Thres)h Fh(<)d(\014)k Fl(or)e Fh(\014)i Fp(=)e(Aspir)p Fh(\014)262 1557 y Fl(where)312 1656 y Fp(1.)20 b Fl(Est)p Fp(:)j(This)17 b(is)f(an)g(estimate)g(of)g(the)h(curren)o(t)h(no)q(de's)f(v)n (alue,)f(mostly)f(dominated)365 1706 y(b)o(y)f(material)e(v)n(alues.)312 1783 y(2.)20 b Fl(Thres)p Fp(:)c(Represen)o(ts)e(the)e(v)n(alue)f(of)g(ha)o (ving)g(the)h(mo)o(v)o(e)e(\(a)i(temp)q(o\))e(and)i(what)g(that)365 1833 y(mo)o(v)o(e)h(migh)o(t)e(ac)o(hiev)o(e.)312 1910 y(3.)20 b Fh(\014)r Fp(:)d(This)10 b(is)g(the)h(curren)o(t)h(v)n(alue)d(of)h(b)q(eta) g(at)g(this)g(no)q(de,)h(whic)o(h)f(therefore)i(represen)o(ts)365 1960 y(either)k(the)g(v)n(alue)e(of)h(the)g(b)q(est)h(v)n(ariation)e(found)g (for)h(this)g(side)g(elsewhere)i(in)e(the)365 2010 y(searc)o(h)g(tree)g(or)f (an)g(initial)e(aspiration)h(v)n(alue.)312 2087 y(4.)20 b Fl(Aspir)p Fh(\014)r Fp(:)c(This)c(is)g(the)g(initial)e(aspiration)h(v)n(alue)g(used)i (for)e(the)i(b)q(est)g(v)n(alue)e(ac)o(hiev-)365 2137 y(able)k(b)o(y)f(the)h (side)g Fl(not)f Fp(to)g(mo)o(v)o(e.)19 b(A)o(t)c(ev)o(en)g(depths)h(b)q(elo) o(w)e(the)h(ro)q(ot,)g(this)f(is)h(the)365 2187 y(initial)d Fh(\014)17 b Fp(v)n(alue;)12 b(at)i(o)q(dd)g(depths,)h(it)e(is)h(the)g (initial)e Fh(\013)i Fp(v)n(alue.)262 2300 y(This)20 b(heuristic)h(is)f (almost)f(an)h(exact)h(mirror)e(image)f(of)i(the)h(one)g(used)g(for)f (threats.)262 2350 y(Giv)o(en)e(that)h(the)h(ab)q(o)o(v)o(e)f(criteria)g(are) h(met,)f(the)h(follo)o(wing)c(threat)k(execution)g(mo)o(v)o(es)262 2399 y(are)13 b(classi\014ed)g(and)g(their)g(appropriate)g(in)o(terest)g(p)q (oin)o(ts)g(added)g(to)g(the)g(curren)o(t)h(in)o(terest)262 2449 y(v)n(alue)f(at)g(this)h(no)q(de.)946 2574 y(103)p eop %%Page: 104 106 104 105 bop 312 307 a Fp(1.)20 b Fl(Capture)365 374 y Fp(This)h(heuristic)h (encourages)g(exploration)e(of)g(in)o(teresting)i(capture)g(sequences.)365 423 y(P)o(articularly)c(where)h(greater)g(v)n(alued)e(pieces)j(are)e(in)o(v)o (olv)o(ed.)30 b Fm(R)n(e)n(c)n(eives)18 b(inter)n(est)365 473 y(p)n(oints)d(dep)n(ending)h(on)f(the)f(typ)n(e)h(of)g(pie)n(c)n(e)f(c)n (aptur)n(e)n(d,)g(wher)n(e)g(p)n(awn)h(=)f(1;)h(knight)g(=)365 523 y(2;)g(bishop)g(=)g(3;)g(r)n(o)n(ok)g(=)f(4)h(and)h(que)n(en)g(=)e(5.)312 606 y Fp(2.)20 b Fl(P)o(a)o(wn)15 b(Promotion)365 672 y Fp(This)d(heuristic)g (also)f(encourages)i(exploration)d(of)h(v)n(ariations)f(whic)o(h)i(are)g(in)o (terest-)365 722 y(ing.)20 b(Assuming)13 b(the)i(promoted)f(pa)o(wn)g(cannot) h(b)q(e)g(captured,)h(the)f(mo)o(v)o(e)e(is)h(v)o(ery)365 772 y(lik)o(ely)k(to)h(b)q(e)h(go)q(o)q(d)f(and)g(therefore)h(in)o(teresting.)35 b(If,)19 b(ho)o(w)o(ev)o(er,)i(the)f(promoted)365 822 y(pa)o(wn)13 b(can)h(b)q(e)g(captured,)g(the)g(opp)q(onen)o(ts)h(options)e(ha)o(v)o(e)g(a) g(degree)i(of)e(forcedness)365 872 y(ab)q(out)k(them)f(whic)o(h)h(therefore,) h(also)e(mak)o(es)g(this)h(mo)o(v)o(e)e(in)o(teresting.)28 b Fm(R)n(e)n(c)n(eives)365 922 y(inter)n(est)13 b(p)n(oints)g(dep)n(ending)i (on)f(the)f(typ)n(e)h(of)f(pie)n(c)n(e)h(pr)n(omote)n(d)f(to,)g(wher)n(e)g (knight)h(=)365 971 y(1;)h(bishop)g(=)g(2;)g(r)n(o)n(ok)g(=)f(3)h(and)h(que)n (en)g(=)e(4.)312 1054 y Fp(3.)20 b Fl(Recapture)365 1121 y Fp(This)12 b(heuristic)g(is)f(used)i(in)e(Hitec)o(h)h([7)o(].)17 b(I)12 b(feel)f(it)g(is)h(of)f(great)h(b)q(ene\014t)g(in)g(that)f(it)g(en-) 365 1171 y(courages)j(not)e(only)g(exploration)g(of)g(simple)f(exc)o(hanges,) j(but)f(also)f(captures)i(with)365 1220 y(p)q(ositional)h(con)o(ten)o(t)i (e.g.)25 b(a)16 b(ro)q(ok)g(exc)o(hanged)h(for)f(knigh)o(t)f(and)h(p)q (ositional)f(com-)365 1270 y(p)q(ensation.)k(This)14 b(heuristic)h(is)f(only) f(applied)28 b(if:)17 b Ff(j)p Fh(LastS)r(ear)q(chV)11 b(al)q(ue)e Ff(\000)h Fh(E)r(st)p Ff(j)h(\024)365 1320 y Fp(25)18 b(and)h(the)g(last)g(2) f(mo)o(v)o(es)f(pla)o(y)o(ed)h(w)o(ere)i(captures.)66 b Fm(R)n(e)n(c)n(eives) 20 b(16)f(p)n(oints)h(of)365 1370 y(inter)n(est.)312 1453 y Fp(4.)g Fl(Mate)c(Threat)f(against)f(the)h(side)g(not)g(to)g(mo)o(v)o(e)365 1519 y Fp(This)20 b(heuristic)g(is)g(only)f(applied)g(during)g(the)i (quiescence)h(searc)o(h)e(after)g(a)g(full)365 1569 y(p)q(osition)15 b(ev)n(aluation.)20 b(It)15 b(is)g(extremely)g(useful)g(for)g(a)o(v)o(oiding) e(early)i(termination)365 1619 y(of)e(the)h(searc)o(h)h(in)d(p)q(ossible)i (mating)d(sequences.)21 b Fm(R)n(e)n(c)n(eives)14 b(16)h(p)n(oints)f(of)h (inter)n(est.)262 1737 y Fp(It)g(should)h(b)q(e)g(noticed)g(that)f(some)g(of) 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y(searc)o(h)20 b(extensions.)35 b(Ho)o(w)o(ev)o(er,)21 b(I)e(ha)o(v)o(e)g(managed)f(to)h (incorp)q(orate)h(dynamic)d(searc)o(h)262 2221 y(information)7 b(in)o(to)i(the)i(searc)o(h)g(heuristics)g(without)e(added)i(cost.)17 b(This)10 b(allo)o(ws)f(the)h(searc)o(h)262 2271 y(heuristics)21 b(to)g(b)q(e)g(quite)f(selectiv)o(e)i(ab)q(out)e(whic)o(h)h(v)n(ariations)e (are)i(w)o(orth)g(extending.)262 2321 y(Additionally)m(,)9 b(some)j(of)f(m)o(y)g(searc)o(h)i(extension)g(heuristics)h(can)e(extend)i (non{forced)e(but)262 2371 y(still)g(in)o(teresting)j(v)n(ariations.)i(I)c (see)j(this)e(as)g(an)f(adv)n(an)o(tage)g(o)o(v)o(er)h(singular)f (extensions.)946 2574 y(104)p eop %%Page: 105 107 105 106 bop 324 307 a Fp(T)m(o)12 b(illustrate)i(ho)o(w)f(these)i(extension)f (heuristics)g(are)g(able)f(to)h(iden)o(tify)e(deep)j(com)o(bi-)262 357 y(nations,)e(I)g(will)g(apply)g(them)g(to)h(the)g(p)q(osition)f(sho)o(wn) h(in)g(\014gure)g(5.1.)p 641 451 673 5 v 641 1115 5 665 v 646 534 a Fg(0ZqsrZnZ)646 617 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b(If)14 b(so,)f(the)h(en)o(try)h(can) f(b)q(e)h(retriev)o(ed.)324 2004 y(Once)j(retriev)o(ed,)h(the)e(en)o(try's)h (p)q(osition)e(score)j(can)e(b)q(e)g(used.)29 b(Dep)q(ending)17 b(on)g(the)262 2054 y(score's)e(t)o(yp)q(e,)e(3)h(outcomes)f(are)i(p)q (ossible.)312 2169 y(1.)20 b Fl(T)l(rue)c(Score)p Fp(:)i(The)d(v)n(alue)f (stored)h(is)g(an)f(exactly)g(calculated)h(v)n(alue.)k(Therefore,)365 2219 y(the)c(v)n(alue)e(of)g(this)h(no)q(de)g(and)g(its)f(subtree)j(is)e(kno) o(wn)f(\(for)h(the)g(required)h(depth)f(of)365 2268 y(searc)o(h\))h(and)f (can)g(b)q(e)h(returned)g(to)f(its)g(paren)o(t)g(no)q(de)h(without)e(searc)o (hing.)312 2350 y(2.)20 b Fl(Upp)q(er)11 b(Bound)p Fp(:)k(The)c(v)n(alue)f (stored)h(is)f(not)h(exact,)g(it)f(w)o(as)h(the)g(result)g(of)f(a)h(cut)g (o\013)365 2399 y(in)h(the)h(subtree)h(b)q(elo)o(w)e(the)g(no)q(de)h(whic)o (h)f(stored)h(it.)k(Therefore,)d(the)e(v)n(alue)g(of)g(this)365 2449 y(no)q(de)k(is)f(not)h(kno)o(wn,)e(ho)o(w)o(ev)o(er,)i(the)g(v)n(alue)f 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b([50)o(])f(suggests)h(that)f(the)h(table)f(is)g(reset)h(in)f(this)g(w)o(a)o (y)f(at)h(the)h(start)g(of)e(eac)o(h)262 1166 y(new)e(searc)o(h.)21 b(Ho)o(w)o(ev)o(er,)14 b(in)g(HIAR)o(CS,)g(the)h(table)f(is)g(not)h(reset)h (b)q(et)o(w)o(een)f(searc)o(hes,)h(but)262 1216 y(adjusted.)27 b(Eac)o(h)17 b(mo)o(v)o(e's)e(v)n(alue)h(is)h(adjusted)g(b)o(y)g(dividing)e (it)i(b)o(y)f(4.)27 b(This)16 b(allo)o(ws)g(the)262 1266 y(table)d(to)h(ha)o (v)o(e)g(some)f(in\015uence)i(on)e(the)i(next)f(searc)o(h.)324 1351 y(The)19 b(history)g(heuristic)h(is)f(applied)g(at)g(eac)o(h)h(in)o (terior)f(no)q(de)g(of)g(the)g(main)e(searc)o(h)262 1401 y(where)d(mo)o(v)o (e)e(generation)h(is)g(required.)19 b(As)13 b(mo)o(v)o(es)f(are)i(generated,) g(their)g(history)f(v)n(alue)262 1451 y(is)g(lo)q(ok)o(ed)g(up)g(in)g(the)h (history)g(table)f(and)g(encorp)q(orated)i(in)o(to)e(a)g(sp)q(ecial)h(mo)o(v) o(e)e(ordering)262 1501 y(score.)19 b(See)c(section)f(6.4.2)e(for)i(more)f (details.)262 1650 y Fu(6.3.6)55 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b(6.4.2)e(for)i(more)f(details.)324 1672 y(All)f(this)h(attac)o(k)h(orien)o (ted)f(information)e(is)i(far)g(to)q(o)g(time)f(consuming)g(to)h(regenerate) 262 1721 y(at)e(eac)o(h)g(new)h(no)q(de.)17 b(In)12 b(fact,)f(eac)o(h)h(mo)o (v)o(e)d(only)h(c)o(hanges)i(some)f(of)f(the)i(attac)o(k)f(prop)q(erties)262 1771 y(of)i(a)h(p)q(osition.)k(F)m(or)13 b(example,)g(in)g(the)i(op)q(ening)f (p)q(osition,)f(the)i(mo)o(v)o(e)d(e4)i(w)o(ould)g(require)262 1821 y(only)h(the)j(attac)o(ks)f(of)f(the)h(white)g(queen,)g(king's)f(bishop) h(and)f(king's)g(pa)o(wn)g(to)h(b)q(e)g(ad-)262 1871 y(justed.)24 b(Therefore,)17 b(an)e(incremen)o(tal)g(approac)o(h)h(seems)f(to)h(b)q(e)g(w) o(arran)o(ted.)24 b(Although)262 1921 y(there)17 b(are)g(mo)o(v)o(es)e(whic)o (h)h(mak)o(e)f(this)h(incremen)o(tal)f(approac)o(h)h(v)o(ery)h(complex,)e (e.g.)25 b(an)262 1970 y(en-passan)o(t)18 b(mo)o(v)o(e;)f(and)h(the)g (programming)c(of)j(suc)o(h)h(an)g(approac)o(h)f(is)h(v)o(ery)g(tric)o(ky)m (,)g(I)262 2020 y(ha)o(v)o(e)13 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b(of)h(eac)o(h)h(mo)o(v)o(e)f(is)g(not)h(c)o(hec)o(k)o(ed)h(at)f(this)g (stage)g(for)g(2)g(reasons:)324 1754 y Ff(\017)20 b Fp(Most)14 b(mo)o(v)o(es)f(ma)o(y)f(not)i(need)h(searc)o(hing)f(at)g(all)e(b)q(ecause)k (of)d Fh(\013\014)k Fp(cut)d(o\013s.)324 1837 y Ff(\017)20 b Fp(Most)14 b(mo)o(v)o(es)f(are)h(legal)f(in)g(p)q(ositions)g(where)i(a)f (king)f(is)g(not)h(in)f(c)o(hec)o(k.)19 b(Therefore)365 1887 y(it)14 b(w)o(ould)f(b)q(e)h(w)o(asteful)g(to)g(test)h(for)e(the)i (exceptional)f(case)h(at)e(this)h(stage.)324 2005 y(All)d(mo)o(v)o(es)h(are)g (generated)i(using)e(an)h(o\013set)g(metho)q(d)f(via)f(a)h(set)i(of)e(mo)o(v) o(e)e(generation)262 2055 y(tables.)35 b(F)m(or)19 b(example,)g(to)g(mo)o(v)o (e)f(in)h(direction)h(3)f(\()p Ff(\000)p Fp(8)h(o\013set\))g(the)g(curren)o (t)h(square,)262 2105 y Fm(sq1)c Fp(sa)o(y)m(,)g(is)f(used)i(as)f(an)g(index) g(in)o(to)g(a)f(table)h(whic)o(h)g(giv)o(es)g(the)h(resulting)f('to)f (square')262 2155 y(\()p Fm(sq1)p Ff(\000)p Fp(8\).)23 b(If)15 b(the)h('to)f(square')h(is)f(o\013)h(the)g(b)q(oard,)f(the)i(n)o(um)o(b)q(er) d(128)h(is)g(returned)j(\(most)262 2205 y(signi\014can)o(t)10 b(bit)h(set\).)18 b(This)11 b(metho)q(d)g(a)o(v)o(oids)f(the)i(need)g(to)f (ha)o(v)o(e)g(a)g(b)q(oundary)g(around)g(the)262 2254 y(b)q(oard,)16 b(therefore)i(allo)o(wing)c(a)i(64)g(square)h(b)q(oard.)25 b(As)17 b(explained)f(earlier,)g(this)h(allo)o(ws)262 2304 y(con)o(v)o(enien)o(t)d(12)f(bit)h(mo)o(v)o(e)e(storage.)324 2389 y(All)h(non)h(capture/sp)q(ecial)h(mo)o(v)o(es)d(are)j(generated)g (using)f(these)h(mo)o(v)o(e)e(tables.)18 b(Cap-)262 2439 y(tures)12 b(are)g(generated)h(directly)f(from)d(the)j(appropriate)g(attac)o(k)f(table.) 18 b(P)o(a)o(wn)11 b(promotion)946 2574 y(122)p eop %%Page: 123 125 123 124 bop 262 307 a Fp(to)17 b(minor)e(pieces)k(is)e(catered)i(for,)e(eac)o (h)h(mo)o(v)o(e)d(ha)o(ving)i(the)g(same)g(12)g(bit)g(mo)o(v)o(e)e(co)q(de,) 262 357 y(but)e(a)h(di\013eren)o(t)h(mo)o(v)o(e)d(t)o(yp)q(e.)18 b(Castling)13 b(mo)o(v)o(es)f(are)j(generated)g(only)e(if)f(the)j(follo)o (wing)c(5)262 407 y(conditions)i(are)h(met:)312 525 y(1.)20 b(The)15 b(king)e(has)h(nev)o(er)h(mo)o(v)o(ed.)312 608 y(2.)20 b(The)15 b(ro)q(ok)e(in)o(v)o(olv)o(ed)g(has)h(nev)o(er)h(mo)o(v)o(ed.)312 691 y(3.)20 b(The)15 b(squares)g(b)q(et)o(w)o(een)g(the)f(king)g(and)f(ro)q (ok)h(are)g(empt)o(y)m(.)312 774 y(4.)20 b(The)15 b(king)e(is)g(not)h(in)g(c) o(hec)o(k.)312 857 y(5.)20 b(The)c(king)f(will)f(not)i(pass)g(through)g(or)f (in)o(to)g(c)o(hec)o(k)i(as)e(part)h(of)f(the)h(castling)f(ma-)365 907 y(no)q(euvre.)262 1026 y(The)f(incremen)o(tal)f(attac)o(k)h(table)f(is)h (v)o(ery)g(useful)g(for)g(c)o(hec)o(king)g(conditions)g(4)f(and)h(5.)324 1111 y(En-passan)o(t)h(mo)o(v)o(es)e(are)h(tested)i(and)e(generated)i(b)o(y)e (c)o(hec)o(king)g(the)h(relev)n(an)o(t)g(attac)o(k)262 1161 y(table)e(for)h(pa)o(wn)f(attac)o(ks)i(on)e(the)i(curren)o(t)g(en-passan)o(t) g(square)f(\(if)f(an)o(y\).)262 1304 y Fl(F)l(ull)h(Legal)g(Mo)o(v)o(e)i (Generation)262 1416 y Fp(When)10 b(the)h(king)e(is)h(in)g(c)o(hec)o(k,)i (most)d(pseudo)i(legal)e(mo)o(v)o(es)g(are)i(in)f(fact)g(illegal.)15 b(Therefore,)262 1466 y(it)e(mak)o(es)g(sense)i(to)f(generate)h(only)e(legal) g(mo)o(v)o(es)g(when)h(the)h(king)e(is)h(in)f(c)o(hec)o(k.)324 1551 y(It)h(is)f(surprising)h(ho)o(w)g(man)o(y)e(c)o(hess)j(programs)d(con)o (tin)o(ue)i(to)g(generate)h(pseudo)g(legal)262 1601 y(mo)o(v)o(es)c(ev)o(en)j (when)f(the)g(king)g(is)f(in)h(c)o(hec)o(k.)18 b(They)13 b(then)h(w)o(aste)f (time)f(pro)o(ving)g(that)h(most)262 1651 y(of)e(the)i(mo)o(v)o(es)e (generated)j(are)f(in)f(fact)g(illegal.)j(Admittedly)m(,)c(it)h(do)q(es)h (tak)o(e)f(some)g(sophis-)262 1701 y(ticated)g(data)f(structures)k(to)c (enable)h(suc)o(h)h(legal)d(mo)o(v)o(e)h(generation)h(to)f(b)q(e)i (accomplished)262 1750 y(e\016cien)o(tly)m(.)j(My)10 b(incremen)o(tal)g (attac)o(k)h(tables)g(do)f(pro)o(vide)g(enough)h(information)d(to)i(allo)o(w) 262 1800 y(suc)o(h)k(mo)o(v)o(e)f(generation)h(to)g(b)q(e)g(done)g(v)o(ery)h (e\016cien)o(tly)m(.)i(In)d(fact,)g(in)f(tests,)i(I)f(ha)o(v)o(e)g(found)262 1850 y(legal)f(mo)o(v)o(e)f(generation)j(is)f(appro)o(ximately)d(10)j(times)f (faster)i(than)f(pseudo)h(legal)e(mo)o(v)o(e)262 1900 y(generation)h(and)f(v) n(alidation,)e(assuming)i(no)g Fh(\013\014)k Fp(cut)d(o\013s)g(o)q(ccur.)324 1985 y(Legal)f(mo)o(v)o(es)g(when)h(in)f(c)o(hec)o(k)i(fall)e(in)o(to)g(one)h (of)f(the)i(follo)o(wing)c(3)j(categories:)312 2104 y(1.)20 b(King)14 b(mo)o(v)o(es)e(to)i(unattac)o(k)o(ed)g(squares.)312 2187 y(2.)20 b(Captures)15 b(of)e(the)i(c)o(hec)o(king)f(piece)h(b)o(y)f (pieces)h(not)f(pinned)g(to)f(the)i(king.)312 2270 y(3.)20 b(In)o(terp)q(osition)10 b(b)q(et)o(w)o(een)g(the)g(king)f(and)g(the)h(c)o (hec)o(king)g(piece,)g(b)o(y)g(pieces)g(not)f(pinned)365 2319 y(to)14 b(the)h(king.)946 2574 y(123)p eop %%Page: 124 126 124 125 bop 262 307 a Fp(In)16 b(category)h(1,)f(it)g(is)g(imp)q(ortan)o(t)f (to)h(tak)o(e)h(accoun)o(t)g(of)e(c)o(hec)o(ks)j(b)o(y)e(v)o(ector)h(t)o(yp)q (e)g(pieces)262 357 y(\(bishop,)e(ro)q(ok)h(and)f(queen\))i(as)f(these)h (e\013ectiv)o(ely)f(attac)o(k)g(squares)h(through)f(the)g(king.)262 407 y(These)f(attac)o(ks)f(are)g(not)g(ob)o(vious)f(from)f(the)j(attac)o(k)f (tables)g(themselv)o(es.)324 492 y(Note)j(when)g(in)f(double)g(c)o(hec)o(k,)h (only)f(king)g(mo)o(v)o(es)f(need)i(to)f(b)q(e)h(generated)h(as)f(it)f(is)262 542 y(imp)q(ossible)c(to)i(get)g(out)f(of)h(c)o(hec)o(k)h(b)o(y)e(pla)o(ying) g(mo)o(v)o(es)f(in)i(categories)g(2)g(or)g(3.)324 627 y(Generating)f(only)g (legal)g(mo)o(v)o(es)f(giv)o(es)h(an)g(added)h(b)q(ene\014t)h(to)f(the)g (program's)d(searc)o(h)262 677 y(extensions:)17 b(It)11 b(is)f(kno)o(wn)g(b)q (efore)h(searc)o(hing)h(an)o(y)e(mo)o(v)o(es,)f(ho)o(w)h(man)o(y)f(legal)g (mo)o(v)o(es)h(exist,)262 727 y(ho)o(w)f(man)o(y)g(legal)g(king)g(mo)o(v)o (es)g(exist)i(and)f(whether)i(the)e(c)o(hec)o(k)i(is)e(doubled)g(or)g(disco)o (v)o(ered.)262 870 y Fl(Selectiv)o(e)j(T)l(actical)i(Mo)o(v)o(e)g(Generation) 262 982 y Fp(Mo)o(v)o(es)f(generated)i(in)d(the)i(quiescence)i(searc)o(h)e (when)g(not)f(in)g(c)o(hec)o(k)h(are)g(rather)g(limited)262 1032 y(to)j(ob)o(vious)g(tactical)h(mo)o(v)o(es.)32 b(Only)18 b(t)o(w)o(o)h(tactical)f(mo)o(v)o(e)g(categories)h(are)h(generated,)262 1082 y(captures)15 b(and)f(pa)o(wn)f(promotions.)324 1167 y(Only)k(pa)o(wn)h (promotions)e(to)h(a)h(queen)h(are)f(considered.)31 b(All)17 b(capture)i(mo)o(v)o(es)d(are)262 1217 y(generated)h(with)e(the)i(exception)g (of)e(en-passan)o(t.)25 b(These)17 b(sp)q(ecial)g(case)g(mo)o(v)o(es)d(are)j (not)262 1267 y(considered)h(cost)g(e\013ectiv)o(e)h(enough)f(to)f(w)o(arran) o(t)g(inclusion)g(in)g(this)h(mo)o(v)o(e)d(generation)262 1316 y(pro)q(cess.)k(All)13 b(mo)o(v)o(es)g(generated)i(b)o(y)f(this)g(phase)g (are)h(only)e(pseudo-legal.)262 1468 y Fu(6.4.2)55 b(Mo)n(v)n(e)19 b(Ordering)262 1580 y Fp(As)f(explained)g(in)g(c)o(hapter)h(3,)f(mo)o(v)o(e)f (ordering)h(is)g(vital)f(to)h(the)h(e\016ciency)g(of)f(the)g Fh(\013\014)262 1630 y Fp(searc)o(h)d(algorithm.)i(T)m(o)c(ac)o(hiev)o(e)i (the)g(optimal)d Fh(\013\014)k Fp(searc)o(h)g(tree,)f(it)f(is)g(not)p 1398 1637 60 2 v 14 w(necessary)j(to)262 1680 y(examine)12 b(mo)o(v)o(es)h(in)g(a)h(strictly)g(b)q(est)h(to)f(w)o(orst)g(order)g(at)g (eac)o(h)h(no)q(de.)324 1765 y(The)f(optimal)d Fh(\013\014)17 b Fp(searc)o(h)e(tree)g(can)f(b)q(e)g(ac)o(hiev)o(ed)h(b)o(y:)324 1883 y Ff(\017)20 b Fp(Along)13 b(a)g(v)n(ariation)e(whic)o(h)i(will)f(b)q (ecome)h(the)h(new)f(principle)g(v)n(ariation,)f(the)h(b)q(est)365 1933 y(mo)o(v)o(e)g(m)o(ust)f(b)q(e)j(examined)e(\014rst)h(at)g(eac)o(h)g (ply)m(.)324 2016 y Ff(\017)20 b Fp(The)e(\014rst)g(mo)o(v)o(e)e(explored)i (at)f(ev)o(en)h(ply)f(depths)h(m)o(ust)f(b)q(e)h(a)f(refutation)g(mo)o(v)o (e,)365 2066 y(e.g.)h(one)c(that)g(causes)h(a)f Fh(\014)i Fp(cut)f(o\013.)324 2149 y Ff(\017)20 b Fp(A)o(t)11 b(o)q(dd)f(ply)g(depths)i(whic)o(h)e(are)h (not)f(part)h(of)f(a)g(new)h(principle)f(v)n(ariation,)g(ordering)365 2199 y(is)16 b(unimp)q(ortan)o(t)f(pro)o(vided)h(a)f(refutation)h(mo)o(v)o(e) f(is)h(examined)f(\014rst)h(at)g(the)h(next)365 2249 y(depth.)262 2367 y(It)c(can)i(b)q(e)f(seen)h(from)d(these)k(p)q(oin)o(ts)d(that)h(it)g (is)f(vital)g(to)h(examine)e(refutation)i(mo)o(v)o(es)f(as)262 2417 y(early)k(as)g(p)q(ossible.)28 b(In)17 b(HIAR)o(CS,)f(the)i(mo)o(v)o(e)e (ordering)h(algorithm's)d(basic)k(aim)d(is)i(to)946 2574 y(124)p eop %%Page: 125 127 125 126 bop 262 307 a Fp(alw)o(a)o(ys)12 b(examine)g(the)i(b)q(est)h(mo)o(v)o (e)d(\014rst.)18 b(Ho)o(w)o(ev)o(er,)c(emphasis)f(is)g(placed)h(on)f (examining)262 357 y(mo)o(v)o(es)f(lik)o(ely)h(to)g(cause)i Fh(\014)i Fp(cut)d(o\013)s('s,)g(e.g.)k(capturing)13 b(the)i(piece)g(just)f (mo)o(v)o(ed.)324 442 y(The)19 b(main)e(mo)o(v)o(e)h(ordering)h(algorithm)e (is)i(p)q(erformed)f(while)h(generating)g(mo)o(v)o(es.)262 492 y(Ho)o(w)o(ev)o(er,)10 b(a)f(signi\014can)o(t)g(prop)q(ortion)g(of)g(the) h(time,)f(HIAR)o(CS)g(do)q(es)h(not)g(need)g(to)f(generate)262 542 y(an)o(y)i(mo)o(v)o(es.)16 b(This)c(is)g(b)q(ecause)h(at)f(eac)o(h)g(no)q (de)h(the)f(refutation)g(and)g(transp)q(osition)f(tables)262 592 y(are)16 b(prob)q(ed,)h(p)q(ossibly)e(resulting)h(in)g(a)f(mo)o(v)o(e)g (b)q(eing)h(prop)q(osed.)25 b(An)o(y)15 b(mo)o(v)o(e)g(prop)q(osed)262 641 y(b)o(y)h(these)j(tables)e(has)h(a)f(high)f(probabilit)o(y)g(of)g (causing)h(a)g(refutation.)28 b(It)17 b(is)g(therefore)262 691 y(explored)d(\014rst)g(without)g(generating)g(an)o(y)f(mo)o(v)o(es.)k(If) d(a)f(cut)i(o\013)f(is)f(ac)o(hiev)o(ed,)h(the)g(costly)262 741 y(exercise)h(of)f(mo)o(v)o(e)e(generation)i(and)g(ordering)f(is)h(a)o(v)o (oided)f(altogether.)324 826 y(Tw)o(o)i(mo)o(v)o(e)g(ordering)h(algorithms)e (are)j(used,)g(one)f(during)g(b)q(oth)g(the)h(pseudo)g(legal)262 876 y(and)12 b(legal)f(mo)o(v)o(e)g(generation)i(routines)g(and)f(one)h 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(returns)457 1403 y(suc)o(h)c(information)d(to)j(its)g(paren)o(t)g(no)q(de.) 415 1469 y Ff(\017)21 b Fp(Sa)o(v)o(es)14 b(information)d(ab)q(out)i(the)i (no)q(de)f(in)g(the)g(transp)q(osition)g(table.)415 1536 y Ff(\017)21 b Fp(Up)q(dates)15 b(killer)e(mo)o(v)o(es)f(and)i(scores)h(for)f (the)g(curren)o(t)i(depth.)415 1602 y Ff(\017)21 b Fp(Up)q(dates)15 b(the)f(history)g(table)g(with)f(the)i(b)q(est)g(mo)o(v)o(e)d(found.)312 1685 y(3.)20 b Fl(Quies)p Fp(:)e(This)d(recursiv)o(e)h(searc)o(h)g(function)f (handles)g(no)q(des)g(b)q(ey)o(ond)g(the)h(horizon)365 1735 y(of)e(the)g(main)e(searc)o(h.)19 b(It)14 b(p)q(erforms)f(the)i(follo)o(wing) c(k)o(ey)j(tasks:)415 1818 y Ff(\017)21 b Fp(Calls)13 b(for)g(ev)n(aluation)g (of)g(no)q(des.)415 1885 y Ff(\017)21 b Fp(Mak)o(es)g(searc)o(h)g(extension,) i(main)c(searc)o(h)i(con)o(tin)o(uation)f(and)g(quiescence)457 1934 y(decisions.)415 2001 y Ff(\017)h Fp(Calls)13 b(for)g(re-en)o(try)i(of)e (the)i(main)d(searc)o(h.)415 2067 y Ff(\017)21 b 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Fp(state.)k(A)o(t)c(program)f(start)h(up,)g(this)g (is)f(also)h(the)g(initial)e(state.)324 554 y(If)h(the)i(program)d(is)h(exp)q (ecting)i(a)f(mo)o(v)o(e,)d(it)j(will)e(start)i(to)g(searc)o(h)h(on)f(the)g (opp)q(onen)o(ts)262 604 y(time)9 b(for)i(its)g(o)o(wn)g(b)q(est)h(resp)q (onse)h(to)e(the)h(exp)q(ected)h(mo)o(v)o(e.)j(This)11 b(is)g(kno)o(wn)g(as)g ("thinking)262 654 y(on)16 b(the)h(opp)q(onen)o(ts)h(time".)25 b(T)m(o)16 b(ac)o(hiev)o(e)h(this)g(the)g Fm(SEAR)o(CHING)h(ON)f(OPP)g Fp(state)h(is)262 704 y(en)o(tered.)26 b(If)16 b(the)h(opp)q(onen)o(t)f (actually)f(mak)o(es)h(a)f(mo)o(v)o(e)g(while)h(in)f(the)i Fm(IDLE)g Fp(state,)g(the)262 754 y(en)o(tered)e(user)g(mo)o(v)o(e)d(is)i (made)f(and)g(the)i(program)d(en)o(ters)k(the)e Fm(SEAR)o(CHING)g Fp(state.)262 896 y Fl(SEAR)o(CHING)262 1008 y Fp(This)j(state)h(carries)g (out)f(the)h(tree)h(searc)o(hing)e(on)g(the)h(computer's)f(time.)27 b(It)18 b(uses)g(the)262 1058 y(aforemen)o(tioned)d(three)k(searc)o(h)f (routines.)28 b(The)17 b(searc)o(h)i(ma)o(y)c(start)i(from)f(the)h(ro)q(ot)g (of)262 1108 y(the)d(tree)h(or)f(con)o(tin)o(ue)g(a)g(previously)f(in)o (terrupted)i(searc)o(h.)324 1193 y(If)j(the)i(searc)o(h)g(deriv)o(es)g(a)f (kno)o(wn)f(v)n(alue)h(for)g(the)g(game)f(tree,)j(lik)o(e)d(c)o(hec)o(kmate)h (in)262 1243 y(3)d(mo)o(v)o(es)g(for)g(example,)g(no)h(more)e(searc)o(hing)j (is)e(required)i(and)f(the)g Fm(SEAR)o(CH)h(COM-)262 1293 y(PLETE)g Fp(state)h(is)f(en)o(tered.)33 b(Ho)o(w)o(ev)o(er,)20 b(if)d(the)i(game)e (tree)i(v)n(alue)f(is)g(not)g(kno)o(wn,)h(the)262 1342 y(program)d(con)o(tin) o(ues)j('thinking')d(un)o(til)i(either,)h(a)f(user)i(in)o(terrupt)f(\()p Ff(")p Fp(C\))f(o)q(ccurs)i(or)e(an)262 1392 y(alarm)e(timer)h(expires,)i (where)h(up)q(on)e(the)h Fm(SEAR)o(CH)g(INTERR)o(UPTED)f Fp(state)h(is)f(en-) 262 1442 y(tered.)262 1584 y Fl(SEAR)o(CHING)e(ON)g(OPP)262 1697 y Fp(Lik)o(e)g(the)i Fm(SEAR)o(CHING)g Fp(state,)g(this)g(state)g (carries)g(out)f(the)h(tree)h(searc)o(hing,)f(except)262 1746 y(in)c(this)i(case)g(on)g(the)g(opp)q(onen)o(ts)g(thinking)e(time.)22 b(Again,)14 b(if)h(the)h(searc)o(h)g(tree)h(v)n(alue)e(is)262 1796 y(kno)o(wn,)g(the)h(searc)o(h)h(terminates)e(and)h(the)g Fm(SEAR)o(CHED)h(ON)g(OPP)e Fp(state)i(is)e(en)o(tered.)262 1846 y(Assuming)g(the)i(game)e(tree)j(v)n(alue)e(is)h(not)f(kno)o(wn,)h(the)g (searc)o(h)h(con)o(tin)o(ues)f(inde\014nitely)262 1896 y(un)o(til)f(the)i (user)h(en)o(ters)g(his/her/it's)f(mo)o(v)o(e,)e(when)i(one)g(of)f(t)o(w)o(o) g(p)q(ossible)h(actions)f(can)262 1946 y(o)q(ccur.)j(If)15 b(the)g(mo)o(v)o(e)d(en)o(tered)17 b(is)d(the)h(exp)q(ected)i(mo)o(v)o(e,)12 b(then)j(the)g(program's)e(e\013orts)j(at)262 1995 y(thinking)9 b(on)i(opp)q(onen)o(ts)h(time)d(ha)o(v)o(e)i(not)g(b)q(een)h(w)o(asted.)17 b(In)11 b(whic)o(h)g(case,)h(the)g Fm(SEAR)o(CH-)262 2045 y(ING)k Fp(state)h(is)f(en)o(tered)j(to)d(con)o(tin)o(ue)h(the)g(searc)o(h)g(on)f (the)h(program's)e(time.)25 b(Ho)o(w)o(ev)o(er,)262 2095 y(if)17 b(the)j(en)o(tered)g(mo)o(v)o(e)d(is)i(unexp)q(ected,)j(this)d(searc)o(h)g (is)g(terminated)f(b)o(y)h(en)o(tering)g(the)262 2145 y Fm(SEAR)o(CH)c (INTERR)o(UPTED)f Fp(state.)262 2287 y Fl(SEAR)o(CH)i(INTERR)o(UPTED)262 2399 y Fp(The)h(ob)r(jectiv)o(e)h(of)f(this)g(state)h(is)f(to)g(allo)o(w)f(a) h(clean)h(bac)o(king)e(up)i(and)f(termination)e(of)262 2449 y(the)h(searc)o(h)h(tree.)26 b(Once)17 b(the)g(searc)o(h)g(has)f(returned)i (to)e(the)h(ro)q(ot)f(p)q(osition,)f(either)i(the)946 2574 y(130)p eop %%Page: 131 133 131 132 bop 262 307 a Fm(SEAR)o(CH)16 b(COMPLETE)e Fp(or)h Fm(SEAR)o(CHED)i(ON)f(OPP)f Fp(state)h(is)e(en)o(tered.)23 b(The)16 b(actual)262 357 y(state)h(dep)q(ends)h(on)f(whether)h(the)f (program)e(w)o(as)h(previously)h(thinking)e(on)i(its)f(o)o(wn)h(or)262 407 y(the)d(opp)q(onen)o(ts)h(time.)262 550 y Fl(SEAR)o(CH)h(COMPLETE)262 662 y Fp(In)g(this)g(state)g(the)h(user)g(is)f(informed)e(of)i(the)g(searc)o (h)i(result)e(b)o(y)g(w)o(a)o(y)f(of)h(a)f(mo)o(v)o(e)g(or)h(an)262 712 y(announcemen)o(t.)h(Some)12 b(searc)o(h)j(v)n(alues)e(are)h(then)g (reset)g(and)g(\014nally)e(the)i Fm(IDLE)g Fp(state)g(is)262 762 y(en)o(tered.)262 905 y Fl(SEAR)o(CHED)i(ON)g(OPP)262 1017 y Fp(This)d(state)i(records)g(the)g(searc)o(h)g(result)g(and)e(en)o(ters)j (the)e Fm(IDLE)h Fp(state.)324 1138 y(Please)i(note,)g(an)f(explanation)f(of) h(the)h(handling)e(of)h(user)h(commands)d(suc)o(h)j(as)g(set)262 1188 y(up)d(p)q(osition)g(for)h(example,)e(en)o(tered)j(while)e(searc)o(hing) i(on)e(opp)q(onen)o(ts)i(time)d(ha)o(v)o(e)h(b)q(een)262 1238 y(omitted)i(for)h(reasons)i(of)e(clarit)o(y)m(.)28 b(They)18 b(are)g(only)e(minor)g(side)i(issues)h(whic)o(h)e(do)h(not)262 1287 y(a\013ect)c(the)h(underlying)e(design.)262 1439 y Fu(6.4.4)55 b(Ev)m(aluation)262 1551 y Fp(The)18 b(ev)n(aluation)f(criteria)i(used)h(in)e (HIAR)o(CS)g(w)o(ere)h(fully)e(explained)i(and)f(illustrated)262 1601 y(in)f(c)o(hapter)i(4.)31 b(Ho)o(w)o(ev)o(er,)19 b(during)f(the)h (implemen)o(tatio)o(n)d(and)i(testing,)h(a)f(n)o(um)o(b)q(er)f(of)262 1651 y(problem)10 b(areas)i(w)o(ere)g(observ)o(ed.)19 b(In)11 b(this)h(section)g(I)g(will)e(explain)h(some)f(of)h(the)i(problems)262 1700 y(encoun)o(tered)i(and)f(the)h(resulting)f(solutions.)324 1786 y(The)h(\014rst)g(ma)r(jor)e(problem)g(noticed)i(w)o(as)g(asso)q(ciated) g(with)g(the)g(application)e(of)h(the)262 1836 y(ev)n(aluation)h(function.)27 b(The)18 b(ev)n(aluation)d(function)i(is)g(usually)f(applied)h(at)g(the)g (leaf)g(or)262 1885 y(horizon)e(no)q(des)i(of)e(the)i(main)d(searc)o(h)870 1870 y Fk(3)889 1885 y Fp(,)i(after)g(whic)o(h)g(a)g(quiescence)i(searc)o(h)f (is)f(applied.)262 1935 y(The)d(p)q(ositional)f(v)n(alue)h(calculated)g(at)g (the)h(horizon)f(no)q(des)h(is)f(carried)h(forw)o(ard)f(in)o(to)f(the)262 1985 y(quiescence)k(searc)o(h)g(to)f(enable)g(the)g(\014nal)f(v)n(alues)g (calculated)h(at)g(the)g(leaf)f(no)q(des)h(of)g(this)262 2035 y(searc)o(h)e(to)f(ha)o(v)o(e)h(reasonably)f(up)h(to)f(date)h(p)q(ositional)e (v)n(alues)h(to)g(go)g(with)g(the)h(calculated)262 2085 y(material)h(v)n (alue.)26 b(When)17 b(pieces)h(are)f(captured)h(during)e(the)i(quiescence)g (searc)o(h,)g(b)q(oth)262 2134 y(the)12 b(material)d(and)j(p)q(ositional)e(v) n(alue)h(of)g(the)h(captured)h(piece)g(should)e(b)q(e)i(lost.)k(Ho)o(w)o(ev)o (er,)262 2184 y(this)e(w)o(as)g(not)g(re\015ected)i(in)e(the)g(p)q(ositional) f(v)n(alue)h(carried)g(forw)o(ard)g(in)g(the)g(quiescence)262 2234 y(searc)o(h.)k(In)14 b(this)g(w)o(a)o(y)f(the)h(p)q(ositional)f(v)n (alue)g(started)i(to)f(b)q(ecome)f('out)h(of)f(date'.)324 2319 y(When)f(the)i(p)q(ositional)d(v)n(alues)h(of)g(pieces)i(are)f(relativ)o(ely) e(lo)o(w,)h(this)g(w)o(as)h(not)f(a)g(ma)r(jor)262 2369 y(problem.)31 b(Ho)o(w)o(ev)o(er,)21 b(unlik)o(e)d(most)g(c)o(hess)i(programs,)f(m)o(y)e (ev)n(aluation)h(function)g(can)p 262 2404 573 2 v 308 2431 a Fj(3)325 2442 y Fi(except)10 b(where)h Fb(\013\014)i Fi(v)n(alues)d (indicate)f(that)h(the)h(p)q(osition)f(cannot)f(a\013ect)h(the)h(searc)o(h)f (result.)946 2574 y Fp(131)p eop %%Page: 132 134 132 133 bop 262 307 a Fp(pro)q(duce)13 b(v)o(ery)g(high)f(p)q(ositional)f (scores.)19 b(Therefore,)14 b(when)f(highly)f(p)q(ositionally)e(v)n(alued)262 357 y(pieces)15 b(are)h(captured,)f(the)g(carried)h(forw)o(ard)e(p)q (ositional)f(v)n(alue)h(w)o(as)h(drastically)f(out)g(of)262 407 y(date,)j(causing)g(serious)g(problems)f(to)h(the)g(searc)o(h,)i(b)q(oth) e(in)f(e\016ciency)i(and)e(accuracy)m(.)262 457 y(F)m(or)c(example,)g(if)h(a) g(passed)h(pa)o(wn)f(p)q(ositionally)f(v)n(alued)g(at)i(200)e(p)q(oin)o(ts)h (\(2)h(pa)o(wns\),)f(w)o(as)262 506 y(captured)19 b(during)f(the)g (quiescence)j(searc)o(h,)f(the)e(p)q(ositional)f(total)h(should)g(ha)o(v)o(e) f(b)q(een)262 556 y(decreased)f(b)o(y)d(around)h(200)f(p)q(oin)o(ts.)324 641 y(The)18 b(solution)e(to)i(this)f(problem)f(la)o(y)h(in)g(incremen)o (tally)f(up)q(dating)h(the)h(p)q(ositional)262 691 y(v)n(alue)10 b(during)g(the)h(quiescence)i(searc)o(h.)18 b(T)m(o)10 b(ac)o(hiev)o(e)h (this,)g(whenev)o(er)h(the)g(full)d(ev)n(aluation)262 741 y(function)h(is)h (applied,)g(all)e(piece)j(p)q(ositional)e(scores)j(are)e(sa)o(v)o(ed)g(in)g (a)g(general)g(Pc/Sq)g(table.)262 791 y(As)k(mo)o(v)o(es)f(are)i(made)e (during)h(the)h(subsequen)o(t)h(searc)o(h)f(this)g(table)f(is)g(main)o (tained)e(and)262 841 y(the)18 b(p)q(ositional)f(v)n(alue)h(of)g(an)o(y)f (captured)j(piece)f(is)f(recorded)i(in)e(the)h('Game)d(History')262 891 y(structure)k(and)e(used)g(to)g(incremen)o(tally)f(up)q(date)h(the)h(p)q (ositional)e(score.)31 b(It)18 b(w)o(as)g(also)262 940 y(found)c(necessary)i (to)f(include)g(promotion)d(mo)o(v)o(es)i(in)o(to)g(this)g(pro)q(cess)j(b)o (y)d(remo)o(ving)f(the)262 990 y(promoted)d(pa)o(wns)i(p)q(ositional)e (score.)19 b(These)13 b(enhancemen)o(ts)f(noticeably)f(impro)o(v)o(ed)f(the) 262 1040 y(standard)k(of)f(pla)o(y)g(b)o(y)h(the)g(program.)324 1125 y(Another)i(area)f(whic)o(h)g(caused)h(some)e(problems)h(w)o(as)g(the)g (concept)i(of)d(temp)q(o.)21 b(The)262 1175 y(pla)o(y)o(er)11 b(to)h(mo)o(v)o(e)e(should)i(receiv)o(e)h(some)e(p)q(ositional)f(b)q(on)o(us) j(for)e(ha)o(ving)g(the)h(mo)o(v)o(e)f(as)h(this)262 1225 y(is)h(adv)n(an)o (tageous)546 1210 y Fk(4)564 1225 y Fp(.)324 1310 y(I)e(tried)g(out)g(v)n (arious)g(temp)q(o)f(v)n(alues)h(based)h(on)f(a)f(direct)i(ratio)f(to)g(the)h (b)q(est)g(p)q(ositional)262 1360 y(increase)k(caused)g(b)o(y)f(an)o(y)g (single)g(mo)o(v)o(e)e(from)h(eac)o(h)h(pla)o(y)o(ers)h(p)q(oin)o(t)e(of)h (view.)22 b(Ho)o(w)o(ev)o(er,)262 1410 y(this)11 b(caused)i(problems)d(b)q (ecause)j(the)f(maxim)n(um)7 b(p)q(ositional)j(c)o(hange)i(o)o(v)o(er)g(ev)o (en)g(a)f(single)262 1460 y(mo)o(v)o(e)j(can)j(b)q(e)g(dramatic)e(o)o(v)o(er) i(a)f(whole)g(searc)o(h.)27 b(I)16 b(\014nally)g(used)h(a)f(constan)o(t)h(v)n (alue)f(of)262 1509 y(20)g(p)q(oin)o(ts)i(for)f(ha)o(ving)f(the)i(mo)o(v)o (e.)27 b(I)17 b(still)f(feel)i(the)g(temp)q(o)e(v)n(alue)h(should)g(b)q(e)h (related)262 1559 y(to)f(p)q(ositional)f(v)n(alues)i(in)f(some)g(w)o(a)o(y)m (,)g(ho)o(w)o(ev)o(er,)h(the)g(v)n(alue)f(c)o(hosen)i(seems)f(to)f(b)q(eha)o (v)o(e)262 1609 y(reasonably)c(in)h(the)g(test)h(games)e(pla)o(y)o(ed.)324 1694 y(In)j(elemen)o(tary)f(endings,)i(where)g(a)f(c)o(hec)o(kmate)f(driv)o (e)h(is)g(required,)h(e.g.)25 b(king)15 b(and)262 1744 y(ro)q(ok)h(v)o(ersus) h(king,)f(a)g(sp)q(ecial)g(routine)h(w)o(as)f(found)g(necessary)i(to)e(force) h(c)o(hec)o(kmate)f(in)262 1794 y(an)c(e\016cien)o(t)h(manor.)j(The)d (routine)g(used)h(is)f(v)o(ery)g(similar)d(to)j(the)g(mop)e(up)i(routine)g (used)262 1844 y(in)g(Chess)i(4.5)e([4)o(].)324 1929 y(Cases)j(of)f (insu\016cien)o(t)h(mating)d(material,)g(e.g.)23 b(king)14 b(and)i(knigh)o(t)e(v)i(king,)e(are)i(also)262 1979 y(detected)d(b)o(y)e(the) h(ev)n(aluation)e(function)h(and)g(the)h(dra)o(w)g(v)n(alue)e(returned.)19 b(This)12 b(enhance-)262 2029 y(men)o(t)j(is)h(v)o(ery)g(e\013ectiv)o(e)i(in) d(the)i(late)f(endgame)f(b)q(ecause)j(it)e(allo)o(ws)e(early)i(termination) 262 2078 y(of)d(man)o(y)f(v)n(ariations,)g(thereb)o(y)j(reducing)f (unnecessary)i(searc)o(h)f(e\013ort.)324 2164 y(In)i(order)i(to)e(ease)i(the) f(debugging)f(of)g(the)h(ev)n(aluation)e(function,)i(all)e(v)n(alues)i(w)o (ere)262 2213 y(sa)o(v)o(ed)12 b(and)g(displa)o(y)o(ed)f(on)h(request.)19 b(This)12 b(allo)o(w)o(ed)f(n)o(umerous)g(small)f(bugs)j(to)e(b)q(e)i(iden)o (ti-)262 2263 y(\014ed,)f(whic)o(h)f(w)o(ould)g(ha)o(v)o(e)g(otherwise)i(b)q (een)g(v)o(ery)f(di\016cult)f(to)g(sp)q(ot)h(as)g(they)g(only)f(sligh)o(tly) 262 2313 y(a\013ected)k(the)f(\014nal)g(ev)n(aluation)e(function)i(score.)p 262 2340 573 2 v 308 2366 a Fj(4)325 2378 y Fi(except)c(in)h(zugzw)o(ang)f(p) q(ositions)946 2574 y Fp(132)p eop %%Page: 133 135 133 134 bop 324 307 a Fp(Ev)o(en)14 b(in)g(the)h(\014nal)e(p)q(erformance)h (tested)i(v)o(ersion,)e(some)f(of)g(these)j(p)q(ositional)d(diag-)262 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(when)h(either)g(the)262 1005 y(mac)o(hines)11 b(w)o(ere)j(thinking)e(on)g (opp)q(onen)o(ts)i(time)d(and)i(an)f(exp)q(ected)j(reply)e(w)o(as)f(made,)g (or)262 1055 y(when)i(c)o(hec)o(kmate)g(w)o(as)f(seen)j(or)e(when)g(only)f (one)h(legal)f(mo)o(v)o(e)f(existed.)324 1140 y(The)f(\014rst)g(thing)e(to)h (do)h(is)f(to)g(analyse)g(ho)o(w)g(v)o(ery)g(strong)h(h)o(uman)e(c)o(hess)i (pla)o(y)o(ers)g(tac)o(kle)262 1190 y(the)i(problem)e(of)h(time)f(allo)q (cation.)16 b(I)c(did)g(not)h(\014nd)f(an)o(y)g(previous)h(researc)o(h)i(w)o (ork)d(whic)o(h)262 1239 y(pro)o(vided)h(the)h(detailed)f(mo)o(v)o(e/time)e (analysis)i(I)g(required,)h(so)g(I)f(decided)i(to)e(collate)g(the)262 1289 y(information)d(m)o(yself.)324 1375 y(I)g(decided)i(to)e(use)h(the)g (1986)e(w)o(orld)h(c)o(hampionship)f(matc)o(h)g(b)q(et)o(w)o(een)j(Gary)e (Kasparo)o(v)262 1424 y(and)16 b(Anatoly)g(Karp)q(o)o(v)g([62)o(])h(as)f(m)o (y)f(case)j(study)m(.)26 b(This)17 b(matc)o(h)e(w)o(as)h(c)o(hosen)i(for)e (three)262 1474 y(main)11 b(reasons:)312 1593 y(1.)20 b(Lik)o(ely)13 b(high)h(qualit)o(y)e(of)h(time)g(allo)q(cation)f(decisions.)312 1676 y(2.)20 b(Same)14 b(pla)o(y)o(ers)g(w)o(ere)i(in)o(v)o(olv)o(ed)d(in)h (all)f(games)h(allo)o(wing)e(pla)o(y)o(er)i(st)o(yle)h(to)g(b)q(e)g(anal-)365 1725 y(ysed.)312 1808 y(3.)20 b(Detailed)c(statistics)g(giving)f(time)f(used) j(for)f(eac)o(h)g(mo)o(v)o(e)e(w)o(as)i(a)o(v)n(ailable)e(in)h(c)o(hess)365 1858 y(magazine.)324 1977 y(I)c(analysed)g(all)f(24)g(games)g(of)g(the)i (matc)o(h.)k(F)m(or)11 b(eac)o(h)g(game,)f(mo)o(v)o(es)g(b)o(y)h(b)q(oth)g (sides)h(up)262 2027 y(to)i(the)i(time)e(con)o(trol)h(at)g(mo)o(v)o(e)e(40)i (w)o(ere)h(collated.)21 b(This)15 b(in)o(v)o(olv)o(ed)e(analysing)h(appro)o (x-)262 2076 y(imately)e(2000)i(mo)o(v)o(e)g(times.)20 b(As)15 b(a)g(result)g(I)g(w)o(as)g(able)g(to)g(pro)q(duce)h(5)e(di\013eren)o(t)i (graphs)262 2126 y(detailing)c(the)j(a)o(v)o(erage)f(time)e(sp)q(en)o(t)j(on) f(eac)o(h)g(mo)o(v)o(e)e(for:)324 2245 y Ff(\017)20 b Fp(Kasparo)o(v)14 b(pla)o(ying)e(white.)324 2328 y Ff(\017)20 b Fp(Kasparo)o(v)14 b(pla)o(ying)e(blac)o(k.)324 2411 y Ff(\017)20 b Fp(Karp)q(o)o(v)14 b(pla)o(ying)e(white.)946 2574 y(133)p eop %%Page: 134 136 134 135 bop 324 307 a Ff(\017)20 b Fp(Karp)q(o)o(v)14 b(pla)o(ying)e(blac)o (k.)324 390 y Ff(\017)20 b Fp(Com)o(bined)12 b(time)h(allo)q(cation.)262 509 y(The)h(graphs)g(pro)q(duced)h(can)f(b)q(e)h(found)e(in)h(app)q(endix)f (C.)324 594 y(Analysing)g(these)j(graphs)e(it)g(can)g(b)q(e)h(seen)g(that)f (b)q(oth)h(pla)o(y)o(ers)f(ha)o(v)o(e)g(distinctly)g(dif-)262 644 y(feren)o(t)e(st)o(yles)h(on)e(time)g(con)o(trol.)17 b(Kasparo)o(v)12 b(allo)q(cates)f(a)h(signi\014can)o(t)f(amoun)o(t)f(of)h(time)g(to)262 694 y(the)i(middle)e(game,)f(mo)o(v)o(es)i(12-28)f(in)h(particular.)18 b(Kasparo)o(v's)12 b(time)f(allo)q(cation)g(usually)262 743 y(has)k(one)g(v)o(ery)g(high)f(p)q(eak)h(around)g(mo)o(v)o(es)f(16)g(to)h(20) f(and)h(then)g(tails)g(o\013)f(dramatically)m(.)262 793 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b(op)q(ening.)25 b(T)m(o)16 b(help)g(the)h (program)e(at)h(this)g(di\016cult)g(stage,)h(the)g(resp)q(onse)h(time)d(is) 262 1023 y(increased)g(b)o(y)e(b)q(et)o(w)o(een)i(0)e(and)h(respTime)f(dep)q (ending)i(on)e(the)h(n)o(um)o(b)q(er)f(of)g(mo)o(v)o(es)g(since)262 1073 y(lea)o(ving)i(the)j(op)q(ening)f(b)q(o)q(ok,)g(e.g.)26 b(the)18 b(\014rst)g(non)f(b)q(o)q(ok)f(mo)o(v)o(e)g(is)g(respTime,)h(and)g (the)262 1123 y(forth)c(is)h(0.)262 1266 y Fl(Time)h(Allo)q(cation)e (Adjustmen)o(t)262 1378 y Fp(The)h(actual)g(time)f(whic)o(h)i(can)f(b)q(e)h (sp)q(en)o(t)h(on)e(a)g(mo)o(v)o(e)f(can)h(v)n(ary)g(b)q(et)o(w)o(een)i (respTime/64)262 1428 y(and)10 b(maxTim)o(e.)k(Therefore,)e(for)e(a)g(time)f (con)o(trol)g(of)h(40)g(mo)o(v)o(es)f(in)g(2)h(hours)h(the)g(minim)n(um)262 1478 y(and)20 b(maxim)n(um)d(times)i(could)i(range)g(from)d(3)j(seconds)h(to) e(2)h(hours.)39 b(Of)20 b(course,)j(if)262 1528 y(the)c(searc)o(h)h(tree)h 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b(the)h(time)e(allo)q(cation)f(is)i(adjusted)h(under)g(5)e (categories.)19 b(Note,)12 b(to)g(facilitate)f(the)262 2097 y(v)n(arying)h(time)h(allo)q(cation)f(c)o(hanges,)i(the)h(concept)g(of)e (extra)p 1130 2104 94 2 v 14 w(time)g(is)h(in)o(tro)q(duced.)262 2240 y Fl(1.)25 b(Best)17 b(Mo)o(v)o(e)g(leads)f(to)h(a)g(Loss:)41 b Fp(While)15 b(no)g(mo)o(v)o(es)f(are)h(found)g(to)g(a)o(v)o(oid)f(losing) 262 2290 y(the)e(game,)e(the)j(allo)q(cated)f(time)e(is)i(set)h(to)f(the)g (maxTime.)i(This)e(allo)o(ws)f(the)h(program)f(to)262 2340 y(con)o(tin)o(ue)k(searc)o(hing)h(un)o(til)e(either)j(mate)d(is)h(found)g(or) h(almost)d(all)h(the)i(program's)e(time)262 2390 y(expires.)20 b(After)14 b(all,)f(the)i(program)e(is)h(v)o(ery)g(lik)o(ely)f(to)h(lose)g (if)g(it)g(pla)o(ys)f(a)h(mo)o(v)o(e)f(it)h(kno)o(ws)262 2439 y(will)e(lead)i(to)f(a)h(loss,)f(therefore)i(it)f(migh)o(t)e(as)i(w)o(ell)f (sp)q(end)i(most)d(of)i(its)f(time)g(attempting)946 2574 y(136)p eop %%Page: 137 139 137 138 bop 262 307 a Fp(to)16 b(\014nd)g(an)g(impro)o(v)o(emen)o(t.)22 b(Of)16 b(course,)i(if)d(the)i(loss)f(is)g(found)f(to)h(b)q(e)h(una)o(v)o (oidable)e(the)262 357 y(mo)o(v)o(e)d(whic)o(h)i(lasts)g(out)f(the)i(longest) f(will)e(b)q(e)j(pla)o(y)o(ed)e(immedia)o(tely)m(.)262 499 y Fl(2.)35 b(New)21 b(Iteration)d(Begun:)41 b Fp(Before)19 b(eac)o(h)f(new)h(iteration)e(b)q(egins)i(the)f(program)262 549 y(calculates)10 b(ho)o(w)f(long)g(the)i(iteration)e(is)h(exp)q(ected)i (to)e(tak)o(e)f(based)i(on)f(the)g(time)f(tak)o(en)h(o)o(v)o(er)262 599 y(previous)g(iterations.)17 b(F)m(or)10 b(example,)f(in)h(the)h(middle)e (game)g(an)h(iteration)g(t)o(ypically)f(tak)o(es)262 649 y(ab)q(out)15 b(6)g(times)f(the)i(length)g(of)e(all)g(previous)i(iterations)1177 634 y Fk(5)1196 649 y Fp(.)22 b(Additionally)m(,)13 b(an)i(iteration)262 699 y(commi)o(tm)o(en)o(t)d(time)i(is)g(calculated.)21 b(If)14 b(the)h(curren)o(t)h(resp)q(onse)h(time)c(will)h(expire)h(b)q(efore)262 748 y(the)f(iteration)f(commi)o(tm)o(en)o(t)e(time,)h(the)i(searc)o(h)g(is)g (ab)q(orted.)k(Ho)o(w)o(ev)o(er,)c(if)e(the)i(program)262 798 y(is)h(committed)f(to)i(the)g(iteration,)g(it)g(allo)o(ws)e(the)j(extra)f (time)f(reasonably)h(exp)q(ected)i(to)262 848 y(ac)o(hiev)o(e)e(some)f (results)i(from)e(the)h(new)h(iteration)f(commitm)n(en)o(t.)23 b(Note)16 b(that)g(the)h(time)262 898 y(previously)c(tak)o(en)h(thinking)f (on)h(opp)q(onen)o(ts)g(time)f(is)h(also)f(tak)o(en)h(in)o(to)f(accoun)o(t.) 504 1011 y(extraTime)g(=)h(iterationTime)e Ff(\000)i Fp(respTime)g(+)g (oppTime)262 1153 y Fl(3.)20 b(Searc)o(h)13 b(F)l(ailed)f(Lo)o(w:)41 b Fp(When)12 b(the)h(searc)o(h)g(has)f(failed)g(lo)o(w,)f(the)h(true)h(v)n (alue)f(of)f(the)262 1203 y(b)q(est)h(mo)o(v)o(e)f(found)g(is)h(not)f(kno)o (wn,)h(it)f(is)h(only)f(kno)o(wn)g(that)h(it)f(is)h(w)o(orse)h(than)e(the)i Fh(\013)e Fp(v)n(alue)262 1253 y(of)h(the)h(initial)e(searc)o(h)j(windo)o(w.) 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y(extraTime)f(=)h(2)g Ff(\001)f Fp(respTime)262 2063 y Fl(5.)41 b(Searc)o(h)21 b(V)l(alue)g(in)h(Aspiration)d(Windo)o(w:)40 b Fp(The)20 b(actual)g(b)q(est)g(mo)o(v)o(e)e(v)n(alue)262 2113 y(is)e(kno)o(wn,)h(therefore,)h(time)e(can)h(b)q(e)g(allo)q(cated)f (directly)h(from)e(the)j(v)n(alue)e(itself.)26 b(The)262 2163 y(judgemen)o(t)17 b(is)h(based)i(on)e(the)h(di\013erence)h(b)q(et)o(w)o(een)g (the)f(b)q(est)h(mo)o(v)o(e's)d(v)n(alue)h(and)g(the)262 2213 y(score)e(at)f(the)h(end)g(of)e(the)i(last)f(iteration.)22 b(If)15 b(this)g(di\013erence)i(is)e(less)h(than)g(or)f(equal)g(to)262 2263 y Ff(\000)p Fp(16,)e(extra)h(time)f(is)g(allo)q(cated)h(as)g(follo)o (ws:)599 2376 y(extraTime)f(=)h(\()p Ff(j)g Fp(di\013)f Ff(j)h Fp(/)f(16)h Ff(\001)f Fp(respTime\))h(/)f(8)p 262 2411 573 2 v 308 2437 a Fj(5)325 2449 y Fi(the)e(fact)f(that)h(o)q(dd)f(ply)h (iterations)e(tak)o(e)i(longer)f(than)g(ev)o(en)g(ones)h(is)g(also)g(tak)o (en)f(in)o(to)h(accoun)o(t)946 2574 y Fp(137)p eop %%Page: 138 140 138 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b(note,)g(this)g(time)e(allo)q(cation)g(adjustmen)o(t)h(pro)q(cess)i(is)f (con)o(tin)o(ually)e(p)q(erformed)262 2045 y(ev)o(ery)14 b(time)f(a)g(new)i (b)q(est)g(mo)o(v)o(e)d(is)i(found)f(or)h(an)g(iteration)f(completes.)262 2188 y Fl(Chec)o(king)h(Time)262 2300 y Fp(Whenev)o(er)g(the)g(allo)q(cated)f (time)f(is)h(adjusted,)h(a)f(new)h(searc)o(h)h(expiry)e(time)f(exists.)19 b(This)262 2350 y(expiry)10 b(time)f(is)h(calculated)h(from)d(the)j(resp)q (onse)i(time,)c(extra)i(time,)e(time)g(sp)q(en)o(t)j(thinking)262 2399 y(on)i(opp)q(onen)o(ts)i(time)d(and)i(the)h(max)d(time.)20 b(Using)15 b(this)g(expiry)g(time,)e(an)i(alarm)e(call)h(is)262 2449 y(set)i(up)g(to)f(signal)g(the)h(program)e(when)i(its)f(searc)o(h)i (time)d(has)i(matured.)23 b(Additionally)m(,)946 2574 y(138)p eop %%Page: 139 141 139 140 bop 262 307 a Fp(b)q(efore)19 b(setting)f(a)g(new)h(alarm)d(call)i (time,)g(the)h(old)e('alarm)f(call')h(m)o(ust)g(b)q(e)i(cancelled.)262 357 y(This)13 b(approac)o(h)h(mak)o(es)f(use)i(of)e(the)h(UNIX)h(system)e (call)g Fm(alarm)p Fp(.)262 530 y Fr(6.5)69 b(E\016ciency)22 b(Asp)r(ects)262 656 y Fp(E\016ciency)f(is)f(v)o(ery)h(imp)q(ortan)o(t)d(to)j (an)o(y)f(c)o(hess)i(program.)36 b(In)20 b(fact,)i(b)q(ecause)g(of)e(the)262 706 y(un)o(usually)14 b(dominan)o(t)g(factor)i(of)f(e\016ciency)m(,)h(c)o (hess)h(programs)e(are)h(usually)f(quite)h(hard)262 756 y(to)h(follo)o(w.)28 b(I)17 b(ha)o(v)o(e)h(tried)g(to)g(mak)o(e)e(HIAR)o(CS)h(as)h(clear)g(and)g (easy)g(to)g(understand)h(as)262 805 y(p)q(ossible,)13 b(while)h(k)o(eeping)f (to)h(the)h(o)o(v)o(erall)d(aims)h(of)g(e\016ciency)m(.)324 891 y(The)e(follo)o(wing)e(sections)j(explain)e(program)g(e\016ciency)i(from) d(three)j(di\013eren)o(t)g(angles:)262 1042 y Fu(6.5.1)55 b(Algorithms)262 1154 y Fp(T)m(ree)17 b(searc)o(hing)h(e\016ciency)g(is)f(of)f(primary)g(imp)q (ortance)g(to)h(the)h(o)o(v)o(erall)e(sp)q(eed)i(of)f(the)262 1204 y(program.)25 b(F)m(or)17 b(example,)f(the)i(di\013erence)h(b)q(et)o(w)o (een)f(applying)e Fh(\013\014)j Fp(to)e(a)g(w)o(ell)f(ordered)262 1254 y(tree)g(and)g(a)f(badly)g(ordered)i(tree)g(is)f(man)o(y)e(orders)i(of)f (magnitude.)22 b(In)16 b(HIAR)o(CS,)f(par-)262 1304 y(ticular)g(atten)o(tion) g(has)h(b)q(een)h(paid)e(to)g(impro)o(ving)e(mo)o(v)o(e)h(ordering)h(to)h (therefore)h(a)o(v)o(oid)262 1354 y(exploration)c(of)g(man)o(y)f(unnecessary) k(no)q(des.)324 1439 y(Other)11 b(areas)g(lik)o(e)e(mo)o(v)o(e)f(generation,) j(for)f(example,)f(ha)o(v)o(e)h(b)q(een)h(made)e(more)g(e\016cien)o(t)262 1489 y(b)o(y)k(the)i(use)f(of)g(suitable)f(data)h(structures.)262 1640 y Fu(6.5.2)55 b(Data)19 b(Structures)262 1752 y Fp(Data)c(structure)k (comp)q(osition)c(mak)o(es)g(a)h(large)h(con)o(tribution)f(to)g(o)o(v)o (erall)g(program)f(ef-)262 1802 y(\014ciency)j(b)o(y)f(allo)o(wing)e(fast)i (storage)g(and)h(retriev)n(al)f(of)f(imp)q(ortan)o(t)g(information.)25 b(The)262 1852 y(incremen)o(tal)13 b(attac)o(k)g(tables)i(and)e(transp)q (osition)h(table)g(are)g(ob)o(vious)g(examples)f(of)g(this.)262 1902 y(The)e(rather)i(complex)d(ev)n(aluation)g(function)h(w)o(ould)f(b)q(e)j (just)e(to)q(o)g(exp)q(ensiv)o(e)i(to)e(compute)262 1952 y(w)o(ere)j(it)g (not)g(for)f(the)i(attac)o(k)f(tables.)324 2037 y(Without)d(the)h(use)g(of)f (a)g(large)g(easily)g(accessible)i(transp)q(osition)e(table,)h(m)o(uc)o(h)e (w)o(asted)262 2087 y(e\013ort)18 b(w)o(ould)f(result)h(from)e(exploring)h (duplicate)h(subtrees.)32 b(The)18 b(impro)o(v)o(emen)o(ts)d(are)262 2137 y(particularly)f(eviden)o(t)j(in)e(the)h(endgame,)f(where)i(a)e(5-fold)g (sp)q(eed)i(impro)o(v)o(emen)o(t)c(is)j(not)262 2186 y(uncommon.)946 2574 y(139)p eop %%Page: 140 142 140 141 bop 262 307 a Fu(6.5.3)55 b(Co)r(de)18 b(Pro)r(duction)262 419 y Fp(Consideration)d(m)o(ust)g(also)g(b)q(e)h(giv)o(en)f(to)h(the)g(co)q (de)h(pro)q(duced)g(b)o(y)e(the)i(C)e(compiler.)23 b(It)262 469 y(ma)o(y)17 b(ha)o(v)o(e)j(b)q(een)h(noted)g(ho)o(w)e(all)g(m)o(y)f(main) g(data)h(structure)j(records)g(are)e(of)f(a)h(size)262 519 y(divisible)e(b)o(y)i(2.)35 b(This)20 b(allo)o(ws)f(the)h(compiler)f(to)g (use)i(a)e(less)i(time)d(consuming)h(shift)262 569 y(op)q(eration,)13 b(instead)h(of)f(m)o(ultiplication,)d(to)k(access)i(individual)11 b(records.)324 654 y(Unsigned)19 b(data)f(t)o(yp)q(es)h(are)g(used)h(where)g (p)q(ossible)e(to)h(impro)o(v)o(e)e(the)i(e\016ciency)g(of)262 704 y(the)13 b(addressing)h(co)q(de)g(pro)q(duced.)20 b(F)m(or)12 b(example,)g(when)i(using)f(a)g(signed)g(16)g(bit)g(in)o(teger)262 754 y(as)k(an)f(index)h(in)o(to)f(an)h(arra)o(y)m(,)f(the)i(compiler)d(m)o (ust)h(pro)q(duce)i(an)f(extra)h(instruction)f(to)262 803 y(p)q(erform)d (sign)i(extensions)h(\(EXT.L)e(on)h(a)f(MC68000\))g(in)h(a)f(32)g(bit)h (addressing)g(mo)q(de.)262 853 y(With)d(unsigned)h(in)o(tegers,)g(none)g(of)g (this)g(is)f(necessary)m(.)324 938 y(All)g(constructs)j(and)e(expressions)i (whic)o(h)e(pro)q(duce)i(time)d(exp)q(ensiv)o(e)i(mac)o(hine)e(co)q(de)262 988 y(are)h(a)o(v)o(oided)f(where)i(p)q(ossible.)j(F)m(or)c(example,)e(few)i (division)e(op)q(erations)i(are)h(used.)324 1073 y(Most)g(functions)g(use)h (register)g(v)n(ariables)e(for)g(the)i(most)d(commonly)f(used)j(data)g(ob-) 262 1123 y(jects.)36 b(Of)19 b(course,)j(ho)o(w)d(often)h(these)h(v)n (ariables)d(are)i(register)h(residen)o(t)g(dep)q(ends)g(on)262 1173 y(UNIX)14 b(and)f(the)i(C)f(Compiler.)324 1258 y(Unfolding)f(lo)q(ops)i (and)f(pro)q(ducing)h(linear)g(co)q(de)g(is)g(another)g(tric)o(k)g(to)g (extract)h(more)262 1308 y(sp)q(eed.)j(Ho)o(w)o(ev)o(er,)12 b(I)g(ha)o(v)o(e)g(a)o(v)o(oided)g(suc)o(h)h(practice)g(on)f(the)h(whole)f (to)g(impro)o(v)o(e)e(readabil-)262 1358 y(it)o(y)j(and)h(ease)g(dev)o (elopmen)o(t)f(testing.)324 1443 y(I)k(ha)o(v)o(e)h(made)e(a)h(n)o(um)o(b)q (er)g(of)g(critical)g(v)n(ariables)g(global)f(to)h(a)o(v)o(oid)f(using)i(up)f (time,)262 1493 y(passing)h(large)g(amoun)o(ts)g(of)g(data)g(on)g(the)i(stac) o(k.)32 b(Ho)o(w)o(ev)o(er,)20 b(I)f(ha)o(v)o(e)f(also)g(emplo)o(y)o(ed)262 1543 y(some)e(data)h(hiding)f(tec)o(hniques)j(where)f(suitable)g(to)f(ease)h (dev)o(elopmen)o(t)e(and)i(testing.)262 1593 y(The)c(HashDriv)o(er)g(mo)q (dule)e(is)i(an)g(ob)o(vious)f(example)g(of)g(this.)324 1678 y(Individually)m(,)18 b(all)g(these)j(impro)o(v)o(em)o(en)o(ts)d(are)h(v)o (ery)h(small.)32 b(Ho)o(w)o(ev)o(er,)21 b(when)f(y)o(ou)262 1728 y(consider)15 b(that)g(a)f(n)o(um)o(b)q(er)g(of)h(co)q(de)g(units)g(are) g(executed)i(man)o(y)c(milli)o(ons)f(of)i(times,)g(the)262 1778 y(o)o(v)o(erall)e(e\013ect)k(can)e(b)q(e)g(quite)g(impressiv)o(e.)946 2574 y(140)p eop %%Page: 141 143 141 142 bop 262 654 a Fn(Chapter)34 b(7)262 897 y Fo(Program)40 b(P)m(erformance)262 1148 y Fp(In)17 b(order)h(to)f(b)q(e)i(able)e(to)g(ev)n (aluate)g(the)h(tec)o(hniques)h(emplo)o(y)o(ed)d(in)h(HIAR)o(CS)g(5.0,)g(the) 262 1198 y(program's)g(strengths)k(and)d(w)o(eaknesses)k(need)e(to)f(b)q(e)g (assessed.)36 b(F)m(ortunately)m(,)19 b(c)o(hess)262 1248 y(pro)o(vides)14 b(man)o(y)e(w)o(a)o(ys)h(of)g(testing)i(a)e('pla)o(y)o(ers')g(abilit)o(y)m(.) 324 1333 y(The)g(ELO)h(c)o(hess)g(rating)f(system)g([19)o(])f(has)h(b)q(een)h (used)g(w)o(orld)f(wide)g(for)g(o)o(v)o(er)g(t)o(w)o(en)o(t)o(y)262 1383 y(y)o(ears)h(to)h(estimate)e(a)h(pla)o(y)o(er's)g(abilit)o(y)f(in)h (terms)g(of)f(rating)h(p)q(oin)o(ts.)20 b(Chess)15 b(ratings)f(are)262 1433 y(ac)o(hiev)o(ed)h(b)o(y)f(pla)o(ying)f(a)i(n)o(um)o(b)q(er)f(of)g (games)g(against)g(already)g(rated)i(pla)o(y)o(ers.)k(Using)15 b(a)262 1483 y(rating/probabilit)o(y)c(table,)i(a)h(rating)f(can)h(b)q(e)h (calculated)f(based)h(on)e(ones)i(p)q(erformance)262 1532 y(against)9 b(the)i(rated)f(pla)o(y)o(ers.)17 b(I)10 b(will)e(use)j(a)f(similar)e(metho)q (d)h(to)h(pro)o(vide)g(a)f(rough)h(estimate)262 1582 y(of)j(HIAR)o(CS's)g(c)o (hess)j(rating.)324 1667 y(Chess)g(ratings)g(can)f(also)g(b)q(e)h(estimated)f (from)f(a)h(set)h(of)f(test)i(p)q(ositions.)22 b(Although)262 1717 y(this)d(metho)q(d)g(is)h(not)f(used)i(o\016cially)d(to)h(rate)h(pla)o (y)o(ers,)h(it)e(can)h(b)q(e)h(used)f(to)g(giv)o(e)f(an)262 1767 y(estimate)11 b(of)h(the)h(tested)h(pla)o(y)o(ers)e(rating.)17 b(Also,)12 b(these)h(tests)h(allo)o(w)d(a)h(pla)o(y)o(er's)g(abilit)o(y)e(in) 262 1817 y(v)n(arious)k(areas)i(of)f(c)o(hess,)h(e.g.)23 b(tactical)15 b(pla)o(y)m(,)e(to)j(b)q(e)g(measured.)22 b(Therefore,)16 b(suc)o(h)h(test) 262 1867 y(p)q(ositions)9 b(will)f(b)q(e)j(useful)f(to)g(me)f(in)g(iden)o (tifying)f(the)j(relativ)o(e)e(strengths)j(and)e(w)o(eaknesses)262 1916 y(of)j(HIAR)o(CS.)324 2002 y(The)j(follo)o(wing)d(tests)k(will)d(b)q(e)i (p)q(erformed)g(to)f(assess)i(the)g(program's)d(o)o(v)o(erall)g(c)o(hess)262 2052 y(rating,)e(st)o(yle,)i(strength)h(and)f(w)o(eakness)h(in)e(the)i(v)n (arious)e(areas)h(of)g(the)g(game:)312 2170 y(1.)20 b Fl(Bratk)o(o-Kop)q(ec)g (T)l(ests)p Fp(:)k(These)19 b(test)g(p)q(ositions)e(will)f(b)q(e)i(used)h(to) e(estimate)g(a)365 2220 y(rating)10 b(and)f(assess)j(b)q(oth)e(the)g (tactical)g(and)f(p)q(ositional)g(strengths)i(of)e(the)i(program.)312 2303 y(2.)20 b Fl(Computer)15 b(Opp)q(osition)p Fp(:)h(A)e(matc)o(h)g(will)f (b)q(e)i(pla)o(y)o(ed)f(b)q(et)o(w)o(een)i(HIAR)o(CS)e(and)365 2353 y(a)g(rated)h(computer)e(opp)q(onen)o(t)h(to)g(illustrate)g(its)g(pla)o (ying)e(st)o(yle)i(and)g(estimate)g(its)365 2402 y(rating.)946 2574 y(141)p eop %%Page: 142 144 142 143 bop 312 307 a Fp(3.)20 b Fl(Human)f(Opp)q(osition)o Fp(:)h(A)d(matc)o(h)e(will)g(b)q(e)i(pla)o(y)o(ed)f(b)q(et)o(w)o(een)i(HIAR)o (CS)f(and)f(a)365 357 y(rated)h(h)o(uman)d(opp)q(onen)o(t)j(to)f(\014nd)g (out)g(ho)o(w)f(it)h(cop)q(es)h(with)f(a)g(h)o(uman's)e(st)o(yle)i(of)365 407 y(pla)o(y)d(and)h(to)g(further)g(estimate)g(its)g(rating.)312 490 y(4.)20 b Fl(Kno)o(wledge)c(v)o(ersus)g(Searc)o(h)p Fp(:)k(A)15 b(matc)o(h)g(will)e(b)q(e)j(pla)o(y)o(ed)f(b)q(et)o(w)o(een)i(HIAR)o(CS)365 540 y(and)c(a)g(v)o(ersion)g(of)f(itself)g(with)h(dramatically)d(reduced)15 b(leaf)d(no)q(de)h(kno)o(wledge)g(and)365 589 y(no)19 b(searc)o(h)g (extensions.)33 b(This)18 b('kno)o(wledge-less')g(v)o(ersion)h(of)f(HIAR)o (CS)g(will)f(b)q(e)365 639 y(allo)o(w)o(ed)h(to)g(searc)o(h)i(3)e(ply)h(deep) q(er)h(than)f(the)g(more)f(in)o(telligen)o(t)f(v)o(ersion.)33 b(This)365 689 y(should)18 b(enable)g(me)f(to)h(estimate)g(what)g(the)g(kno)o (wledge)g(is)g(w)o(orth)g(in)f(terms)h(of)365 739 y(searc)o(h)d(depth.)324 857 y(All)h(tests)j(are)f(p)q(erformed)f(with)g(HIAR)o(CS)g(5.0)f(running)h (on)g(a)g(SUN)h(3/80,)f(whic)o(h)262 907 y(pro)o(vides)d(a)f(rate)i(of)e (appro)o(ximately)e(300)i(to)h(1200)f(\(legal\))g(no)q(des)i(p)q(er)g (second.)262 1080 y Fr(7.1)69 b(Bratk)n(o-Kop)r(ec)23 b(T)-6 b(ests)262 1206 y Fp(A)10 b(series)i(of)d(24)h(test)h(p)q(ositions)f(w)o(as)h 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y(b)q(est)g(four)f(mo)o(v)o(es)e(in)i(order)h(of)e(merit)g (for)h(eac)o(h)h(p)q(osition.)24 b(A)16 b(correct)i(mo)o(v)o(e)c(w)o(as)i (then)262 1910 y(scored)j(as)f(follo)o(ws:)25 b(1)17 b(p)q(oin)o(t)h(for)g(a) f(correct)j(1st)e(c)o(hoice,)1226 1894 y Fk(1)p 1226 1901 17 2 v 1226 1925 a(2)1265 1910 y Fp(p)q(oin)o(t)g(for)f(a)h(correct)i(2nd)262 1960 y(c)o(hoice,)401 1944 y Fk(1)p 401 1951 V 401 1974 a(3)437 1960 y Fp(p)q(oin)o(t)13 b(for)h(a)f(correct)j(3rd)e(c)o(hoice)g(and)1065 1944 y Fk(1)p 1065 1951 V 1065 1974 a(4)1100 1960 y Fp(p)q(oin)o(t)g(for)f(a) h(correct)h(4th)f(c)o(hoice.)324 2045 y(The)f(problem)f(with)h(computer)f (test)j(sub)r(jects)f(is)f(that)g(the)h Fh(\013\014)i Fp(algorithm)10 b(do)q(es)k(not)262 2095 y(pro)o(vide)f(an)f(accurate)j(b)q(est)f(n)f(c)o (hoices,)h(only)f(the)g(b)q(est)i(mo)o(v)o(e)c(found)i(so)g(far.)18 b(Therefore,)262 2145 y(Bratk)o(o)g(and)f(Kop)q(ec)i(suggested)h(the)e (computers)h(c)o(hoice)f(after)g(120,)g(180,)g(30)f(and)h(60)262 2195 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y(the)f(b)q(est)g(mo)o(v)o(e.)k(This)c(highligh)o(ts)e(one)i(of)e(the)j (ma)r(jor)c(de\014ciencies)13 b(of)d(the)h(Bratk)o(o-Kop)q(ec)262 1730 y(tests:)20 b(no)14 b(merit)f(is)h(giv)o(en)g(for)g(c)o(hosen)h(mo)o(v)o (es)e(whic)o(h,)h(although)g(not)g(correct,)i(are)e(v)o(ery)262 1779 y(strong)g(alternativ)o(es.)k(After)d(all,)d(p)q(ositional)h(mo)o(v)o (es)f(are)j(sometimes)d(a)i(matter)f(of)g(st)o(yle)262 1829 y(and)g('p)q(ersonal')h(preference.)324 1915 y(T)m(ests)h(10)f(and)g(22)g(w)o (ere)h(just)g(to)q(o)f(deep,)h(tactically)f(sp)q(eaking,)g(for)g(HIAR)o(CS)g (to)g(see)262 1964 y(in)h(the)h(allotted)e(t)o(w)o(o)h(min)o(utes.)22 b(T)m(ests)16 b(20)f(and)h(23)f(are)h(v)o(ery)f(di\016cult)g(p)q(ositional)f (tests)262 2014 y(whic)o(h)f(HIAR)o(CS,)g(lik)o(e)g(almost)f(all)h(other)i (strong)f(programs)e(w)o(as)i(unable)g(to)g(solv)o(e.)324 2099 y(I)21 b(w)o(as)f(particularly)g(impressed)h(b)o(y)g(HIAR)o(CS's)f(correct)i (c)o(hoice)g(in)e(tests)i(3)f(and)262 2149 y(17.)27 b(None)18 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b(Ho)o(w)o(ev)o(er,)13 b(I)g(w)o(as)h(more)262 395 y(afraid)g(of)h(16.)22 b(...)g(Qh4!)h(to)16 b(whic)o(h)f(I)h(w)o(ould)e(ha)o(v)o(e)i(pla)o(y)o(ed)f(17.)22 b(Qe2;)16 b(not)g(17)f(hg)g(Nxg4)262 445 y(whic)o(h)e(lo)q(oks)h(v)o(ery)g (promising)e(e.g.)17 b(18.)h(Nf3)13 b(Qxf2+)h(19.)j(Kh1)d(Qg3!)781 542 y(17.)41 b(Qe2)70 b(Rfd8)781 592 y(18.)41 b(Red1)48 b(Rc5!?)781 642 y(19.)41 b(e4)102 b(a6)781 692 y(20.)41 b(f4)107 b(Ng6)781 741 y(21.)41 b(Qf2)75 b(Qc7)781 791 y(22.)41 b(Nde2)48 b(Rc4!)18 b(\(+48\))p 641 918 673 5 v 641 1582 5 665 v 646 1001 a Fg(0Z0s0ZkZ)646 1084 y(Zbl0Zpop)646 1167 y(po0ZpmnZ)646 1250 y(Z0Z0Z0Z0)646 1333 y(0ZrZPO0Z)646 1416 y(Z0M0Z0ZP)646 1499 y(PO0ZNLPZ)646 1582 y(ZBSRZ0J0)p 1310 1582 V 641 1586 673 5 v 745 1705 a Fp(P)o(osition)13 b(after)h(22.)k(...)f(Rc4!)324 1823 y(I)e(w)o(an)o(ted)g(to)h(form)d(a)i (strong)h(pa)o(wn)f(cen)o(ter,)i(ho)o(w)o(ev)o(er,)e(in)g(hindsigh)o(t)g(I)g (feel)g(I)h(o)o(v)o(er-)262 1873 y(stretc)o(hed)g(m)o(yself.)g(The)e(pa)o (wns)g(on)g(e4)g(and)g(f4)f(are)h(under)h(extreme)f(pressure.)781 2050 y(23.)41 b(Rxd8+)12 b(Qxd8)781 2099 y(24.)41 b(Rd1)66 b(Qc7)781 2149 y(25.)41 b(Rd4?)946 2574 y(155)p eop %%Page: 156 158 156 157 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(0Z0Z0ZkZ)646 482 y(Zbl0Zpop)646 565 y(po0ZpmnZ)646 648 y(Z0Z0Z0Z0)646 731 y(0ZrSPO0Z)646 814 y(Z0M0Z0ZP)646 897 y(PO0ZNLPZ)646 980 y(ZBZ0Z0J0)p 1310 980 V 641 984 673 5 v 765 1163 a Fp(P)o(osition)13 b(after)h(25.)k(Rd4?) 324 1257 y(I)c(though)o(t)h(Rd4)f(w)o(ould)g(reliev)o(e)h(the)g(pressure)i (on)d(the)i(white)e(cen)o(ter)j(pa)o(wns.)j(After)262 1307 y(25.)k(...)g(Rxd4)15 b(26.)24 b(Qxd4,)17 b(I)f(though)o(t)g(m)o(y)e(f-pa)o (wn)h(w)o(as)h(secure)j(b)q(ecause)e(of)f(the)h(mate)262 1357 y(threat)g(on)g(d8,)g(e.g.)26 b(26.)g(...)g(Nxf4)16 b(27.)27 b(Nxf4)16 b(Qxf4??)26 b(28.)g(Qd8+)18 b(Ne8)f(29.)26 b(Qxe8+)262 1407 y(mate.)16 b(Ho)o(w)o(ev)o(er,)e(I)g(missed)f(27.)18 b(...)f(e5)d(whic)o (h)g(wins)f(the)i(pa)o(wn.)781 1491 y(25.)41 b(...)105 b(Rxd4)781 1541 y(26.)41 b(Qxd4)i(Nxf4!)781 1591 y(27.)e(Nxf4)54 b(e5)781 1641 y(28.)41 b(Qd2)65 b(ef)781 1691 y(29.)41 b(a3)99 b(Kf8)14 b(\(+133\))p 641 1781 V 641 2445 5 665 v 646 1864 a Fg(0Z0Z0j0Z)646 1947 y(Zbl0Zpop)646 2030 y(po0Z0m0Z)646 2113 y(Z0Z0Z0Z0)646 2196 y(0Z0ZPo0Z)646 2279 y(O0M0Z0ZP)646 2362 y(0O0L0ZPZ)646 2445 y(ZBZ0Z0J0)p 1310 2445 V 641 2449 673 5 v 946 2574 a Fp(156)p eop %%Page: 157 159 157 158 bop 747 307 a Fp(P)o(osition)13 b(after)h(29.)k(...)f(Kf8.)324 422 y(HIAR)o(CS)10 b(is)h(preparing)g(to)f(bring)h(its)g(king)f(in)o(to)g (pla)o(y)m(.)15 b(I)c(pla)o(y)o(ed)f(29.)17 b(a3)10 b(to)h(allo)o(w)e(Ba2)262 472 y(at)15 b(an)g(opp)q(ortune)h(momen)o(t.)j(In)d(fact,)f(I)g(w)o(as)g (hoping)g(to)g(pla)o(y)f(Nd5;)i(sw)o(ap)f(o\013)g(knigh)o(ts)262 522 y(and)g(obtain)g(a)g(supp)q(orted)i(passed)f(d)g(pa)o(wn.)23 b(Ho)o(w)o(ev)o(er,)16 b(I)f(missed)g(31.)22 b(Qc5+)17 b(and)e(the)262 572 y(mate)d(threat)j(on)f(g2)f(sa)o(ving)g(blac)o(ks)h(b)g(and)f(f)h(pa)o (wns.)k(After)c(whic)o(h)g(the)h(game)d(is)i(lost.)781 736 y(30.)41 b(Nd5?)46 b(Nxd5)781 786 y(31.)41 b(ed)100 b(Qc5+)781 836 y(32.)41 b(Kh2?)k(Qxd5)14 b(\(+201\))781 886 y(33.)41 b(Qxd5)i(Bxd5)14 b(\(+248\))262 1001 y(Blac)o(ks)g(h-pa)o(wn)g(is)g(safe)g(as)h(Bxh7)f(is)g (met)f(b)o(y)h(g6!)19 b(The)14 b(mo)o(v)o(e)f(33.)18 b(Qxd5)d(w)o(as)f(bad,)f (but)262 1050 y(I)f(did)g(not)h(feel)g(lik)o(e)f(a)g(long)g(hard)h(queen)g (and)g(bishop)f(ending)h(whic)o(h)g(w)o(as)f(lost)h(an)o(yw)o(a)o(y)m(.)781 1144 y(34.)41 b(Bd3)68 b(b5)781 1194 y(35.)41 b(Kg1)67 b(h5)781 1244 y(36.)41 b(Be2)73 b(g6)781 1294 y(37.)41 b(a4)99 b(ba)781 1343 y(38.)41 b(Bxa6)48 b(Bc6)781 1393 y(39.)41 b(Kf2)75 b(Ke7)781 1443 y(40.)41 b(Be2)73 b(Kf6)781 1493 y(41.)41 b(Bc4)73 b(h4)781 1543 y(42.)41 b(Be2)73 b(Ke5)15 b(\(+292\))p 641 1666 673 5 v 641 2330 5 665 v 646 1749 a Fg(0Z0Z0Z0Z)646 1832 y(Z0Z0ZpZ0)646 1915 y(0ZbZ0ZpZ)646 1998 y(Z0Z0j0Z0)646 2081 y(pZ0Z0o0o)646 2164 y(Z0Z0Z0ZP)646 2247 y(0O0ZBJPZ)646 2330 y(Z0Z0Z0Z0)p 1310 2330 V 641 2334 673 5 v 744 2449 a Fp(P)o(osition)e(after)h(42.)k(...)f(Ke5.) 946 2574 y(157)p eop %%Page: 158 160 158 159 bop 324 307 a Fp(I)14 b(cannot)h(defend)h(the)f(b-pa)o(wn,)f(g-pa)o (wn)g(and)h(hold)f(bac)o(k)h(the)g(ev)o(en)o(tual)g(f5,)f(g5)g(and)262 357 y(g4,)19 b(therefore,)i(I)e(decided)i(to)d(simplify)f(and)i(attempt)f(to) h(pic)o(k)g(o\013)g(blac)o(ks)g(king)f(side)262 407 y(pa)o(wns)c(while)g (HIAR)o(CS)g(attempts)g(to)g(promote)f(its)i(a-pa)o(wn.)k(Ho)o(w)o(ev)o(er,) 14 b(HIAR)o(CS)g(did)262 457 y(not)f(allo)o(w)g(me)f(an)i(inkling)e(of)i (coun)o(ter)g(pla)o(y)m(.)781 625 y(43.)41 b(Bf3)78 b(Bxf3)14 b(\(+315\))781 675 y(44.)41 b(Kxf3)53 b(Kf5)781 725 y(45.)41 b(Kf2)75 b(Ke4)781 774 y(46.)41 b(Ke2)70 b(f5)14 b(\(+401\))781 824 y(47.)41 b(Kf2)75 b(Kd3)14 b(\(+670\))781 874 y(48.)41 b(Kf3)75 b(g5)14 b(\(+973\))876 924 y(resigns)899 974 y(0)47 b Ff(\000)42 b Fp(1)510 1023 y(Times:)242 b(1:46:33)12 b(1:59:47)262 1142 y(HIAR)o(CS)19 b(pla)o(y)o(ed)f(this)i(game)e(v)o(ery)h(solidly)m(,)g (punishing)g(m)o(y)e(mistak)o(es)i(e\016cien)o(tly)m(.)34 b(I)262 1192 y(think)14 b(it)h(w)o(ould)f(b)q(e)i(hard)f(to)g(tell)g(whether)h(a)f (computer)g(of)f(h)o(uman)f(w)o(as)i(blac)o(k)g(in)g(this)262 1241 y(game.)324 1327 y(In)h(game)f(2,)h(I)g(w)o(as)g(also)g(under)h(some)e (pressure,)k(ho)o(w)o(ev)o(er,)e(I)f(slo)o(wly)f(mano)q(euvred)262 1377 y(m)o(y)e(2)h(knigh)o(ts)g(in)o(to)g(activ)o(e)h(p)q(ositions)g(on)f (the)i(queen)f(side.)21 b(I)15 b(w)o(as)g(then)g(able)g(to)f(break)262 1426 y(the)i(p)q(osition)g(op)q(en)h(to)f(m)o(y)f(adv)n(an)o(tage.)24 b(I)17 b(ev)o(en)o(tually)f(reac)o(hed)h(the)g(ending,)g(a)f(queen)262 1476 y(for)g(ro)q(ok)g(and)g(bishop)g(up.)26 b(I)17 b(pla)o(y)o(ed)f(w)o(ell) f(and)i(w)o(as)f(able)g(to)g(simplify)e(in)o(to)i(an)g(easily)262 1526 y(w)o(on)d(king)g(and)h(pa)o(wn)f(ending.)324 1611 y(Although)k(HIAR)o (CS)g(c)o(hose)h(a)f(king)g(side)h(attac)o(k)f(plan)g(during)g(this)h(game,)e (it)h(did)262 1661 y(not)h(execute)j(it)d(e\016cien)o(tly)m(.)32 b(By)19 b(the)h(time)d(HIAR)o(CS)h(had)h(ac)o(hiev)o(ed)g(an)g(op)q(en)g (h-\014le)262 1711 y(for)e(its)h(ro)q(oks,)h(m)o(y)d(o)o(wn)i(plan)f(w)o(as)h (already)f(w)o(ell)h(dev)o(elop)q(ed.)31 b(This)17 b(illustrates)i(that)262 1761 y(the)i(planning)e(mec)o(hanism)f(used)k(in)e(HIAR)o(CS)g(still)g (requires)h(a)g(lot)f(of)g(tuning)g(and)262 1810 y(enhancemen)o(t.)324 1896 y(I)e(will)e(not)i(use)h(this)f(matc)o(h)f(to)h(calculate)g(a)g(c)o (hess)i(rating)d(as)h(the)h(sample)e(is)h(to)q(o)262 1946 y(small.)24 b(Ho)o(w)o(ev)o(er,)17 b(it)g(w)o(as)f(clear)h(from)e(pla)o(ying)h(HIAR)o (CS,)g(that)g(it)h(has)g(a)f(distinctiv)o(e,)262 1995 y(uncomputer)9 b(lik)o(e,)h(pla)o(ying)e(st)o(yle)i(and)g(w)o(ould)f(mak)o(e)f(a)i(w)o(orth) o(y)g(opp)q(onen)o(t)g(for)g(an)o(y)f(pla)o(y)o(er)262 2045 y(rated)14 b(at)g(around)g(2000)e(ELO.)262 2218 y Fr(7.4)69 b(Kno)n(wledge)22 b(v)n(ersus)h(Searc)n(h)262 2344 y Fp(HIAR)o(CS)15 b(5.0)g(con)o(tains)i(a)e(signi\014can)o(t)h(amoun)o(t)e(of)i(c)o(hess)i(kno) o(wledge)d(compared)h(with)262 2394 y(the)c(t)o(ypical)e(Shannon)h(t)o(yp)q (e)h(A)g(program.)j(Muc)o(h)d(of)f(the)h(c)o(hess)h(kno)o(wledge)e(is)g (applied)g(at)262 2444 y(the)g(horizon)f(no)q(des)h(of)f(the)h(main)d(searc)o (h.)18 b(Although)10 b(this)g(approac)o(h)h(allo)o(ws)e(application)946 2574 y(158)p eop %%Page: 159 161 159 160 bop 262 307 a Fp(of)16 b(up)h(to)g(date)g(p)q(ositional)f(kno)o (wledge,)h(it)f(is)h(quite)g(time)f(consuming,)f(and)i(therefore)262 357 y(results)e(in)e(sligh)o(tly)f(shallo)o(w)o(er)i(searc)o(hes)i(b)q(eing)d (p)q(erformed.)324 442 y(It)j(w)o(ould)g(therefore)i(b)q(e)f(in)o(teresting)g (to)f(classify)g(what)h(the)g(kno)o(wledge)f(is)h('w)o(orth')262 492 y(in)f(terms)g(of)g(searc)o(h)h(depth.)27 b(This)17 b('w)o(orth')e(could) h(then)i(b)q(e)f(compared)f(to)g(its)h(cost)g(to)262 542 y(determine)c (whether)j(the)e(kno)o(wledge)g(is)f(cost)i(e\013ectiv)o(e.)324 627 y(I)g(ha)o(v)o(e)g(compared)g(kno)o(wledge)g(and)h(searc)o(h)g(b)o(y)g(p) q(erforming)e(a)h(4)g(game)f(matc)o(h)g(b)q(e-)262 677 y(t)o(w)o(een)j(HIAR)o (CS)g(5.0)f(and)g(a)h(v)o(ersion)g(of)f(itself)h(con)o(taining)f(only)g (piece)i(square)f(tables)262 727 y(for)11 b(its)h(horizon)g(no)q(de)h(ev)n (aluations)e(and)h(no)g(searc)o(h)h(extension)g(heuristics.)18 b(This)12 b(sp)q(ecial)262 777 y(v)o(ersion)i(of)f(HIAR)o(CS)g(will)g(b)q(e)h (referred)i(to)e(as)g Fm(NOKNO)o(W)p Fp(.)324 862 y(In)h(the)h(matc)o(h,)e (NOKNO)o(W)i(w)o(as)f(allo)o(w)o(ed)f(to)h(p)q(erform)f(a)h(full)f(width)h(6) g(ply)f(searc)o(h)262 912 y(and)f(HIAR)o(CS)h(5.0)f(w)o(as)h(restricted)i(to) d(a)h(\014xed)g(depth)h(3)f(ply)f(searc)o(h.)19 b(NOKNO)o(W)c(to)q(ok)262 961 y(b)q(et)o(w)o(een)20 b(30)f(seconds)i(and)e(20)g(min)o(utes)f(o)o(v)o (er)i(eac)o(h)g(mo)o(v)o(e,)e(whereas)j(HIAR)o(CS)e(to)q(ok)262 1011 y(around)e(1)g(to)g(10)f(seconds)j(p)q(er)f(mo)o(v)o(e.)27 b(Thinking)16 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y(at)i(no)q(des)h(in)f(their)g(subtree.)27 b(Hence,)18 b(when)f(the)g(transp)q(osition)f(table)h(is)f(prob)q(ed,)h(the)262 1956 y(required)j(searc)o(h)g(depth)h(ma)o(y)c(b)q(e)j(incorrect)h(b)q (ecause)g(it)e(do)q(es)h(not)g(tak)o(e)f(accoun)o(t)h(of)262 2005 y(p)q(ossible)15 b(extensions)h(n)f(ply)f(do)o(wn)h(the)h(subtree.)23 b(Therefore,)16 b(the)g(transp)q(osition)f(table)262 2055 y(ma)o(y)f(retriev) o(e)j(an)f(en)o(try)h(whic)o(h)f(satis\014es)h(the)g(depth)g(requiremen)o(t)f (at)g(this)h(no)q(de,)f(but)262 2105 y(w)o(ould)10 b(not)h(satisfy)g(the)h ('true')f(depth)h(requiremen)o(t)f(if)g(searc)o(h)h(extensions)g(w)o(ere)g (to)g(o)q(ccur)262 2155 y(in)h(the)h(subtree.)324 2240 y(In)d(tactical)h(p)q (ositions,)f(this)h(often)f(causes)i(HIAR)o(CS)f(to)f(require)i(1)e(or)h(2)f (more)f(searc)o(h)262 2290 y(iterations)20 b(than)h(w)o(ould)e(normally)f(b)q (e)k(exp)q(ected.)40 b(This)20 b(is)h(most)e(noticeable)i(when)262 2340 y(HIAR)o(CS's)13 b(searc)o(h)i(fails)e(high,)g(indicating)g(it)h(has)g (found)f(a)h(clearly)g(b)q(etter)h(mo)o(v)o(e,)d(only)262 2390 y(for)h(the)i(re-searc)o(h)g(to)f(terminate)f(early)h(b)q(ecause)h(of)f(a)f (premature)h(en)o(try)h(matc)o(h.)946 2574 y(162)p eop %%Page: 163 165 163 164 bop 324 307 a Fp(The)14 b(solution)f(to)h(this)g(problem)f(lies)h(in) f(dramatically)e(expanding)j(eac)o(h)g(transp)q(osi-)262 357 y(tion)f(table)g(en)o(try)h(to)g(store)h(information)10 b(ab)q(out)k (extensions)h(in)e(the)h(subtree)i(b)q(elo)o(w)d(the)262 407 y(no)q(de)d(resp)q(onsible)i(for)e(storing)g(the)h(en)o(try)m(.)17 b(On)10 b(retriev)n(al,)h(this)f(information)d(can)k(then)g(b)q(e)262 457 y(used)j(to)g(determine)f(more)g(accurately)h(whether)h(an)e(en)o(try)i (should)e(cause)i(termination.)324 542 y(The)d(cost)g(e\013ectiv)o(eness)i (of)d(eac)o(h)h(ev)n(aluation)e(de\014nition)i(is)f(y)o(et)h(to)f(b)q(e)h (determined.)18 b(I)262 592 y(susp)q(ect,)13 b(most)c(criteria)i(will)f(need) i(mo)q(di\014cation)c(of)i(some)g(sort,)i(while)e(others)i(ma)o(y)d(ev)o(en) 262 641 y(b)q(e)16 b(unrequired.)25 b(Certainly)15 b(new)i(criteria)f(are)g (required)h(for)e(signi\014can)o(t)h(p)q(erformance)262 691 y(impro)o(v)o(em)o(en)o(t.)946 2574 y(163)p eop %%Page: 164 166 164 165 bop 262 654 a Fn(Chapter)34 b(8)262 897 y Fo(Conclusion)262 1148 y Fp(This)19 b(c)o(hapter)i(concludes)f(the)h(rep)q(ort)f(b)o(y)g (reviewing)f(what)h(has)g(b)q(een)g(in)o(v)o(estigated,)262 1198 y(discussing)14 b(the)h(ma)r(jor)d(ac)o(hiev)o(emen)o(ts)i(and)f (exploring)h(the)g(future)h(implications)c(of)i(m)o(y)262 1248 y(\014ndings.)36 b(Before)21 b(I)f(review)g(the)h(pro)r(ject)g(and)f(examine) f(its)h(ac)o(hiev)o(emen)o(ts,)h(let)f(me)262 1298 y(re-iterate)15 b(the)f(pro)r(ject)h(aims:)312 1374 y(1.)20 b(Ov)o(erview)15 b(the)f(tec)o(hniques)h(used)g(in)f(curren)o(t)h(c)o(hess)g(programs.)312 1454 y(2.)20 b(Dev)o(elop)13 b(an)g(ev)n(aluation)f(function)h(whic)o(h)g 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y(time)18 b(scale)i(plan)f(w)o(as)g(pro)q(duced)i(whic)o(h)e(set)i(time) d(scales)i(for)f(eac)o(h)i(ma)r(jor)c(activit)o(y)m(.)262 2250 y(Regularly)m(,)12 b(during)i(the)h(pro)r(ject,)h(progress)f(w)o(as)g (measured)f(and)g(review)o(ed)i(against)e(set)262 2300 y(ob)r(jectiv)o(es)h (and)g(time)f(scales.)23 b(This)15 b(allo)o(w)o(ed)e(me)h(to)h(iden)o(tify)g (and)f(set)i(sub-goals,)f(and)262 2350 y(k)o(ept)g(me)f(a)o(w)o(are)h(of)g (the)g(implications)e(an)o(y)h(problems)h(w)o(ould)f(ha)o(v)o(e)h(on)g(the)g (rest)i(of)d(m)o(y)262 2399 y(pro)r(ject.)38 b(This)21 b(in)f(turn)g(enabled) h(me)f(to)g(rep)q(ort)h(progress)h(at)e(m)o(y)f(regular)i(pro)r(ject)262 2449 y(meetings)13 b(and)g(allo)o(w)o(ed)g(the)i(pro)r(ject)f(to)g(dev)o (elop)g(smo)q(othly)m(.)946 2574 y(164)p eop %%Page: 165 167 165 166 bop 324 307 a Fp(In)13 b(c)o(hapters)h(1)f(and)g(2)f(I)h(in)o(tro)q (duced)h(the)g(sub)r(ject)g(of)f(computer)f(c)o(hess.)19 b(This)13 b(ga)o(v)o(e)g(a)262 357 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y(zo)o(witsc)o(h,)g (help)q(ed)h(enormously)e(at)h(this)h(di\016cult)e(stage.)20 b(I)14 b(also)g(felt)g(it)g(w)o(as)g(imp)q(ortan)o(t)262 1225 y(to)f(dev)o(elop)h(a)g(set)h(of)e(pseudo)h(co)q(de)h(functions)f(for)g(use)g (in)g(de\014ning)g(the)g(ev)n(aluation)f(cri-)262 1275 y(teria.)23 b(These)17 b(functions)f(w)o(ere)g(broad)g(enough)g(to)f(allo)o(w)f(me)h(to)g (express)j(a)d(signi\014can)o(t)262 1324 y(amoun)o(t)d(of)h(c)o(hess)i(kno)o (wledge,)e(while)h(b)q(eing)g(precise)h(enough)f(to)g(b)q(e)g(implemen)o (ted.)324 1410 y(In)g(c)o(hapter)g(5,)g(I)f(attempted)h(to)g(de\014ne)g(a)g (metho)q(d)f(of)g(tree)i(searc)o(hing)g(whic)o(h)e(w)o(ould)262 1460 y(enable)g(most)g(searc)o(h)h(e\013ort)h(to)e(b)q(e)h(exp)q(ended)i(in)d (pursuit)h(of)f(go)q(o)q(d)g(or)h(in)o(teresting)g(v)n(ari-)262 1509 y(ations.)k(My)d(hop)q(e)g(w)o(as)f(to)g(sim)o(ulate)f(the)h(greatly)h (v)n(ariable)e(depth)i(of)f(a)g(strong)g(h)o(uman)262 1559 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y(More)d(surprisingly)m(,)e(tree)j(searc)o (hing)f(w)o(as)f(seen)i(to)e(signi\014can)o(tly)f(impro)o(v)o(e)g(p)q (ositional)262 1138 y(abilit)o(y)m(.)15 b(This)c(w)o(as)h(clearly)f (illustrated)g(when)i(I)e(dev)o(elop)q(ed)h(an)g(almost)d('kno)o(wledge)i (less')262 1187 y(v)o(ersion)20 b(of)f(HIAR)o(CS,)h(whic)o(h)g(con)o(tained)g (only)f(Pc/Sq)i(tables.)37 b(When)20 b(this)g(sp)q(ecial)262 1237 y(v)o(ersion)c(w)o(as)f(searc)o(hing)i(6)f(plies)f(in)h(the)g(matc)o(h)f (against)g(HIAR)o(CS)h(5.0,)f(its)h(p)q(ositional)262 1287 y(pla)o(y)h(w)o(as)h(found)g(to)g(b)q(e)g(of)g(a)g(higher)g(calibre)g(than)g (could)g(b)q(e)h(exp)q(ected)h(considering)262 1337 y(its)f(rudimen)o(tary)f (c)o(hess)j(kno)o(wledge.)33 b(The)20 b(searc)o(h)g(w)o(as)f(actually)g (bridging)f(some)g(of)262 1387 y(the)c(program's)d(kno)o(wledge)i (de\014ciency)i(gap)e(b)o(y)g(allo)o(wing)f(higher)h(lev)o(el)g(concepts,)i (suc)o(h)262 1436 y(as)20 b(m)o(ultim)o(o)o(v)o(e)d(piece)22 b(path)o(w)o(a)o(ys,)f(to)f(b)q(e)h(considered.)39 b(This)20 b(in)g(part)h(explains)f(wh)o(y)262 1486 y(Deep)d(Though)o(t)f(is)g(able)h (to)f(displa)o(y)f(a)i(p)q(ositional)e(kno)o(wledge)h(m)o(uc)o(h)f(higher)i (than)g(its)262 1536 y(ev)n(aluation)12 b(function)i(w)o(ould)f(suggest.)324 1621 y(The)j(amoun)o(t)d(of)i(kno)o(wledge)g(whic)o(h)g(can)g(b)q(e)h (bridged)g(b)o(y)f(tree)h(searc)o(hing)g(dep)q(ends)262 1671 y(on)h(the)h(depth)h(of)e(searc)o(h.)30 b(Ho)o(w)o(ev)o(er,)19 b(some)e(c)o(hess)i(concepts)g(are)f(so)g(deep,)h(40)e(or)h(50)262 1721 y(plies,)12 b(that)h(it)g(will)e(b)q(e)j(almost)d(imp)q(ossible)g(for)i (searc)o(hing)h(alone)e(to)h(bridge)g(suc)o(h)h(a)f(gap.)262 1771 y(This)h(explains)h(wh)o(y)f(b)q(oth)i(the)f(Hitec)o(h)h(and)e(Deep)i (Though)o(t)e(teams)g(are)i(encoun)o(tering)262 1821 y(diminishing)8 b(returns)13 b(from)d(eac)o(h)i(additional)e(ply)h(of)g(searc)o(h.)18 b(In)12 b(order)g(to)g(a)o(v)o(oid)e(similar)262 1870 y(problems)k(and)h (reduce)i(HIAR)o(CS's)d(dep)q(endency)k(on)c(tree)j(searc)o(hing,)e(I)g(ha)o (v)o(e)g(instilled)262 1920 y(a)h(signi\014can)o(t)h(amoun)o(t)e(of)h(static) h(kno)o(wledge)g(in)f(the)i(w)o(a)o(y)e(of)g(p)q(ositional)g(criteria)h(and) 262 1970 y(dynamic)12 b(tactical)h(kno)o(wledge)h(in)f(the)i(w)o(a)o(y)e(of)g (selectiv)o(e)i(searc)o(h)g(extensions.)324 2055 y(HIAR)o(CS's)9 b(p)q(erformance)g(has)h(clearly)f(illustrated)h(that)f(extra)h(kno)o(wledge) g(can)g(more)262 2105 y(than)k(comp)q(ensate)h(for)g(reduced)i(searc)o(h)f (capacit)o(y)m(.)k(A)15 b(pa)o(wn)f(outside)i(the)f(quadrate)g(of)262 2155 y(the)i(opp)q(osing)f(king)f(is)i(a)f(clear)h(example)e(of)h(this:)24 b(without)16 b(direct)h(kno)o(wledge)g(ab)q(out)262 2205 y(king-pa)o(wn)12 b(quadrates,)j(a)e(full)g(width)h(searc)o(h)h(program)e(ma)o(y)f(require)j (up)f(to)g(an)g(11)f(ply)262 2255 y(searc)o(h)j(to)g(realise)g(the)g(pa)o(wn) f(can)h(queen.)24 b(HIAR)o(CS)15 b(5.0)g(is)g(capable)h(of)f(realising)g (this)262 2304 y(after)f(a)f(mere)h(1)f(ply)h(searc)o(h)h(b)q(ecause)g(of)f (its)g(c)o(hess)h(kno)o(wledge.)324 2390 y(Ho)o(w)d(far)g(c)o(hess)h(kno)o (wledge)g(can)f(b)q(e)h(increased)h(at)e(the)h(exp)q(ense)h(of)d(searc)o (hing,)i(with-)262 2439 y(out)h(degrading)g(o)o(v)o(erall)g(p)q(erformance)g (is)h(still)f(op)q(en)h(to)f(question.)21 b(Ho)o(w)o(ev)o(er,)15 b(I)f(b)q(eliev)o(e)946 2574 y(166)p eop %%Page: 167 169 167 168 bop 262 307 a Fp(full)10 b(width)i(searc)o(hing)g(can)g(b)q(e)g (reduced)i(in)d(fa)o(v)o(our)g(of)h(sophisticated)g(searc)o(h)h(extensions.) 262 357 y(The)i(lev)o(el)g(to)g(whic)o(h)g(the)g(full)f(width)h(p)q(ortion)g (of)f(the)i(searc)o(h)g(can)f(b)q(e)h(reduced)h(greatly)262 407 y(dep)q(ends)i(on)e(ho)o(w)g(comprehensiv)o(e)h(and)f(e\013ectiv)o(e)i (the)f(searc)o(h)h(extensions)f(are.)30 b(T)m(ak-)262 457 y(ing)15 b(this)g(approac)o(h)h(to)g(its)f(extreme)h(w)o(ould)f(result)i(in)e(a)h (totally)e(selectiv)o(e)j(searc)o(h)g(of)e(a)262 506 y(narro)o(w,)e(deep)i (game)d(tree.)324 592 y(When)18 b(long)g(term)f(c)o(hess)j(kno)o(wledge)e(is) g(con)o(tained)h(in)f(the)g(ev)n(aluation)f(function,)262 641 y(suc)o(h)f(as)g(pa)o(wn)g(structure)i(information)13 b(for)j(example,)f(eac) o(h)h(additional)e(ply)i(do)q(es)h(not)262 691 y(seem)d(to)h(su\013er)g(suc)o (h)h(diminishing)c(returns)k(as)f(seen)h(when)f(the)g(kno)o(wledge)f(con)o (ten)o(t)i(is)262 741 y(lo)o(w)o(er.)22 b(This)15 b(w)o(as)g(made)g(clear)g (b)o(y)h(the)g(un)o(usually)e(large)h(impro)o(v)o(emen)o(t)e(in)i(HIAR)o (CS's)262 791 y(pla)o(y)d(b)q(et)o(w)o(een)k(30)d(seconds)i(and)f(3)g(min)o (utes)f(a)g(mo)o(v)o(e.)324 876 y(The)19 b(ac)o(hiev)o(emen)o(t)f(of)f(iden)o (tifying)g(and)i(com)o(bining)d(tactical)i(uncertain)o(t)o(y)h(in)f(the)262 926 y(ev)n(aluation)12 b(function)h(has)h(b)q(een)h(b)q(ene\014cial.)j(Allo)o (wing)12 b(the)i(searc)o(h)h(heuristics)g(to)e(mak)o(e)262 976 y(use)19 b(of)f(this)h(information)d(has)j(help)q(ed)h(reduce)g(the)g (programs)d(susceptibilit)o(y)i(to)g(the)262 1026 y(horizon)13 b(e\013ect.)324 1111 y(Not)d(only)g(is)h(HIAR)o(CS's)f(p)q(ositional)f(pla)o (y)h(signi\014can)o(tly)g(impro)o(v)o(ed,)f(but)i(the)g(tactical)262 1161 y(standard)h(pro)q(duced)i(from)c(ev)o(en)j(shallo)o(w)e(searc)o(h)i (depths)h(is)e(impressiv)o(e.)17 b(F)m(or)11 b(example,)262 1210 y(on)j(one)g(o)q(ccasion,)g(HIAR)o(CS)g(solv)o(ed)g(a)g("mate)f(in)h(5)g (problem")f(while)g(only)h(at)g(the)h(\014rst)262 1260 y(ply)e(of)h(full)f (width)h(searc)o(h.)20 b(The)15 b(tactical)f(impro)o(v)o(em)o(en)o(t)e(is)i (only)g(eviden)o(t,)g(ho)o(w)o(ev)o(er,)g(in)262 1310 y(v)n(ariations)g(con)o (taining)g(mo)o(v)o(es)h(that)g(can)h(b)q(e)g(iden)o(ti\014ed)g(b)o(y)f(the)i (extension)f(heuristics.)262 1360 y(Ho)o(w)o(ev)o(er,)d(as)h(the)h(tactical)e (co)o(v)o(erage)i(is)e(quite)h(large,)g(the)g(o)o(v)o(erall)f(a\013ect)i(is)e (b)q(ene\014cial.)324 1445 y(A)d(lot)f(of)h(progress)h(has)f(b)q(een)i(made)d (on)g(the)i(sub)r(ject)h(of)d(time)g(allo)q(cation)f(and)i(con)o(trol.)262 1495 y(The)16 b(resulting)g(algorithm)d(has)j(certainly)g(impro)o(v)o(ed)f (HIAR)o(CS's)g(o)o(v)o(erall)g(standard)h(of)262 1545 y(pla)o(y)c(b)o(y)i (allo)q(cating)e(and)i(adjusting)f(time)g(relativ)o(e)h(to)f(the)i(needs)g (of)e(the)i(p)q(osition.)324 1630 y(The)i(results)h(pro)q(duced)g(on)f(the)g (Bratk)o(o-Kop)q(ec)h(test)g(p)q(ositions)e(clearly)h(illustrate)262 1680 y(that)c(HIAR)o(CS)h(do)q(es)h(displa)o(y)d(the)j(tactical)f(and)f(p)q (ositional)g(abilit)o(y)f(of)h(an)h(exp)q(ert)h(lev)o(el)262 1730 y(pla)o(y)o(er,)9 b(hence)i(meeting)e(the)i(aims)d(set)i(out)g(at)g(the) g(b)q(eginning)f(of)g(the)i(pro)r(ject.)17 b(What)10 b(w)o(as)262 1779 y(most)j(surprising)h(ab)q(out)g(HIAR)o(CS's)g(results)i(on)e(the)h (test)g(p)q(ositions)f(w)o(as)g(its)h(balanced)262 1829 y(p)q(ositional)g (and)h(tactical)g(abilit)o(y)m(.)24 b(These)18 b(results)g(are)e (particularly)g(impressiv)o(e)g(when)262 1879 y(compared)f(to)g(the)i (results)g(obtained)e(from)f(other)j(c)o(hess)g(programs)e(on)g(the)i(same)e (test)262 1929 y(p)q(ositions.)324 2014 y(The)d(results)h(ac)o(hiev)o(ed)g (in)e(the)i(matc)o(hes)e(pla)o(y)o(ed)h(b)o(y)f(HIAR)o(CS)h(against)f(b)q (oth)h(h)o(uman)262 2064 y(and)17 b(computer)g(opp)q(osition)f(re-enforce)j (the)f(results)h(ac)o(hiev)o(ed)f(in)f(the)h(Bratk)o(o-Kop)q(ec)262 2114 y(exp)q(erimen)o(t.)946 2574 y(167)p eop %%Page: 168 170 168 169 bop 262 307 a Fr(8.3)69 b(Implications)20 b(and)k(F)-6 b(uture)23 b(Prosp)r(ects)262 434 y Fp(Ov)o(er)16 b(the)h(last)e(10)h(y)o (ears,)g(full)f(width)g(Shannon)h(t)o(yp)q(e)g(A)g(programs)f(ha)o(v)o(e)h (made)e(great)262 483 y(adv)n(ances,)c(partly)g(due)h(to)f(adv)n(anced)g(sp)q (ecial)h(purp)q(ose)g(hardw)o(are)g(and)f(partly)g(to)g(sophis-)262 533 y(ticated)17 b(searc)o(h)i(algorithms)c(suc)o(h)j(as)f(PVS)g(with)g (singular)g(extensions,)h(for)f(example.)262 583 y(V)m(ery)g(little)g(or)h (no)f(progress)i(has)f(b)q(een)g(made)f(o)o(v)o(er)g(the)h(same)f(p)q(erio)q (d)h(in)f(dev)o(eloping)262 633 y(purely)i(kno)o(wledge)h(based)g(programs)e (capable)i(of)f(high)g(lev)o(el)g(pla)o(y)f(throughout)i(the)262 683 y(game.)c(It)e(seems)g(that)f(the)i(problems)e(of)g(kno)o(wledge)g (acquisition,)f(represen)o(tation)k(and)262 732 y(\014nally)d(implemen)o (tation)f(are)j(at)g(presen)o(t)h(to)q(o)f(great)g(to)g(mak)o(e)f(suc)o(h)h (kno)o(wledge)g(based)262 782 y(programs)g(successful.)28 b(Certainly)m(,)16 b(the)h(k)o(ey)g(to)g(these)h(t)o(yp)q(es)f(of)f(program)f(remains)h(in)262 832 y(the)e(b)q(etter)i(understanding)e(of)f(ho)o(w)h(strong)g(pla)o(y)o(ers) g(think.)324 917 y(There)e(seems)g(to)f(b)q(e)h(t)o(w)o(o)e(main)g(approac)o (hes)i(to)f(dev)o(eloping)f(an)h(in)o(telligen)o(t)g(selectiv)o(e)262 967 y(searc)o(h)k(program.)312 1081 y(1.)20 b(Creating)14 b(an)g(in)o (telligen)o(t,)e(kno)o(wledge)i(based)g(program)e(from)h(scratc)o(h.)312 1162 y(2.)20 b(Gradual)13 b(c)o(hange)h(to)g(a)g(full)e(width)i(Shannon)g(t)o (yp)q(e)g(A)g(program.)262 1276 y(An)9 b(approac)o(h)h(of)f(gradual)f(c)o (hange)i(to)g(existing)f(programs)f(seems)i(to)g(me)e(to)i(o\013er)g(a)f(b)q (etter)262 1326 y(hop)q(e)k(of)g(ev)o(en)o(tual)g(success.)21 b(I)13 b(feel)g(a)h(program)d(lik)o(e)i(HIAR)o(CS)g(5.0)f(could)h(represen)o (t)j(the)262 1376 y(\014rst)e(step)g(in)f(a)g(gradual)f(transition)h(from)e (a)i(sophisticated)h(Shannon)f(t)o(yp)q(e)h(A)f(program)262 1426 y(to)18 b(an)g(in)o(telligen)o(t)f(Shannon)i(t)o(yp)q(e)g(B/C)f (program.)31 b(The)19 b(ma)r(jor)d(adv)n(an)o(tage)i(of)g(suc)o(h)262 1476 y(an)c(approac)o(h)g(is)h(that)f(the)i(program)d(can)h(serv)o(e)i(as)f (a)f(v)o(ehicle)h(for)f(exp)q(erimen)o(ting)g(with)262 1525 y(ideas.)34 b(Hop)q(efully)m(,)20 b(this)f(will)f(in)h(turn)h(enable)g(the)g (researc)o(her)i(to)d(acquire)h(a)f(b)q(etter)262 1575 y(understanding)14 b(of)f(the)i(problems)e(and)g(issues)i(in)o(v)o(olv)o(ed.)324 1660 y(The)d(3)f(ma)r(jor)g(di\016culties)g(a\013ecting)h(the)g(dev)o (elopmen)o(t)f(of)g(a)h(go)q(o)q(d)f(ev)n(aluation)g(func-)262 1710 y(tion)i(remain)f(kno)o(wing:)324 1824 y Ff(\017)20 b Fl(whic)o(h)13 b Fp(ev)n(aluation)f(criteria)j(are)f(imp)q(ortan)o(t.)324 1905 y Ff(\017)20 b Fl(when)14 b Fp(ev)n(aluation)e(criteria)i(are)h(imp)q (ortan)o(t.)324 1986 y Ff(\017)20 b Fl(what)14 b Fp(the)g(relativ)o(e)g (merits)f(of)h(eac)o(h)g(ev)n(aluation)e(criterion)j(should)e(b)q(e.)262 2100 y(The)i(solution)f(to)g(these)j(problems)d(lie)g(in)g(a)h(signi\014can)o (t)f(con)o(tribution)h(from)e(high)h(lev)o(el)262 2150 y(pla)o(y)o(ers)h(and) h(the)g(con)o(tin)o(ual)f(ev)o(olution)g(of)g(ev)n(aluation)f(criteria.)24 b(The)17 b(problems)e(asso-)262 2200 y(ciated)g(with)g(assigning)f(discrete)j (v)n(alues)e(to)g(c)o(hess)i(concepts)g(is)e(a)g(ma)r(jor)f(di\016cult)o(y)g (for)262 2250 y(the)e(exp)q(ert)h(c)o(hess)g(pla)o(y)o(er.)k(Applying)11 b(v)n(alue)g(ranges)h(instead)g(of)f(single)g(v)n(alues)h(ma)o(y)e(b)q(e)i(a) 262 2300 y(p)q(ossibilit)o(y)m(.)j(This)e(com)o(bined)f(with)g(a)g(range)h (and)g(probabilit)o(y)e(based)i(searc)o(h)h(algorithm)262 2350 y(w)o(ould)f(b)q(e)i(an)f(in)o(teresting)h(p)q(ossibilit)o(y)m(.)j(Learning)c (ma)o(y)e(pla)o(y)i(an)g(imp)q(ortan)o(t)f(role)h(here,)262 2399 y(ho)o(w)o(ev)o(er,)i(man)o(y)e(of)h(the)h(problems)f(outlined)g(in)h(c) o(hapter)h(3)e(m)o(ust)g(b)q(e)h(solv)o(ed)g(if)f(this)h(is)262 2449 y(to)d(b)q(e)i(the)f(case.)946 2574 y(168)p eop %%Page: 169 171 169 170 bop 324 307 a Fp(The)11 b(com)o(bination)e(of)i(the)g(transp)q (osition)h(table)f(and)g(searc)o(h)h(extensions)g(has)f(pro)o(v)o(ed)262 357 y(problematical.)j(The)e(expansion)e(of)g(eac)o(h)i(table)e(en)o(try)i (to)e(include)h(mo)o(v)o(e)e(sequences)14 b(and)262 407 y(extension)j (information)d(is)i(required.)27 b(As)18 b(w)o(ell)e(as)g(easing)h(the)g (problems)f(outlined)g(in)262 457 y(section)i(7.6,)e(this)i(impro)o(v)o(em)o (en)o(t)d(could)i(allo)o(w)f(a)h(h)o(uman)f(pla)o(y)o(er)g(to)i(ask)f("what)g (if)f(?")262 506 y(questions.)31 b(The)18 b(transp)q(osition)g(table)g(could) g(b)q(e)h(prob)q(ed)g(after)f(a)g(searc)o(h)h(to)f(answ)o(er)262 556 y(suc)o(h)c(questions)h(with)f(mo)o(v)o(e)e(sequences)17 b(and)d(scores.)20 b(The)14 b Fh(\013\014)j Fp(algorithm)11 b(w)o(ould)i(limit)262 606 y(suc)o(h)j(a)g(metho)q(d)f(b)q(ecause)j(of)d(p)q (ossible)h(cut)h(o\013s,)f(but)g(still)f(a)h(step)h(in)e(the)i(direction)f (of)262 656 y(understanding)i(mo)o(v)o(e)e(selection)j(w)o(ould)e(b)q(e)h (made.)29 b(Another)19 b(p)q(ossibilit)o(y)e(is)g(the)i(use)262 706 y(of)c(the)h(ev)n(aluation)f(function)h(to)f(answ)o(er)i(questions)f(ab)q (out)g(the)h(p)q(osition)e(e.g.)24 b("whic)o(h)262 756 y(squares)13 b(are)h(w)o(eak)e(around)h(the)g(white)g(king)f(?".)17 b(Suc)o(h)c(approac)o (hes)h(w)o(ould)e(help)g(strong)262 805 y(c)o(hess)h(pla)o(y)o(ers)f(to)g (iden)o(tify)g(program)e(w)o(eaknesses)15 b(and)d(allo)o(w)e(the)j(program)e (designer)i(to)262 855 y(w)o(ork)g(more)g(closely)h(with)f(c)o(hess)j(pla)o (y)o(ers)e(ha)o(ving)e(little)i(programmi)o(ng)d(kno)o(wledge.)324 940 y(HIAR)o(CS)16 b(5.0)f(con)o(tains)h(man)o(y)e(searc)o(h)j(extension)g (heuristics)g(whic)o(h)f(mak)o(e)f(a)g(p)q(os-)262 990 y(itiv)o(e)i(con)o (tribution)g(to)h(its)g(tactical)f(abilit)o(y)m(.)28 b(The)18 b(next)h(step)f(w)o(ould)f(not)h(only)f(b)q(e)i(to)262 1040 y(enhance)c(and)f(tune)h(these)h(existing)e(heuristics,)h(but)f(to)g(in)o (tro)q(duce)h(new)g(heuristics.)21 b(In)262 1090 y(particular,)13 b(there)h(seems)g(no)g(reason)g(wh)o(y)f(p)q(ositional)g(t)o(yp)q(e)h(searc)o (h)h(extensions)f(cannot)262 1140 y(b)q(e)i(in)o(tro)q(duced.)27 b(Although)15 b(the)i(asso)q(ciated)g(di\016culties)f(are)h(man)o(y)m(,)d (the)j(rew)o(ards)g(are)262 1189 y(great.)324 1275 y(Ov)o(er)d(the)f(coming)e (mon)o(ths,)h(I)h(will)f(endev)o(our)i(to)e(correct)j(man)o(y)c(of)i(the)h(w) o(eaknesses)262 1324 y(iden)o(ti\014ed)20 b(in)h(HIAR)o(CS)f(5.0's)g(pla)o(y) m(.)37 b(HIAR)o(CS)20 b(5.n)g(will)g(b)q(e)h(en)o(tered)h(in)f(the)g(c)o (hess)262 1374 y(tournamen)o(t)10 b(of)h(the)h(2nd)f(Computer)g(Olympiad)e (later)j(this)f(y)o(ear.)18 b(Hop)q(efully)m(,)10 b(HIAR)o(CS)262 1424 y(will)16 b(b)q(e)j(using)f(a)g(25Mhz)h(68030)e(for)h(this)g(ev)o(en)o (t.)32 b(The)19 b(result)g(this)g(summer)d(will)h(b)q(e)262 1474 y(in)o(teresting.)324 1559 y(Man)o(y)e(of)f(the)i(tec)o(hniques)g(used)g (in)f(computer)g(c)o(hess)i(programs)d(ma)o(y)f(b)q(e)j(useful)f(in)262 1609 y(other)f(problem)e(domains.)k(I)e(con)o(tacted)h(Hans)f(Berliner)g(at)g (CMU)g(ab)q(out)f(the)h(p)q(ossibil-)262 1659 y(ities)i(of)f(applying)g(some) g(of)g(the)i(latest)f(searc)o(h)h(tec)o(hniques)h(to)d(Theorem)h(Pro)o(ving)f ([8].)262 1709 y(Although)i(no)i(one)f(has)h(built)f(sp)q(ecial)g(purp)q(ose) i(hardw)o(are,)f(the)g('c)o(hess)h(approac)o(h')e(is)262 1758 y(apparen)o(tly)13 b(b)q(eing)h(lo)q(ok)o(ed)f(up)q(on)h(fa)o(v)o(ourably)m (.)324 1844 y(I)g(hop)q(e)g(this)g(pro)r(ject)h(has)f(sho)o(wn)g(that)f(b)q (oth)h(c)o(hess)i(kno)o(wledge)d(and)h(searc)o(hing)g(can)262 1893 y(complemen)o(t)f(eac)o(h)k(other)g(and)e(that)h(a)g(go)q(o)q(d)g (balance)g(b)q(et)o(w)o(een)h(the)g(t)o(w)o(o)e(can)h(ac)o(hiev)o(e)262 1943 y(results.)946 2574 y(169)p eop %%Page: 170 172 170 171 bop 262 675 a Fo(Bibliog)q(raph)m(y)324 913 y Fp([1])19 b(G.)e(M.)g(Adelson-V)m(elskiy)h(and)f(M.)g(V.)h(Donsk)o(o)o(y)e(\(1975\))h (:)26 b Fm(Some)19 b(Metho)n(ds)g(of)388 963 y(Contr)n(ol)r(ling)g(the)g(T)m (r)n(e)n(e)g(Se)n(ar)n(ch)g(in)h(Chess)f(Pr)n(o)n(gr)n(ams.)f Fp(Arti\014cial)g(In)o(telligence,)388 1012 y(V)m(ol)13 b(6)h(No)f(4,)h(pp)g (361-371.)324 1095 y([2])19 b(G.)g(M.)f(Adelson-V)m(elskiy)m(,)i(V.)f(L.)f (Arlazaro)o(v,)i(A.)f(R.)f(Bitman,)h(A.)f(A.)h(Zhiv)o(o-)388 1145 y(to)o(vskiy)h(and)f(A.)h(V.)f(Usk)o(o)o(v)h(\(1970\))f(:)30 b Fm(Pr)n(o)n(gr)n(amming)20 b(a)g(Computer)g(to)h(Play)388 1195 y(Chess.)14 b Fp(Russian)f(Math.)h(Surv)o(eys,)g(pp)g(221-262)324 1278 y([3])19 b(T.)14 b(Anan)o(tharaman,)f(M.)g(Campb)q(ell,)g(F.)h(Hsu)h (\(1988\))e(:)19 b Fm(Singular)d(Extensions)g(:)388 1328 y(A)n(dding)i(Sele)n (ctivity)e(to)h(Brute{F)m(or)n(c)n(e)g(Se)n(ar)n(ching.)f Fp(ICCA)h(Journal,) f(V)m(ol)f(11)h(No)388 1378 y(4,)d(pp)h(135-143.)324 1461 y([4])19 b(L.)f(R.)f(A)o(tkin)h(and)g(D.)f(J.)h(Slate)g(\(1977\))f(:)26 b Fm(CHESS)20 b(4.5)e(-)h(The)g(Northwestern)388 1510 y(University)14 b(Chess)g(Pr)n(o)n(gr)n(am.)f Fp(Chess)h(Skill)e(in)h(Man)g(and)g(Mac)o (hine,)g(P)m(.)g(W.)f(F)m(rey)388 1560 y(\(ed\),)j(pp)e(82-118,)f(Springer{V) m(erlag,)h(New)i(Y)m(ork.)324 1643 y([5])k(D.)13 b(F.)h(Beal)g(\(1989\))f(:) 18 b Fm(Exp)n(eriments)c(with)g(the)h(Nul)r(l)f(Move.)h Fp(Adv)n(ances)f(in)f (Com-)388 1693 y(puter)20 b(Chess)g(5,)f(D.)f(F.)g(Beal)g(\(ed\),)j(pp)d (65-79,)g(Elsevier)i(Science)g(Publishers)388 1743 y(B.V.,)13 b(North)i(Holland.)324 1826 y([6])k(H.)f(J.)f(Berliner)i(\(1979\))e(:)26 b Fm(The)18 b(B*)h(T)m(r)n(e)n(e)e(Se)n(ar)n(ch)i(A)o(lgorithm)e(:)26 b(A)18 b(Best)h(First)388 1876 y(Pr)n(o)n(of)c(Pr)n(o)n(c)n(e)n(dur)n(e.)e Fp(Arti\014cial)g(In)o(telligence,)h(V)m(ol)f(12,)f(No)i(1,)f(pp)h(23-40.)324 1959 y([7])19 b(H.)11 b(J.)h(Berliner)g(\(1989\))f(:)16 b Fm(Some)e (Innovations)f(Intr)n(o)n(duc)n(e)n(d)g(by)g(Hite)n(ch.)e Fp(Adv)n(ances)388 2009 y(in)h(Computer)f(Chess)j(5,)d(D.)h(F.)g(Beal)g(\(ed\),)h(pp)f(283-293,) e(Elsevier)j(Science)g(Pub-)388 2058 y(lishers)i(B.V.,)e(North)h(Holland.)324 2141 y([8])19 b(H.)14 b(J.)g(Berliner)g(:)k Fm(Personal)d(Communic)n(ation,)g (F)m(eb)g(1990.)324 2224 y Fp([9])k(A.)14 b(Bernstein)h(and)f(M.)f(de)h(V.)f (Rob)q(erts)i(\(1958\))e(:)k Fm(Computer)e(vs)g(Chess)f(Player.)388 2274 y Fp(Scien)o(ti\014c)h(American,)d(198,)h(pp)h(96-105.)303 2357 y([10])19 b(P)m(.)14 b(Bettadapur)h(\(1986\))f(:)19 b Fm(In\015uenc)n(e)e(of)e(Or)n(dering)f(on)i(Captur)n(e)f(Se)n(ar)n(ch.)g Fp(ICCA)388 2407 y(Journal,)e(V)m(ol)g(9,)g(No)h(4,)f(pp)h(180-188.)946 2574 y(170)p eop %%Page: 171 173 171 172 bop 303 307 a Fp([11])19 b(J.)12 b(A.)g(Birmingham)d(and)j(P)m(.)f (Ken)o(t)i(\(1977\))e(:)17 b Fm(T)m(r)n(e)n(e-se)n(ar)n(ching)12 b(and)i(T)m(r)n(e)n(e-pruning)388 357 y(T)m(e)n(chniques.)h Fp(Adv)n(ances)g(in)f(Computer)f(Chess)j(1,)e(M.)f(Clark)o(e)h(\(ed\),)h(pp)g (89-107.)388 407 y(Edin)o(burgh)f(Univ)o(ersit)o(y)g(Press.)303 487 y([12])19 b(I.)g(Bratk)o(o)h(and)f(D.)f(Kop)q(ec)j(\(1982\))e(:)29 b Fm(The)20 b(Br)n(atko{Kop)n(e)n(c)g(Exp)n(eriment)g(:)29 b(A)388 536 y(Comp)n(arison)16 b(of)f(Human)i(and)f(Computer)f(Performanc)n (e)h(in)f(Chess.)g Fp(Adv)n(ances)388 586 y(in)10 b(Computer)g(Chess)i(3,)e (Clark)o(e)h(M.)f(\(ed\),)h(pp)g(51-72.)e(P)o(ergamon)g(Press,)j(Oxford.)303 666 y([13])19 b(M.)12 b(S.)g(Campb)q(ell)f(and)h(T.)g(A.)g(Marsland)g (\(1983\))g(:)17 b Fm(A)c(Comp)n(arison)h(of)f(Minimax)388 716 y(T)m(r)n(e)n(e)h(Se)n(ar)n(ch)h(A)o(lgorithms.)e Fp(Arti\014cial)g(In)o (telligence,)h(V)m(ol)e(20)i(No)f(4,)h(pp)g(347-367.)303 795 y([14])19 b(J.)g(H.)f(Condon)g(and)g(K.)g(Thompson)f(\(1982\))h(:)27 b Fm(Bel)r(le)19 b(Chess)g(Har)n(dwar)n(e.)e Fp(Ad-)388 845 y(v)n(ances)d(in)e(Computer)g(Chess)h(3,)g(M.)f(Clark)o(e)g(\(ed\),)h(pp)g (45-54,)e(P)o(ergamon)g(Press,)388 895 y(Oxford.)303 975 y([15])19 b(S.)14 b(M.)f(Cracraft)h(\(1984\))f(:)18 b Fm(Bitmap)c(Move)i(Gener)n(ation) f(in)f(Chess.)g Fp(ICCA)f(Jour-)388 1024 y(nal,)g(V)m(ol)g(7,)g(No)h(3,)f(pp) h(146-153.)303 1104 y([16])19 b(A.)26 b(D.)f(de)h(Gro)q(ot)f(\(1978\))g(:)42 b Fm(Thought)26 b(and)h(Choic)n(e)f(in)g(Chess.)f Fp(Mouton-)388 1154 y(DeGruyter,)15 b(2nd)e(edition.)303 1234 y([17])19 b(A.)e(D.)g(de)h (Gro)q(ot)f(and)h(R.)e(W.)h(Jongman)e(\(1966\))i(:)25 b Fm(Heuristics)18 b(in)g(p)n(er)n(c)n(eptual)388 1284 y(pr)n(o)n(c)n(esses.)c Fp(In)o(ternational)f(Congress)i(of)e(Psyc)o(hology)m(,)g(Mosco)o(w,)g (August)h(1966.)303 1363 y([18])19 b(C.)10 b(Eb)q(eling)f(\(1986\))h(:)16 b Fm(A)o(l)r(l)10 b(the)h(R)o(ight)h(Moves)f({)h(A)f(VLSI)g(A)o(r)n(chite)n (ctur)n(e)f(for)h(Chess.)388 1413 y Fp(PhD)j(thesis,)h(Carnegie{Mellon)e (Univ)o(ersit)o(y)m(.)303 1493 y([19])19 b(A.)i(E.)f(Elo)h(\(1978\))f(:)32 b Fm(The)21 b(R)n(atings)g(of)h(Chess)f(Players)g(Past)g(and)h(Pr)n(esent.) 388 1543 y Fp(Batsford)15 b(Bo)q(oks,)e(London.)303 1622 y([20])19 b(M.)d(Eu)o(w)o(e)h(\(1970\))f(:)23 b Fm(Computers)17 b(and)h(Chess.)e Fp(The)h(Encyclopaedia)f(of)g(Chess,)388 1672 y(A.)e(Sunn)o(uc)o(ks)g (\(ed\),)h(St)f(Martin's)f(Press,)i(New)g(Y)m(ork.)303 1752 y([21])k Fm(Discussion)d(with)e(T)m(om)h(F)m(urstembur)n(g,)e(Fidelity)i(Ele) n(ctr)n(onics,)f(A)o(ugust)h(1989.)303 1831 y Fp([22])k(J.)c(J.)f(Gillogly)e (\(1972\))i(:)19 b Fm(The)d(T)m(e)n(chnolo)n(gy)g(Chess)f(Pr)n(o)n(gr)n(am.)f Fp(Arti\014cial)g(In)o(telli-)388 1881 y(gence,)h(V)m(ol)e(3,)g(pp)h (145-163.)303 1961 y([23])19 b(R.)f(D.)f(Green)o(blatt,)i(D.)f(E.)g(Eastlak)o (e)g(I)q(I)q(I)h(and)f(S.)g(D.)f(Cro)q(c)o(k)o(er)i(\(1967\))f(:)27 b Fm(The)388 2011 y(Gr)n(e)n(enblatt)15 b(Chess)f(Pr)n(o)n(gr)n(am.)f Fp(Pro)q(c.)i(FJCC,V)m(ol)d(31,)h(pp)h(801-810)303 2090 y([24])19 b(G.)14 b(Grottling)g(\(1986\))g(:)19 b Fm(The)d(Swe)n(dish)f(r)n(ating)h (list.)d Fp(ICCA)i(Journal,)f(V)m(ol)g(9,)g(No)388 2140 y(1,)f(pp)h(56.)303 2220 y([25])19 b(J.)i(Hamlen)e(\(1989\))g(:)32 b Fm(T)m(r)n(e)n(e)19 b(Se)n(ar)n(ching)j(A)o(lgorithms)e(and)h(Computer)g(Chess.)388 2270 y Fp(M.Sc.)14 b(Thesis,)g(Univ)o(ersit)o(y)g(of)f(London.)303 2350 y([26])19 b(L.)12 b(R.)f(Harris)i(\(1977\))e(:)17 b Fm(The)d(Heuristic)e (Se)n(ar)n(ch)h(:)18 b(A)o(n)c(alternative)f(to)g(the)g(alpha-)388 2399 y(b)n(eta)19 b(minimax)f(pr)n(o)n(c)n(e)n(dur)n(e.)f Fp(Chess)i(Skill)d (in)h(Man)h(and)f(Mac)o(hine.)h(P)m(.)f(W.)f(F)m(rey)388 2449 y(\(ed\),)f(pp)e(157-166,)f(Springer{V)m(erlag,)h(New)i(Y)m(ork.)946 2574 y(171)p eop %%Page: 172 174 172 173 bop 303 307 a Fp([27])19 b(D.)d(Hartmann)g(\(1989\))g(:)24 b Fm(Notions)17 b(of)h(Evaluation)g(F)m(unctions)g(T)m(este)n(d)f(against)388 357 y(Gr)n(andmaster)g(Games.)f Fp(Adv)n(ances)h(in)f(Computer)f(Chess)i(5,)f (D.)f(F.)h(Beal)g(\(ed\),)388 407 y(pp)e(91-141,)e(Elsevier)j(Science)g (Publishers)g(B.V.,)e(North)h(Holland.)303 487 y([28])19 b(E.)c(Hearst)i (\(1977\))d(:)21 b Fm(Man)c(and)g(Machine)g(:)k(Chess)16 b(A)n(chievements)h (and)g(Chess)388 536 y(Thinking.)f Fp(Chess)h(Skill)d(in)h(Man)g(and)h(Mac)o (hine.)f(P)m(.)g(W.)f(F)m(rey)i(\(ed\),)g(Springer{)388 586 y(V)m(erlag,)d(New)i(Y)m(ork.)303 666 y([29])k(R.)14 b(M.)g(Hy)o(att)g (\(1983\))f(:)19 b Fm(Cr)n(ay)c(Blitz)g(-)g(A)g(Computer)g(Chess)g(Playing)h (Pr)n(o)n(gr)n(am.)388 716 y Fp(M.Sc.)e(Thesis.)303 795 y([30])19 b(R.)12 b(M.)g(Hy)o(att)h(\(1984\))f(:)17 b Fm(Using)d(Time)f(Wisely.)f Fp(ICCA)h(Journal,)f(V)m(ol)g(7)g(No)g(1,)h(pp)388 845 y(4-9.)303 925 y([31])19 b(R.)10 b(M.)f(Hy)o(att,)i(A.)e(E.)h(Go)o(w)o(er)g(and)g(H.)g (L.)g(Nelson)g(\(1984\))g(:)16 b Fm(Cr)n(ay)11 b(Blitz.)e Fp(Adv)n(ances)388 975 y(in)j(Computer)f(Chess)i(4,)e(D.)g(F.)h(Beal)g(\(ed\),)g(pp)g(8-18,)f(P) o(ergamon)g(Press,)i(Oxford.)303 1054 y([32])19 b(B.)11 b(M.)f(Kazic)i (\(1980\))e(:)16 b Fm(The)c(Chess)g(Comp)n(etitor's)f(Handb)n(o)n(ok.)h Fp(Batsford)f(Bo)q(oks,)388 1104 y(London.)303 1184 y([33])19 b(D.)9 b(E.)h(Kn)o(uth)g(and)f(R.)g(W.)f(Mo)q(ore)i(\(1975\))f(:)16 b Fm(A)o(n)11 b(analysis)g(of)g(alpha-b)n(eta)g(pruning.)388 1234 y Fp(Arti\014cial)j(In)o(telligence,)f(V)m(ol)g(6)h(No)f(4,)g(pp)h (293-326.)303 1313 y([34])19 b(D.)11 b(Kop)q(ec,)h(M.)e(Newb)q(orn)i(and)f (W.)f(Y)m(u)h(\(1986\))f(:)17 b Fm(Exp)n(eriments)12 b(in)h(Chess)f(Co)n (gni-)388 1363 y(tion.)d Fp(Adv)n(ances)i(in)e(Computer)f(Chess)j(4,)e(D.)g (F.)g(Beal)g(\(ed\),)i(pp)e(59-79.)f(P)o(ergamon)388 1413 y(Press,)15 b(Oxford.)303 1493 y([35])k(A.)e(Kotok)h(\(1962\))e(:)25 b Fm(A)18 b(Chess)h(Playing)f(Pr)n(o)n(gr)n(am)f(for)h(the)g(IBM)h(7090.)f Fp(B.Sc.)388 1543 y(Thesis,)c(MIT.)303 1622 y([36])19 b(D.)13 b(Levy)h(\(1976\))g(:)k Fm(Chess)c(and)i(Computers.)d Fp(Batsford)i(Bo)q (oks,)e(London.)303 1702 y([37])19 b(D.)c(Levy)h(\(1979\))g(:)22 b Fm(Chess)16 b(Pr)n(o)n(gr)n(amming.)f Fp(P)o(ersonal)h(Computer)f(W)m (orld,)g(Ma)o(y)388 1752 y(1979,)e(pp)h(25-27.)303 1831 y([38])19 b(D.)12 b(Levy)m(,)g(D.)f(Brough)o(ton,)h(M.)g(T)m(a)o(ylor)f(\(1989\))h(:)17 b Fm(The)c(SEX)h(A)o(lgorithm)e(in)i(Com-)388 1881 y(puter)h(Chess.)f Fp(ICCA)g(Journal,)f(V)m(ol)f(12)i(No)g(1,)f(pp)h(10-21.)303 1961 y([39])19 b(T.)f(A.)f(Marsland)h(\(1985\))f(:)26 b Fm(Evaluation)19 b(F)m(unction)g(F)m(actors.)e Fp(ICCA)h(Journal,)388 2011 y(V)m(ol)13 b(8)h(No)f(2,)h(pp)g(47-57.)303 2090 y([40])19 b(T.)10 b(A.)f(Marsland)h (\(1986\))f(:)16 b Fm(A)c(R)n(eview)f(of)g(Game-T)m(r)n(e)n(e)f(Pruning.)g Fp(ICCA)g(Journal,)388 2140 y(V)m(ol)j(9)h(No)f(1,)h(pp)g(3-19.)303 2220 y([41])19 b(T.)10 b(A.)f(Marsland)g(\(1990\))g(:)16 b Fm(The)11 b(Br)n(atko-Kop)n(e)n(c)g(T)m(est)g(R)n(evisite)n(d.)e Fp(ICCA)g(Journal,)388 2270 y(V)m(ol)k(13,)g(No)h(1,)f(pp)h(15-19.)303 2350 y([42])19 b(A.)12 b(New)o(ell,)f(J.)h(C.)f(Sha)o(w)g(and)h(H.)f(A.)h (Simon)d(\(1958\))i(:)17 b Fm(Chess)c(Playing)g(Pr)n(o)n(gr)n(ams)388 2399 y(and)k(the)e(Pr)n(oblem)h(of)f(Complexity.)f Fp(IBM)h(Journal)g(of)f (Researc)o(h)i(and)e(Dev)o(elop-)388 2449 y(men)o(t,)f(Oct)i(1958,)d(pp)i (320-335.)946 2574 y(172)p eop %%Page: 173 175 173 174 bop 303 307 a Fp([43])19 b(A.)13 b(Nimzo)o(witsc)o(h)f(\(1929\))g(:) 18 b Fm(My)c(System.)f Fp(Mo)q(dern)h(Chess)g(Masterpieces,)h(Bats-)388 357 y(ford)f(Bo)q(oks,)g(London.)303 440 y([44])19 b(A.)11 b(Nimzo)o(witsc)o(h)f(\(1936\))g(:)17 b Fm(Chess)12 b(Pr)n(axis.)f Fp(Batsford)g(Chess)i(Classics,)e(Batsford)388 490 y(Bo)q(oks,)j(London.)303 573 y([45])19 b(T.)c(Nitsc)o(he)h(\(1982\))e(:)20 b Fm(A)c(L)n(e)n(arning)f (Chess)h(Pr)n(o)n(gr)n(am.)e Fp(Adv)n(ances)i(in)e(Computer)388 623 y(Chess)h(3,)f(M.)f(Clark)o(e)h(\(ed\),)g(pp)g(113-120.)d(P)o(ergamon)i (Press,)i(Oxford.)303 706 y([46])k(A.)f(Reinefeld)f(\(1983\))g(:)25 b Fm(A)o(n)18 b(Impr)n(ovement)h(of)f(the)g(Sc)n(out)h(T)m(r)n(e)n(e-Se)n(ar) n(ch)e(A)o(lgo-)388 756 y(rithm.)c Fp(ICCA)h(Journal,)f(V)m(ol)g(6)h(No)f(4,) g(pp)h(4-14.)303 839 y([47])19 b(F.)14 b(Rein\014eld)f(\(1945\))h(:)j Fm(Win)f(A)o(t)e(Chess.)g Fp(Do)o(v)o(er)f(Bo)q(oks.)303 922 y([48])19 b(A.)h(L.)e(Sam)o(uels)h(\(1959\))f(:)30 b Fm(Some)20 b(Studies)h(in)f(Machine)h(L)n(e)n(arning)f(using)h(the)388 971 y(Game)f(of)f(Che)n(ckers.)e Fp(IBM)i(Journal)f(of)g(Researc)o(h)h(and)f (Dev)o(elopmen)o(t,)g(3,)h(pp)388 1021 y(211-229.)303 1104 y([49])g(A.)h(L.)e(Sam)o(uels)h(\(1967\))f(:)30 b Fm(Some)20 b(Studies)h(in)f(Machine)h(L)n(e)n(arning)f(using)h(the)388 1154 y(Game)d(of)f(Che)n(ckers,)g(II)g(-)g(R)n(e)n(c)n(ent)g(Pr)n(o)n(gr)n (ess.)e Fp(IBM)i(Journal)f(of)f(Researc)o(h)j(and)388 1204 y(Dev)o(elopmen)o(t,)13 b(V)m(ol)f(2)i(No)g(6,)f(pp)h(601-617.)303 1287 y([50])19 b(J.)14 b(Sc)o(hae\013er)h(\(1983\))e(:)18 b Fm(The)d(History)f(Heuristic.)f Fp(ICCA)h(Journal,)f(V)m(ol)g(6,)g(No)g(3,) 388 1337 y(pp)h(16-19.)303 1420 y([51])19 b(J.)12 b(Sc)o(hae\013er)h (\(1984\))e(:)17 b Fm(The)c(R)n(elative)f(Imp)n(ortanc)n(e)h(of)g(Know)r(le)n (dge.)f Fp(ICCA)f(Jour-)388 1469 y(nal,)i(V)m(ol)g(7)g(No)h(3,)f(pp)h (138-145.)303 1553 y([52])19 b(G.)14 b(Sc)o(hrufer)i(\(1989\))e(:)20 b Fm(A)15 b(Str)n(ate)n(gic)g(Quiesc)n(enc)n(e)h(Se)n(ar)n(ch.)f Fp(ICCA)g(Journal,)f(V)m(ol)388 1602 y(12)g(No)f(1,)h(pp)g(3-9.)303 1685 y([53])19 b(C.)f(E.)g(Shannon)g(\(1950\))g(:)27 b Fm(Pr)n(o)n(gr)n (amming)18 b(a)i(Computer)e(for)h(Playing)g(Chess.)388 1735 y Fp(Philosophical)13 b(Mag,)g(V)m(ol)g(41,)f(pp)i(256-275.)303 1818 y([54])19 b(A.)12 b(Shapiro)f(and)g(T.)g(Niblett)h(\(1982\))f(:)17 b Fm(A)o(utomatic)12 b(Induction)i(of)f(Classi\014c)n(ation)388 1868 y(R)o(ules)j(for)e(a)i(Chess)f(Endgame.)g Fp(Adv)n(ances)g(in)f (Computer)f(Chess)j(3,)d(M.)h(Clark)o(e)388 1918 y(\(ed\),)h(pp)e(73-91.)g(P) o(ergamon)f(Press,)j(Oxford.)303 2001 y([55])k(H.)14 b(A.)f(Simon)f(and)i(K.) f(A.)h(Gilmartin)d(\(1973\))i(:)18 b Fm(A)c(Simulation)h(of)g(Memory)g(for) 388 2051 y(Chess)g(Positions.)f Fp(Cognitiv)o(e)f(Psyc)o(hology)m(,)f(5,)h (pp)h(29-46.)303 2134 y([56])19 b(H.)10 b(A.)f(Simon)f(and)h(W.)g(G.)g(Chase) i(\(1973\))e(:)15 b Fm(Skil)r(l)c(in)g(Chess.)f Fp(American)f(Scien)o(tist,) 388 2183 y(61,)k(pp)h(394-403.)303 2267 y([57])19 b(S.)f(S.)f(Skiena)h (\(1986\))g(:)26 b Fm(A)o(n)19 b(Overview)e(of)i(Machine)g(L)n(e)n(arning)g (in)g(Computer)388 2316 y(Chess.)14 b Fp(ICCA)g(Journal,)f(V)m(ol)g(9)g(No)h (1,)f(pp)h(20-27.)303 2399 y([58])19 b(D.)c(J.)g(Slate)g(\(1987\))g(:)21 b Fm(A)16 b(Chess)g(Pr)n(o)n(gr)n(am)f(that)h(uses)h(its)e(T)m(r)n(ansp)n (osition)h(T)m(able)388 2449 y(to)f(L)n(e)n(arn)g(fr)n(om)f(Exp)n(erienc)n (e.)g Fp(ICCA)g(Journal,)f(V)m(ol)g(10)g(No)h(2,)f(pp)h(59-71.)946 2574 y(173)p eop %%Page: 174 176 174 175 bop 303 307 a Fp([59])19 b(E.)i(Slater)g(\(1950\))f(:)32 b Fm(Statistics)20 b(for)h(the)g(Chess)h(Computer)f(and)h(the)f(F)m(actor)388 357 y(of)e(Mobility.)d Fp(Symp)q(osium)f(on)i(Information)e(Theory)m(,)j (London)f(:)26 b(Ministry)17 b(of)388 407 y(Supply)m(,)c(pp)h(150-152.)303 490 y([60])19 b(A.)11 b(M.)h(T)m(uring)e(\(1950\))h(:)17 b Fm(Computing)c(Machinery)g(and)g(Intel)r(ligenc)n(e.)f Fp(Mind,)f(V)m(ol)388 540 y(59,)i(pp)h(433-460.)303 623 y([61])19 b(D.)g(E.)f(Wilkins)g(\(1980\))g (:)28 b Fm(Using)20 b(Patterns)f(and)h(Plans)g(in)g(Chess.)e Fp(Arti\014cial)388 672 y(In)o(telligence,)c(V)m(ol)f(14,)g(No)g(1,)h(pp)f (165-203.)303 756 y([62])19 b(B.)14 b(H.)g(W)m(o)q(o)q(d)e(\(1986\))i(:)k Fm(The)c(World)h(Chess)g(Championship.)f Fp(Chess)h(Magazine,)388 805 y(B.)f(H.)g(W)m(o)q(o)q(d)f(\(ed\),)h(August)g(-)g(No)o(v)o(em)o(b)q(er)f (86,)g(V)m(ol)g(51,)f(Nos)j(987-994.)303 888 y([63])k(A.)f(L.)e(Zobrist)i (\(1970\))f(:)25 b Fm(A)19 b(Hashing)f(Metho)n(d)h(with)f(Applic)n(ations)g (for)f(Game)388 938 y(Playing.)d Fp(T)m(ec)o(hnical)f(rep)q(ort)i(88,)e (Computer)g(Sciences)i(Dept,)f(Univ)f(of)g(Wiscon-)388 988 y(sin,)h(Madison)f(WI,)g(April)g(1970.)303 1071 y([64])19 b(A.L.)f(Zobrist)h (and)f(F.)h(R.)e(Carlson,)i(Jr)g(\(1973\))f(:)27 b Fm(A)o(n)19 b(A)n(dvic)n(e{T)m(aking)h(Chess)388 1121 y(Computer.)14 b Fp(Scien)o(ti\014c)g(American,)f(228,)f(pp)i(92-105.)946 2574 y(174)p eop %%Page: 175 177 175 176 bop 262 654 a Fn(App)s(endix)33 b(A)262 897 y Fo(Glossary)321 1120 y Fl(ABF)254 b(A)p Fp(v)o(erage)14 b Fl(B)p Fp(ranc)o(hing)g Fl(F)p Fp(actor.)321 1220 y Fl(AI)300 b Fp(Arti\014cial)13 b(In)o(telligence.)321 1320 y Fl(ELO)258 b Fp(A)14 b(c)o(hess)h(rating)f (system)f(used)i(b)o(y)f(the)g(w)o(orld)f(c)o(hess)j(federation.)321 1419 y Fl(en-prise)187 b Fp(A)14 b(piece)h(is)e Fm(en-prise)h Fp(if)f(it)h(can)g(b)q(e)g(pro\014tably)g(captured.)321 1519 y Fl(HIAR)o(CS)167 b(H)p Fp(igher)14 b Fl(I)p Fp(n)o(telligence)g Fl(A)p Fp(uto)g Fl(R)p Fp(esp)q(onse)i Fl(C)p Fp(hess)f Fl(S)p Fp(ystem.)321 1619 y Fl(ply)288 b Fp(One)15 b(half)d(mo)o(v)o(e)h(e.g.)k(a)d (mo)o(v)o(e)e(for)i(white.)321 1718 y Fl(P)o(osition)o(al)e(Pla)o(y)39 b Fp(The)14 b(mano)q(euv)o(ering)f(of)g(pieces)i(to)f(b)q(etter)h(squares.) 321 1818 y Fl(Pc/Sq)g(table)104 b Fp(Piece)15 b(Square)f(T)m(able.)321 1918 y Fl(PVS)258 b(P)p Fp(rinciple)13 b Fl(V)p Fp(ariation)g Fl(S)p Fp(earc)o(h.)321 2017 y Fl(T)l(actical)i(Pla)o(y)81 b Fp(Sequence)16 b(of)d(threat)i(and)e(capture)i(t)o(yp)q(e)g(mo)o(v)o(es.) 321 2117 y Fl(T)l(emp)q(o)211 b Fp(A)14 b(single)f(mo)o(v)o(e)g(as)h(a)f (unit)h(of)f(time)g(in)g(c)o(hess,)i(e.g.)j(the)c(loss)g(of)f(a)h(temp)q(o) 675 2167 y(w)o(ould)f(b)q(e)h(caused)h(b)o(y)f(taking)f(t)o(w)o(o)h(mo)o(v)o (es)e(to)i(accomplish)e(something)675 2216 y(whic)o(h)i(could)f(b)q(e)i(ac)o (hiev)o(ed)f(in)f(one)i(mo)o(v)o(e.)321 2316 y Fl(USCF)226 b(U)p Fp(nited)14 b Fl(S)p Fp(tates)g Fl(C)p Fp(hess)i Fl(F)p Fp(ederation)e(rating)f(system.)18 b(Ratings)675 2366 y(on)c(this)g(scale)g (are)g(t)o(ypically)f(100-150)f(p)q(oin)o(ts)i(higher)g(than)f(the)675 2416 y(equiv)n(alen)o(t)g(ELO)h(rating,)f(e.g.)18 b(2100)13 b(USCF)h Ff(\031)g Fp(2000)f(ELO.)946 2574 y(175)p eop %%Page: 176 178 176 177 bop 262 654 a Fn(App)s(endix)33 b(B)262 897 y Fo(Pseudo)40 b(F)-10 b(unctions)262 1148 y Fp(This)15 b(app)q(endix)g(con)o(tains)h(a)f (description)h(of)e(the)i(pseudo)h(functions)e(used)h(in)f(the)h(de\014-)262 1198 y(nition)11 b(of)h(m)o(y)f(ev)n(aluation)g(function.)18 b(The)13 b(functions)f(are)h(giv)o(en)f(in)h(alphab)q(etical)e(order.)946 2574 y(176)p eop %%Page: 177 179 177 178 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(A)n(ttac)n(k)n(ed)19 b(:)24 b(PieceList)17 b(x)h(Colour)h(x)f(Square)h Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(A)o(ttac)o(k)o(ed\(pl,c)o(ol,sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(TR)o(UE)g (if)f(square)i Fm(sq)f Fp(is)f(attac)o(k)o(ed)h(b)o(y)g(an)o(y)g(of)f(the)h (pieces)h(in)f(piecelist)g Fm(pl)g Fp(of)321 910 y(colour)f Fm(c)n(ol)p Fp(.)321 960 y(Otherwise)i(F)-5 b(ALSE.)262 1309 y Fu(FUNCTION)p 262 1316 309 2 v 262 1408 a(A)n(ttac)n(king)18 b(:)25 b(Piece)17 b(x)i(Colour)g(x)f(Square)g(x)g(Square)g Ft(=)-8 b Fa(\))19 b Fu(Bo)r(olean)262 1508 y Fl(Example)p 262 1523 182 2 v 262 1612 a Ft(A)o(ttac)o(king\(p)q(c,col,sq1,sq2\))262 1711 y Fl(Descripti)o(on)p 262 1726 241 2 v 321 1812 a Fp(Returns)14 b(TR)o(UE)g(if)f(piece)i Fm(p)n(c)f Fp(of)f(colour)h Fm(c)n(ol)f Fp(on)h(square)h Fm(sq1)f Fp(is)f(attac)o(king)h(square)g Fm(sq2)p Fp(.)321 1862 y(Otherwise)h(F)-5 b(ALSE.)946 2574 y(177)p eop %%Page: 178 180 178 179 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a Fs(])p Fu(A)n(ttac)n(ks)19 b(:)24 b(PieceList)17 b(x)h(Colour)h(x)f(Square) g Ft(=)-8 b Fa(\))19 b Fu(In)n(teger)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Fs(])p Ft(A)o(ttac)o(ks\(pl,col,sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)14 b(the)h(n)o(um)o(b)q(er)e(of)g(attac)o(ks)h(on)g(square)h Fm(sq)f Fp(b)o(y)f(an)o(y)h(of)f(the)i(pieces)g(in)e(piecelist)h Fm(pl)321 910 y Fp(of)f(colour)g Fm(c)n(ol)p Fp(.)262 1259 y Fu(FUNCTION)p 262 1266 309 2 v 262 1359 a(Bishop)18 b(:)24 b(Colour)19 b(x)g(Colour)f Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 1458 y Fl(Example)p 262 1473 182 2 v 262 1562 a Ft(Bishop\(col1,col2\))262 1661 y Fl(Descripti)o(on)p 262 1676 241 2 v 321 1762 a Fp(Returns)c(TR)o(UE)g(if)f (colour)h Fm(c)n(ol1)f Fp(still)g(has)h(a)g(bishop)g(whic)o(h)f(op)q(erates)j (on)d(squares)i(of)321 1812 y(colour)e Fm(c)n(ol2)p Fp(.)946 2574 y(178)p eop %%Page: 179 181 179 180 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(Castled)18 b(:)25 b(Colour)18 b Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(Castled\(col\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(TR)o(UE)g (if)f(colour)h Fm(c)n(ol)f Fp(has)h(castled.)19 b(Otherwise)c(F)-5 b(ALSE.)262 1060 y Fu(FUNCTION)p 262 1067 309 2 v 262 1159 a(Cen)n(tralP)n(oin)n(t)19 b(:)24 b(Square)19 b Ft(=)-8 b Fa(\))18 b Fu(Square)262 1259 y Fl(Example)p 262 1274 182 2 v 262 1363 a Ft(Cen)o(tralP)o(oin)o(t\(sq\))262 1462 y Fl(Descripti)o(on)p 262 1477 241 2 v 321 1563 a Fp(Returns)c(an)g(o\013set)h(square,)f Fm(csq)g Fp(whic)o(h)g(represen)o(ts)i(the)f(cen)o(tral)f(p)q(oin)o(t)f(of)h (the)g(defensiv)o(e)321 1613 y(kings)f(p)q(osition.)k(Returns)e Fm(csq)f Fp(where)380 1713 y(csq)g(=)g(sq)380 1762 y Fl(if)e Fp(\(OnRank\(sq\))i(=)h(1\))439 1812 y(csq)f(=)g(csq)h(+)f(8)380 1862 y Fl(else)439 1912 y(if)e Fp(\(OnRank\(sq\))j(=)f(8\))498 1962 y(csq)g(=)g(csq)h(-)f(8)439 2012 y Fl(endif)380 2061 y(endif)380 2111 y(if)e Fp(\(OnFile\(sq\))j(=)f(1\))439 2161 y(csq)g(=)g(csq)h(+)f(1)380 2211 y Fl(else)439 2261 y(if)e Fp(\(OnFile\(sq\))j(=)f(8\))498 2310 y(csq)g(=)g(csq)h(-)f(1)439 2360 y Fl(endif)380 2410 y(endif)946 2574 y Fp(179)p eop %%Page: 180 182 180 181 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(Con)n(trol)19 b(:)24 b(Square)18 b Ft(=)-8 b Fa(\))18 b Fu(Con)n(troller) 262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(Con)o(trol\(sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(the)h(con)o (troller)f(of)f(square)i Fm(sq)p Fp(.)j(The)c(con)o(troller)g(is)g(de\014ned) h(to)e(b)q(e)i(the)321 910 y(colour)e(who)h(attac)o(ks)g(the)h(square)f Fm(sq)g Fp(with)g(more)f(pieces)i(of)e(a)h(sp)q(eci\014c)h(t)o(yp)q(e)f(than) 321 960 y(the)g(opp)q(onen)o(t)g(and)g(the)g(n)o(um)o(b)q(er)g(of)f(all)g (other)h(attac)o(ks)g(b)o(y)g(lo)o(w)o(er)f(v)n(alued)h(pieces)321 1010 y(are)g(equal.)321 1060 y(A)o(ttac)o(ks)g(are)g(compared)g(in)f(the)h (order)h(:)j(P)m(,N,B,R,Q,K.)12 b(If)h(all)g(attac)o(ks)h(b)o(y)g(eac)o(h)321 1110 y(piece)g(are)h(equal)e(in)h(n)o(um)o(b)q(er)f(then)h(the)h(con)o (troller)f(is)f('None'.)262 1408 y Fu(FUNCTION)p 262 1415 309 2 v 262 1508 a Fs(])p Fu(Di\013A)n(ttac)n(ks)18 b(:)24 b(Colour)19 b(x)g(Square)f Ft(=)-8 b Fa(\))18 b Fu(In)n(teger)262 1608 y Fl(Example)p 262 1622 182 2 v 262 1711 a Fs(])p Ft(Di\013A)o(ttac)o (ks\(col,sq\))262 1811 y Fl(Descripti)o(on)p 262 1826 241 2 v 321 1912 a Fp(Returns)c(:)k Fh(])p Fp(A)o(ttac)o(ks\([An)o(y],col,sq\))13 b Ff(\000)p Fh(])p Fp(A)o(ttac)o(ks\([An)o(y],Opp\(col\),sq\))946 2574 y(180)p eop %%Page: 181 183 181 182 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(Distance)17 b(:)25 b(Square)18 b(x)g(Square)h Ft(=)-8 b Fa(\))18 b Fu(In)n(teger)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(Distance\(sq1,sq2\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(:)380 910 y(max\()p Ff(j)d Fp(OnRank\(white,)p Fm(sq1)p Fp(\))j(-)g(OnRank\(white,)p Fm(sq2)p Fp(\))g Ff(j)f Fp(,)g Ff(j)h Fp(OnFile\()p Fm(sq1)p Fp(\))g(-)g(OnFile\()p Fm(sq2)p Fp(\))g Ff(j)f Fp(\))262 1259 y Fu(FUNCTION)p 262 1266 309 2 v 262 1359 a(Doubled)18 b(:)24 b(Colour)19 b(x)f(File)g Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 1458 y Fl(Example)p 262 1473 182 2 v 262 1562 a Ft(Doubled\(col,f)s(\))262 1661 y Fl(Descripti)o(on)p 262 1676 241 2 v 321 1762 a Fp(Returns)c(TR)o(UE)g (if)f(more)g(than)h(one)g(pa)o(wn)f(of)h(colour)f Fm(c)n(ol)h Fp(is)g(on)f(\014le)h Fm(f)p Fp(.)321 1812 y(Otherwise)h(F)-5 b(ALSE.)946 2574 y(181)p eop %%Page: 182 184 182 183 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(Escap)r(e)17 b(:)25 b(Colour)19 b(x)f(Square)g(x)g(Square)h Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(Escap)q(e\(col,sq1,sq2\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(TR)o(UE)g(if)f (the)h(king)g(of)f(colour)g Fm(c)n(ol)h Fp(can)g(escap)q(e)i(a)d(c)o(hec)o(k) i(from)d(square)j Fm(sq2)321 910 y Fp(b)o(y)e(a)h(piece)h(mo)o(v)o(ed)d(from) g(square)j Fm(sq1)p Fp(.)262 1259 y Fu(FUNCTION)p 262 1266 309 2 v 262 1359 a(Has)j(:)25 b(PieceList)17 b(x)h(Colour)h Ft(=)-8 b Fa(\))18 b Fu(In)n(teger)262 1458 y Fl(Example)p 262 1473 182 2 v 262 1562 a Ft(Has\(pl,col\))262 1661 y Fl(Descripti)o(on)p 262 1676 241 2 v 321 1762 a Fp(Returns)c(the)h(n)o(um)o(b)q(er)e(of)g(pieces) i(in)f(piecelist)g Fm(pl)g Fp(of)f(colour)h Fm(c)n(ol)f Fp(whic)o(h)h(are)g (still)321 1812 y(on)f(the)i(b)q(oard.)946 2574 y(182)p eop %%Page: 183 185 183 184 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(InsideQuadrate)18 b(:)24 b(Colour)19 b(x)f(Square)g Ft(=)-8 b Fa(\))19 b Fu(Bo)r(olean)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(InsideQuadrate\(col,sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)14 b(TR)o(UE)g(if)f(the)h(king)g(of)f (colour)g Fm(c)n(ol)h Fp(is)g(inside)g(the)g("queening)g(square")g(or)321 910 y("quadrate")f(with)h(resp)q(ect)i(to)e(square)g Fm(sq)p Fp(,)g(taking)f(in)o(to)g(accoun)o(t)h(who)g(has)g(the)321 960 y(\014rst)g(mo)o(v)o(e.)262 1309 y Fu(FUNCTION)p 262 1316 309 2 v 262 1408 a(Isolated)j(:)25 b(Colour)19 b(x)f(File)g Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 1508 y Fl(Example)p 262 1523 182 2 v 262 1612 a Ft(Isolated\(col,f)s(\))262 1711 y Fl(Descripti)o(on)p 262 1726 241 2 v 321 1812 a Fp(Returns)c(TR)o(UE)g(if)f (there)i(do)q(es)g(not)f(exist)g(a)f(pa)o(wn)h(of)f(colour)h Fm(c)n(ol)g Fp(on)f(either)i(\014le)321 1862 y(adjacen)o(t)f(to)f(\014le)h Fm(f)p Fp(.)321 1912 y(Otherwise)h(F)-5 b(ALSE.)946 2574 y(183)p eop %%Page: 184 186 184 185 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(K)n(CRigh)n(ts)19 b(:)24 b(Colour)19 b Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(K)o(CRigh)o(ts\(col\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(TR)o(UE)g(if)f(king)g(side)h(castling) g(righ)o(ts)g(for)f(colour)h Fm(c)n(ol)f Fp(are)i(in)o(tact.)321 910 y(Otherwise)g(F)-5 b(ALSE.)262 1259 y Fu(FUNCTION)p 262 1266 309 2 v 262 1359 a(KingDistance)17 b(:)25 b(Square)18 b(x)g(Square)g Ft(=)-8 b Fa(\))18 b Fu(In)n(teger)262 1458 y Fl(Example)p 262 1473 182 2 v 262 1562 a Ft(KingDistance\(sq1,sq2\))262 1661 y Fl(Descripti)o(on)p 262 1676 241 2 v 321 1762 a Fp(Returns)c(:)380 1812 y(min\()p Ff(j)d Fp(OnRank\(white,)p Fm(sq1)p Fp(\))j(-)g (OnRank\(white,)p Fm(sq2)p Fp(\))f Ff(j)h Fp(,)f Ff(j)h Fp(OnFile\()p Fm(sq1)p Fp(\))g(-)g(OnFile\()p Fm(sq2)p Fp(\))g Ff(j)f Fp(\))946 2574 y(184)p eop %%Page: 185 187 185 186 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(KingSq)18 b(:)24 b(Colour)19 b Ft(=)-8 b Fa(\))18 b Fu(square)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(KingSq\(col\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(the)h (square)f(the)h(king)e(of)g(colour)h Fm(c)n(ol)g Fp(is)f(curren)o(tly)i(on.) 262 1209 y Fu(FUNCTION)p 262 1216 309 2 v 262 1309 a(Lev)n(erSq)i(:)24 b(File)18 b(x)g(Colour)h Ft(=)-8 b Fa(\))18 b Fu(Square)262 1408 y Fl(Example)p 262 1423 182 2 v 262 1512 a Ft(Lev)o(erSq\(f,col\))262 1612 y Fl(Descripti)o(on)p 262 1626 241 2 v 321 1713 a Fp(Returns)c(the)h (\014rst)f(square)h(where)g(a)f(pa)o(wn)f(of)h(colour)f Fm(c)n(ol)h Fp(on)g(\014le)f Fm(f)h Fp(w)o(ould)f(lev)o(er)h(an)g(enem)o(y)321 1762 y(pa)o(wn)f(on)h(an)f(adjacen)o(t)h(\014le.)946 2574 y(185)p eop %%Page: 186 188 186 187 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a Fs(])p Fu(Mo)n(v)n(es)18 b(:)25 b(Piece)18 b(x)g(Colour)h(x)f(Square)g Ft(=)-8 b Fa(\))18 b Fu(In)n(teger)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Fs(])p Ft(Mo)o(v)o(es\(p)q(c,col,sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(the)h(n)o (um)o(b)q(er)e(of)g(mo)o(v)o(es)g(p)q(ossible)h(b)o(y)g(piece)g Fm(p)n(c)g Fp(of)g(colour)f Fm(c)n(ol)h Fp(from)e(square)j Fm(sq)p Fp(.)262 1209 y Fu(FUNCTION)p 262 1216 309 2 v 262 1309 a(Occupied)j(:)24 b(Square)18 b(x)h(Square)f Ft(=)-8 b Fa(\))18 b Fu(In)n(teger)262 1408 y Fl(Example)p 262 1423 182 2 v 262 1512 a Ft(Occupied\(sq1,sq2\))262 1612 y Fl(Descripti)o(on)p 262 1626 241 2 v 321 1713 a Fp(Returns)c(the)h(n)o(um)o(b)q(er)e(of)g (squares)i(whic)o(h)f(are)g(o)q(ccupied)h(b)q(et)o(w)o(een)g(square)g Fm(sq1)f Fp(and)321 1762 y Fm(sq2)g Fp(inclusiv)o(e)f(in)h(one)g(linear)f (direction.)946 2574 y(186)p eop %%Page: 187 189 187 188 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(Occup)n(y)18 b(:)25 b(PieceList)17 b(x)h(Colour)h(x)f(Square)g Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(Occup)o(y\(pl,col,sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(TR)o(UE)g(if)f(one)h(of)f(the)i (pieces)g(in)e(piecelist)i Fm(pl)e Fp(of)h(colour)f Fm(c)n(ol)h Fp(is)g(on)f(square)i Fm(sq)p Fp(.)321 910 y(Otherwise)g(F)-5 b(ALSE.)262 1259 y Fu(FUNCTION)p 262 1266 309 2 v 262 1359 a(On)18 b(:)25 b(Square)18 b Ft(=)-8 b Fa(\))18 b Fu(Piece)262 1458 y Fl(Example)p 262 1473 182 2 v 262 1562 a Ft(On\(sq\))262 1661 y Fl(Descripti)o(on)p 262 1676 241 2 v 321 1762 a Fp(Returns)c(the)h (piece)g(t)o(yp)q(e)f(o)q(ccup)o(ying)g(square)h Fm(sq)e Fp(regardless)j(of)d (colour.)946 2574 y(187)p eop %%Page: 188 190 188 189 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(OnFile)17 b(:)25 b(Square)18 b Ft(=)-8 b Fa(\))18 b Fu(File)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(OnFile\(sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(the)h (\014le)f(of)f(square)i Fm(sq)p Fp(.)262 1209 y Fu(FUNCTION)p 262 1216 309 2 v 262 1309 a(OnRank)j(:)25 b(Colour)18 b(x)h(Square)f Ft(=)-8 b Fa(\))18 b Fu(Rank)262 1408 y Fl(Example)p 262 1423 182 2 v 262 1512 a Ft(OnRank\(col,sq\))262 1612 y Fl(Descripti)o(on)p 262 1626 241 2 v 321 1713 a Fp(Returns)c(the)h(rank)f(of)f(square)i Fm(sq)e Fp(with)h(resp)q(ect)i(to)e(colour)g Fm(c)n(ol)p Fp(.)946 2574 y(188)p eop %%Page: 189 191 189 190 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(OnWing)18 b(:)24 b(Flank)19 b(x)f(Square)g Ft(=)-8 b Fa(\))19 b Fu(Bo)r(olean)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(OnWing\(\015k,sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)14 b(TR)o(UE)g(if)f(square)i Fm(sq)f Fp(is)f(on)h(\015ank)g Fm(\015k)p Fp(.)321 910 y(Otherwise)h(F)-5 b(ALSE.)262 1259 y Fu(FUNCTION)p 262 1266 309 2 v 262 1359 a(Op)r(en)18 b(:)24 b(File)18 b Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 1458 y Fl(Example)p 262 1473 182 2 v 262 1562 a Ft(Op)q(en\(f)s(\))262 1661 y Fl(Descripti)o(on)p 262 1676 241 2 v 321 1762 a Fp(Returns)c(TR)o(UE)g (if)f(\014le)h Fm(f)f Fp(has)h(no)g(pa)o(wns)g(of)f(an)o(y)h(colour)f(on)h (it.)321 1812 y(Otherwise)h(F)-5 b(ALSE.)946 2574 y(189)p eop %%Page: 190 192 190 191 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(Opp)19 b(:)24 b(Colour)19 b Ft(=)-8 b Fa(\))18 b Fu(Colour)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(Opp\(col\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(the)h(opp)q (osite)f(colour)g(of)f(colour)h Fm(c)n(ol)p Fp(.)262 1209 y Fu(FUNCTION)p 262 1216 309 2 v 262 1309 a(Opp)r(ositeFlanks)j(:)24 b Ft(=)-8 b Fa(\))19 b Fu(Bo)r(olean)262 1408 y Fl(Example)p 262 1423 182 2 v 262 1509 a Ft(Opp)q(ositeFlanks)262 1609 y Fl(Descripti)o(on)p 262 1624 241 2 v 321 1710 a Fp(Returns)14 b(:)380 1760 y(\(\(OnFile\(KingSq\(White\)\))g Ff(\024)g Fp(3)f Fl(and)h Fp(OnFile\(KingSq\(Blac)o(k\)\))f Ff(\025)i Fp(5\))e Fl(or)380 1810 y Fp(\(OnFile\(KingSq\(Blac)o(k\)\))h Ff(\024)g Fp(3)f Fl(and)g Fp(OnFile\(KingSq\(White\)\))h Ff(\025)g Fp(5\)\))946 2574 y(190)p eop %%Page: 191 193 191 192 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(PSq)18 b(:)25 b(Colour)18 b(x)h(Square)f Ft(=)-8 b Fa(\))18 b Fu(Square)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(PSq\(col,sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(the)h(promotion)d(square)i(for)g(a)f(pa)o(wn)h(on) g(square)g Fm(sq)g Fp(of)f(colour)h Fm(c)n(ol)p Fp(.)262 1209 y Fu(FUNCTION)p 262 1216 309 2 v 262 1309 a(P)n(assed)19 b(:)25 b(Colour)18 b(x)h(Square)f Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 1408 y Fl(Example)p 262 1423 182 2 v 262 1512 a Ft(P)o(assed\(col,sq\))262 1612 y Fl(Descripti)o(on)p 262 1626 241 2 v 321 1713 a Fp(Returns)c(TR)o(UE)g (if)f(there)i(do)q(es)g(not)f(exist)g(an)f(enem)o(y)h(pa)o(wn)f(on)h(the)g (same)f(or)h(adjacen)o(t)321 1762 y(\014le,)f(whic)o(h)h(can)g(hinder)g(the)h (pa)o(wns)f(adv)n(ance)f(to)h(the)h(promotion)c(square.)946 2574 y(191)p eop %%Page: 192 194 192 193 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(P)n(a)n(wnHole)19 b(:)25 b(Colour)18 b(x)h(Square)f Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(P)o(a)o(wnHole\(col,sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(TR)o(UE)g(if)f(square)i Fm(sq)f Fp(cannot)g(ev)o(er)g(b)q(e)h(attac)o(k)o(ed)f(b)o(y)g(pa)o(wns)g(of) f(colour)h Fm(c)n(ol)p Fp(.)321 910 y(Otherwise)h(F)-5 b(ALSE.)262 1259 y Fu(FUNCTION)p 262 1266 309 2 v 262 1359 a(P)n(a)n(wnLev)n(er)19 b(:)24 b(File)18 b(x)g(Colour)h Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 1458 y Fl(Example)p 262 1473 182 2 v 262 1562 a Ft(P)o(a)o(wnLev)o (er\(f,col\))262 1661 y Fl(Descripti)o(on)p 262 1676 241 2 v 321 1762 a Fp(Returns)c(TR)o(UE)g(if)f(a)h(pa)o(wn)f(of)g(colour)h Fm(c)n(ol)g Fp(can)g(b)q(e)g(a)g(pa)o(wn)f(lev)o(er)i(on)e(\014le)h Fm(f)g Fp(and)321 1812 y(incur)g(no)f(enem)o(y)h(pa)o(wn)f(blo)q(c)o(k)n(ade) h(b)q(efore)g(the)h(pa)o(wn)e(lev)o(erage)i(square.)321 1862 y(Otherwise)g(F)-5 b(ALSE.)946 2574 y(192)p eop %%Page: 193 195 193 194 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a Fs(])p Fu(P)n(a)n(wns)20 b(:)25 b Ft(=)-8 b Fa(\))18 b Fu(In)n(teger)262 556 y Fl(Example)p 262 571 182 2 v 262 657 a Fs(])p Ft(P)o(a)o(wns)262 757 y Fl(Descripti)o(on)p 262 772 241 2 v 321 858 a Fp(Returns)c(the)h(n)o (um)o(b)q(er)e(of)g(pa)o(wns)h(curren)o(tly)h(on)f(the)g(b)q(oard.)262 1207 y Fu(FUNCTION)p 262 1214 309 2 v 262 1306 a(Pin)k(:)25 b(Colour)18 b(x)h(Square)f(x)g(Square)g(x)h(Square)f Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 1406 y Fl(Example)p 262 1421 182 2 v 262 1509 a Ft(Pin\(col,sq1,sq2,sq3\))262 1609 y Fl(Descripti)o(on)p 262 1624 241 2 v 321 1710 a Fp(Returns)c(TR)o(UE)g(if)f(a)h(piece)g(of)g (colour)f Fm(c)n(ol)h Fp(on)g(square)g Fm(sq1)g Fp(pins)g(a)g(piece)h(of)321 1760 y(colour)e(OPP\(col\))i(on)f(square)g Fm(sq2)g Fp(against)g(a)f(piece)i (also)e(of)g(colour)h(Opp\(col\))321 1810 y(on)f(square)i Fm(sq3)p Fp(.)380 1860 y(where)131 b(On\(sq1\))14 b Ff(2)g Fp([Bishop,Ro)q(ok,Queen])e Fl(and)616 1909 y Fp(On\(sq2\))i Ff(2)g Fp([Knigh)o(t,Bishop,Ro)q(ok,Queen])e Fl(and)616 1959 y Fp(On\(sq3\))i Ff(2)g Fp([Knigh)o(t,Bishop,Ro)q (ok,Queen,King].)946 2574 y(193)p eop %%Page: 194 196 194 195 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(P)n(oten)n(tialChec)n(k)18 b(:)25 b(Colour)18 b(x)h(Square)f(x)g(Square)g Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(P)o(oten)o(tialChec)o(k\(col,sq1,sq2\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(TR)o(UE)g (if)f(a)h(piece)g(of)g(colour)f Fm(c)n(ol)h Fp(on)g(square)g Fm(sq1)g Fp(can)g(mo)o(v)o(e)f(to)g(square)i Fm(sq2)321 910 y Fp(and)e(giv)o(e)h(c)o(hec)o(k.)262 1259 y Fu(FUNCTION)p 262 1266 309 2 v 262 1359 a(QCRigh)n(ts)19 b(:)24 b(Colour)19 b Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 1458 y Fl(Example)p 262 1473 182 2 v 262 1562 a Ft(QCRigh)o(ts\(col\))262 1661 y Fl(Descripti)o(on)p 262 1676 241 2 v 321 1762 a Fp(Returns)c(TR)o(UE)g(if)f (queen)i(side)f(castling)f(righ)o(ts)h(for)g(colour)f Fm(c)n(ol)h Fp(are)g(in)o(tact.)321 1812 y(Otherwise)h(F)-5 b(ALSE.)946 2574 y(194)p eop %%Page: 195 197 195 196 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a Fs(])p Fu(SafeBlo)r(c)n(ks)17 b(:)25 b(Colour)19 b(x)f(Square)g(x)g(Square) g Ft(=)-8 b Fa(\))19 b Fu(In)n(teger)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Fs(])p Ft(SafeBlo)q(c)o(ks\(col,sq1,sq2\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)14 b(the)h(sum)e(of)g(:)380 910 y Fh(])p Fp(Di\013A)o(ttac)o(ks\(col,)p Fh(sq)719 916 y Fe(n)741 910 y Fp(\))321 960 y(if)g(and)g(only)g(if)g(\()p Fh(])p Fp(Di\013A)o(ttac)o(ks\(col,)p Fh(sq)923 966 y Fe(n)946 960 y Fp(\))h Fh(>)g Fp(1\))g(and)f(where)i Fh(sq)1311 966 y Fe(n)1348 960 y Fp(is)f(ev)o(ery)g(square)321 1010 y(on)f(a)h(piece)h(mo)o (v)o(emen)o(t)c(direction)j(b)q(et)o(w)o(een)h Fm(sq1)f Fp(and)g Fm(sq2)g Fp(inclusiv)o(e.)262 1359 y Fu(FUNCTION)p 262 1366 309 2 v 262 1458 a(SameDiagonal)j(:)24 b(Square)18 b(x)h(Square)f Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 1558 y Fl(Example)p 262 1573 182 2 v 262 1661 a Ft(SameDiagonal\(sq1,sq2\))262 1761 y Fl(Descripti)o(on)p 262 1776 241 2 v 321 1862 a Fp(Returns)c(TR)o(UE)g (if)f(squares)i Fm(sq1)f Fp(and)g Fm(sq2)g Fp(are)g(on)g(the)g(same)f (diagonal.)321 1912 y(Otherwise)i(F)-5 b(ALSE.)946 2574 y(195)p eop %%Page: 196 198 196 197 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(SemiOp)r(en)16 b(:)24 b(Colour)19 b(x)f(File)g Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(SemiOp)q(en\(col,f)s(\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(TR)o(UE)g(if)f(there)i(are)f(no)g(pa)o (wns)g(of)f(colour)h Fm(c)n(ol)g Fp(on)f(\014le)h Fm(f)p Fp(.)321 910 y(Otherwise)h(F)-5 b(ALSE.)262 1259 y Fu(FUNCTION)p 262 1266 309 2 v 262 1359 a(Side)18 b(:)24 b(Square)18 b Ft(=)-8 b Fa(\))18 b Fu(Colour)262 1458 y Fl(Example)p 262 1473 182 2 v 262 1562 a Ft(Side\(sq\))262 1661 y Fl(Descripti)o(on)p 262 1676 241 2 v 321 1762 a Fp(Returns)c(the)h(colour)e(whose)i(territory)f (square)h Fm(sq)f Fp(is)g(in.)321 1812 y(Where)g(eac)o(h)h(colour's)e (territory)i(is)f(de\014ned)h(to)e(b)q(e)i(within)e(its)h(\014rst)g(4)g (ranks.)946 2574 y(196)p eop %%Page: 197 199 197 198 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(SqColour)18 b(:)24 b(Square)19 b Ft(=)-8 b Fa(\))18 b Fu(Colour)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(SqColour\(sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(the)h (colour)e(of)h(the)g(square)h Fm(sq)p Fp(.)262 1209 y Fu(FUNCTION)p 262 1216 309 2 v 262 1309 a(T)-5 b(axicab)18 b(:)25 b(Square)18 b(x)g(Square)g Ft(=)-8 b Fa(\))18 b Fu(In)n(teger)262 1408 y Fl(Example)p 262 1423 182 2 v 262 1512 a Ft(T)l(axicab\(sq1,sq2\))262 1612 y Fl(Descripti)o(on)p 262 1626 241 2 v 321 1713 a Fp(Returns)c(:)321 1762 y(\()p Ff(j)f Fp(OnRank\(white,)p Fm(sq1)p Fp(\))h(-)f(OnRank\(white,)p Fm(sq2)p Fp(\))h Ff(j)g Fp(+)g Ff(j)f Fp(OnFile\()p Fm(sq1)p Fp(\))h(-)g(OnFile\()p Fm(sq2)p Fp(\))g Ff(j)p Fp(\))946 2574 y(197)p eop %%Page: 198 200 198 199 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(T)-5 b(rapp)r(ed)18 b(:)25 b(Colour)18 b(x)h(Square)f Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(T)l(rapp)q(ed\(col,sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(TR)o(UE)g(if)f(ev)o(ery)i(square,)f Fm(sq2)p Fp(,)f(a)h(piece)h(on)e(square)i Fm(sq)f Fp(can)g(mo)o(v)o(e)e(to,)i (meets)f(the)321 910 y(follo)o(wing)e(condition)i(:)380 960 y(Con)o(trol\(sq2\))g(=)h(Opp\(col\))321 1010 y(Otherwise)h(F)-5 b(ALSE.)262 1359 y Fu(FUNCTION)p 262 1366 309 2 v 262 1458 a Fs(])p Fu(UnMo)n(v)n(ed)19 b(:)24 b(Colour)19 b(x)f(Piece)g Ft(=)-8 b Fa(\))18 b Fu(In)n(teger)262 1558 y Fl(Example)p 262 1573 182 2 v 262 1661 a Fs(])p Ft(UnMo)o(v)o(ed\(col,p)q(c\))262 1761 y Fl(Descripti)o(on)p 262 1776 241 2 v 321 1862 a Fp(Returns)c(the)h(n)o (um)o(b)q(er)e(of)g(pieces)i(of)f(colour)f Fm(c)n(ol)h Fp(and)g(t)o(yp)q(e)g Fm(p)n(c)g Fp(whic)o(h)g(ha)o(v)o(e)g(nev)o(er)g(mo)o(v)o(ed.)946 2574 y(198)p eop %%Page: 199 201 199 200 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(V)-5 b(alue)18 b(:)25 b(Square)18 b Ft(=)-8 b Fa(\))18 b Fu(In)n(teger)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(V)l(alue\(sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(a)g(v)n(alue)f(for)h(the)g(piece)h(on)f(square)g Fm(sq)g Fp(regardless)h(of)f(colour.)321 910 y(De\014ned)g(b)o(y)g(:)380 960 y(P)o(a)o(wn)77 b(=)14 b(1)380 1010 y(Knigh)o(t)51 b(=)14 b(3)380 1060 y(Bishop)53 b(=)14 b(3)380 1110 y(Ro)q(ok)81 b(=)14 b(5)380 1159 y(Queen)63 b(=)14 b(9)380 1209 y(King)89 b(=)14 b(14)262 1508 y Fu(FUNCTION)p 262 1515 309 2 v 262 1608 a(W)-5 b(eak)18 b(:)24 b(Colour)19 b(x)f(Square)h Ft(=)-8 b Fa(\))18 b Fu(Bo)r(olean)262 1707 y Fl(Example)p 262 1722 182 2 v 262 1811 a Ft(W)l(eak\(col,sq\))262 1910 y Fl(Descripti)o(on)p 262 1925 241 2 v 321 2012 a Fp(Returns)c(:)380 2061 y Fl(not)e Fp(\()79 b(A)o(ttac)o(k)o(ed\([P)o(a)o(wn],col,sq\))12 b Fl(or)557 2111 y Fp(A)o(ttac)o(k)o(ed\([P)o(a)o(wn],col,)p Fh(sq)972 2117 y Fe(inf)s(r)q(ont)1090 2111 y Fp(\))i Fl(or)557 2161 y Fp(A)o(ttac)o(k)o(ed\([P)o(a)o(wn],col,)p Fh(sq)972 2167 y Fe(behind)1072 2161 y Fp(\))f(\).)946 2574 y(199)p eop %%Page: 200 202 200 201 bop 262 357 a Fu(FUNCTION)p 262 364 309 2 v 262 457 a(Wing)18 b(:)24 b(Square)19 b Ft(=)-8 b Fa(\))18 b Fu(Flank)262 556 y Fl(Example)p 262 571 182 2 v 262 660 a Ft(Wing\(sq\))262 759 y Fl(Descripti)o(on)p 262 774 241 2 v 321 860 a Fp(Returns)c(the)h (\015ank)e(the)i(square)g Fm(sq)e Fp(is)h(on.)946 2574 y(200)p eop %%Page: 201 203 201 202 bop 324 307 a Fp(Pre{De\014ned)15 b(t)o(yp)q(es)g(are)f(as)g(follo)o (ws)e(:)321 475 y(Bo)q(olean)90 b(:)18 b(TR)o(UE)13 b Ff(j)h Fp(F)-5 b(ALSE)321 525 y(Colour)113 b(:)18 b(White)13 b Ff(j)h Fp(Blac)o(k)321 575 y(Con)o(troller)52 b(:)18 b(White)13 b Ff(j)h Fp(Blac)o(k)g Ff(j)f Fp(None)321 625 y(File)167 b(:)18 b(Cardinal)13 b(Range)g(1)h(to)f(8)321 675 y(Flank)131 b(:)18 b(QueenSide)d Ff(j)e Fp(KingSide)321 725 y(In)o(teger)110 b(:)18 b(In)o(teger)d(Range)321 774 y(Piece)142 b(:)18 b(P)o(a)o(wn)13 b Ff(j)h Fp(Knigh)o(t)f Ff(j)h Fp(Bishop)g Ff(j)f Fp(Ro)q(ok)g Ff(j)g Fp(Queen)i Ff(j)f Fp(King)f Ff(j)h Fp(An)o(y)321 824 y(PieceList)72 b(:)18 b(Set)c(of)g(Piece)321 874 y(Rank)139 b(:)18 b(Cardinal)13 b(Range)g(1)h(to)f(8)321 924 y(Square)113 b(:)18 b(Cardinal)13 b(Range)g(1)h(to)f(64)321 1023 y(Note:)18 b(An)o(y)c(is)g(a)f('wild)g(card')h(piece.)946 2574 y(201)p eop %%Page: 202 204 202 203 bop 262 654 a Fn(App)s(endix)33 b(C)262 897 y Fo(Time)40 b(Allo)s(catio)q(n)i(Graphs)262 1148 y Fp(This)13 b(app)q(endix)g(con)o (tains)g(the)g(time)f(allo)q(cation)g(graphs)h(for)g(Kasparo)o(v)g(and)g (Karp)q(o)o(v)g(in)262 1198 y(their)h(1986)f(w)o(orld)g(c)o(hampionship)f (matc)o(h.)946 2574 y(202)p eop %%Page: 203 205 203 204 bop 526 2156 a Fp(Figure)14 b(C.1:)j(Time)c(Allo)q(cation,)f(Kasparo) o(v)i(as)g(White.)946 2574 y(203)p eop %%Page: 204 206 204 205 bop 532 2156 a Fp(Figure)14 b(C.2:)j(Time)12 b(Allo)q(cation,)g (Kasparo)o(v)i(as)g(Blac)o(k.)946 2574 y(204)p eop %%Page: 205 207 205 206 bop 544 2156 a Fp(Figure)14 b(C.3:)j(Time)c(Allo)q(cation,)f(Karp)q (o)o(v)i(as)g(White.)946 2574 y(205)p eop %%Page: 206 208 206 207 bop 550 2156 a Fp(Figure)14 b(C.4:)j(Time)12 b(Allo)q(cation,)g(Karp) q(o)o(v)i(as)g(Blac)o(k.)946 2574 y(206)p eop %%Page: 207 209 207 208 bop 401 2156 a Fp(Figure)14 b(C.5:)j(Time)c(Allo)q(cation,)f(Kasparo) o(v)i(and)f(Karp)q(o)o(v)h(Com)o(bined.)946 2574 y(207)p eop %%Page: 208 210 208 209 bop 262 654 a Fn(App)s(endix)33 b(D)262 897 y Fo(Bratk)m(o-Kop)s(ec) 40 b(T)-10 b(est)262 1021 y(P)m(ositions)946 2574 y Fp(208)p eop %%Page: 209 211 209 210 bop 641 301 673 5 v 641 965 5 665 v 646 384 a Fg(0j0s0Z0Z)646 467 y(opZbZRZ0)646 550 y(0Z0l0Zpo)646 633 y(Z0Z0o0Z0)646 716 y(0ZBZ0Z0Z)646 799 y(Z0Z0L0Z0)646 882 y(POPZ0A0Z)646 965 y(Z0J0Z0Z0)p 1310 965 V 641 969 673 5 v 423 1087 a Fp(T)m(est)15 b(1)e(\(T\):)h Fm(A)o(ndersson)h(v)g(Knuttson)p Fp(,)f(Blac)o(k)g(to)g(Pla)o(y)m(,)e Fl(...)22 b(Qd1+)p Fp(.)p 641 1450 V 641 2114 5 665 v 646 1533 a Fg(0Z0s0j0Z)646 1616 y(Z0Z0mpo0)646 1699 y(0ops0Z0o)646 1782 y(o0Z0Z0ZP)646 1865 y(PZ0OPOPZ)646 1948 y(ZNS0Z0Z0)646 2031 y(0Z0Z0J0Z)646 2114 y(Z0S0Z0Z0)p 1310 2114 V 641 2118 673 5 v 467 2237 a Fp(T)m(est)14 b(2)g(\(L\):)f Fm(Bo)n(golyub)n(ow)j(v)f (Spielmann)p Fp(,)f(White)f(to)h(Pla)o(y)m(,)e Fl(d5)p Fp(.)946 2574 y(209)p eop %%Page: 210 212 210 211 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(0ZqZrs0j)646 482 y(Z0Zbanmp)646 565 y(pZ0o0opZ)646 648 y(Z0oPo0Z0)646 731 y(PoPZPZPZ)646 814 y(ZPZ0ANMP)646 897 y(0ZBL0ORJ)646 980 y(Z0Z0Z0ZR)p 1310 980 V 641 984 673 5 v 500 1102 a Fp(T)m(est)14 b(3)g(\(L\):)g Fm(Evans)h(v)g(R)n(ossolimo)p Fp(,)f(Blac)o(k)f(to)h(Pla)o(y)m(,)e Fl(...)22 b(f5)p Fp(.)p 641 1465 V 641 2129 5 665 v 646 1548 a Fg(rmblka0s)646 1631 y(o0Z0opop)646 1714 y(0o0Z0Z0Z)646 1797 y(Z0opO0Z0)646 1880 y(0Z0M0Z0Z)646 1963 y(Z0O0Z0Z0)646 2046 y(POPZQOPO)646 2129 y(S0A0JBZR)p 1310 2129 V 641 2133 673 5 v 511 2252 a Fp(T)m(est)14 b(4)g(\(L\):)g Fm(Spielmann)h(v)g(Walter)p Fp(,)e(White)h(to)g(Pla)o(y)m(,)e Fl(e6)p Fp(.)946 2574 y(210)p eop %%Page: 211 213 211 212 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(rZbZ0skZ)646 482 y(Z0l0a0op)646 565 y(pZ0opm0Z)646 648 y(ZpZ0Z0Z0)646 731 y(0Z0LPZ0Z)646 814 y(ZBM0A0Z0)646 897 y(POPZ0ZPO)646 980 y(S0Z0ZRJ0)p 1310 980 V 641 984 673 5 v 492 1102 a Fp(T)m(est)14 b(5)g(\(T\):)f Fm(R)n(o)n(golewicz)i(v)g(Jar)n(e)n(cz)p Fp(,)e(White)g(to)h(Pla)o(y)m(,)e Fl(Nd5)p Fp(.)p 641 1465 V 641 2129 5 665 v 646 1548 a Fg(0ZrZ0ZkZ)646 1631 y(opoRZpo0)646 1714 y(0Z0ZpZ0Z)646 1797 y(Z0Z0O0O0)646 1880 y(0Z0Z0O0Z)646 1963 y(ZPZ0Z0J0)646 2046 y(PZPZ0Z0Z)646 2129 y(Z0Z0Z0Z0)p 1310 2129 V 641 2133 673 5 v 552 2252 a Fp(T)m(est)i(6)g (\(L\):)f Fm(Pachman)j(D222)p Fp(,)f(White)e(to)h(Pla)o(y)m(,)e Fl(g6)p Fp(.)946 2574 y(211)p eop %%Page: 212 214 212 213 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(0mkZrZrZ)646 482 y(opZ0m0op)646 565 y(0Z0ZpZ0Z)646 648 y(l0ZpOpZN)646 731 y(bZpO0O0Z)646 814 y(A0O0ZRZ0)646 897 y(0ZPZBZPO)646 980 y(S0ZQZ0J0)p 1310 980 V 641 984 673 5 v 524 1102 a Fp(T)m(est)14 b(7)g(\(T\):)f Fm(Golyak)j(v)e(Gaiduk)p Fp(,)g(White)g(to)g(Pla)o(y)m(,)e Fl(Nf6)p Fp(.)p 641 1465 V 641 2129 5 665 v 646 1548 a Fg(0Z0ZbZ0Z)646 1631 y(o0Z0jpZ0)646 1714 y(0Z0Z0ZpZ)646 1797 y(Z0ZpO0Zp)646 1880 y(0ZpO0O0Z)646 1963 y(Z0Z0J0O0)646 2046 y(PZ0ZNZ0O)646 2129 y(Z0Z0Z0Z0)p 1310 2129 V 641 2133 673 5 v 544 2252 a Fp(T)m(est)i(8)g (\(L\):)g Fm(A)o(lekhine)g(v)h(Y)m(ates)p Fp(,)e(White)h(to)g(Pla)o(y)m(,)e Fl(f5)p Fp(.)946 2574 y(212)p eop %%Page: 213 215 213 214 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(0Zks0ans)646 482 y(oboqZ0Z0)646 565 y(0onZpo0Z)646 648 y(Z0ZpZ0Zp)646 731 y(0Z0O0O0A)646 814 y(Z0M0ZNZQ)646 897 y(POPZ0ZPO)646 980 y(Z0JRZBZR)p 1310 980 V 641 984 673 5 v 539 1102 a Fp(T)m(est)15 b(9)e(\(L\):)h Fm(Jansa)h(v)g(Ornstein)p Fp(,)e(White)h(to)g(Pla)o(y)m(,)e Fl(f5)p Fp(.)p 641 1465 V 641 2129 5 665 v 646 1548 a Fg(0Z0srZkZ)646 1631 y(opZ0Zpo0)646 1714 y(0lnZ0mpZ)646 1797 y(Z0Z0Z0Z0)646 1880 y(0Z0o0Z0Z)646 1963 y(OPZRZPZ0)646 2046 y(0ZPZNLPO)646 2129 y(S0A0Z0J0)p 1310 2129 V 641 2133 673 5 v 427 2252 a Fp(T)m(est)i(10)f (\(T\):)h Fm(Kab)n(adzjan)i(v)e(Cib)n(elasvili)p Fp(,)e(Blac)o(k)i(to)g(Pla)o (y)m(,)e Fl(...)22 b(Ne5)p Fp(.)946 2574 y(213)p eop %%Page: 214 216 214 215 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(0ZrZnskZ)646 482 y(o0ZqZpop)646 565 y(bo0o0Z0Z)646 648 y(m0oPo0Z0)646 731 y(PZPZPZ0Z)646 814 y(Z0OBA0M0)646 897 y(0Z0ZQOPO)646 980 y(S0Z0ZRJ0)p 1310 980 V 641 984 673 5 v 552 1102 a Fp(T)m(est)15 b(11)e(\(L\):)h Fm(Byrne)h(v)g(Kotov)p Fp(,)e(White)h(to)g(Pla)o(y)m(,)e Fl(f4)p Fp(.)p 641 1465 V 641 2129 5 665 v 646 1548 a Fg(rZ0ZrZkZ)646 1631 y(oplbZpop)646 1714 y(0Z0Z0Z0Z)646 1797 y(Z0Z0o0MQ)646 1880 y(0Z0Z0Z0Z)646 1963 y(Z0O0Z0Z0)646 2046 y(PO0Z0OPO)646 2129 y(S0Z0S0J0)p 1310 2129 V 641 2133 673 5 v 523 2252 a Fp(T)m(est)i(12)g (\(T\):)f Fm(Pachman)j(D3)p Fp(,)e(Blac)o(k)g(to)g(Pla)o(y)m(,)e Fl(...)22 b(Bf5)p Fp(.)946 2574 y(214)p eop %%Page: 215 217 215 216 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(rZ0l0skZ)646 482 y(Z0Z0apop)646 565 y(pZ0o0Z0Z)646 648 y(Z0oPZ0Z0)646 731 y(0Z0oPZ0Z)646 814 y(Z0ZQZ0Z0)646 897 y(PO0A0OPO)646 980 y(S0Z0S0J0)p 1310 980 V 641 984 673 5 v 483 1102 a Fp(T)m(est)14 b(13)g(\(L\):)f Fm(Pfei\013er)i(v)g(T)m(rifunovich)p Fp(,)e(White)g(to)h(Pla)o(y)m(,)e Fl(b4)p Fp(.)p 641 1465 V 641 2129 5 665 v 646 1548 a Fg(rmbZ0s0j)646 1631 y(opZ0o0Zp)646 1714 y(0Zpo0ZpZ)646 1797 y(l0ZPZpZ0)646 1880 y(0Z0Z0Z0Z)646 1963 y(ZPa0ZNO0)646 2046 y(PA0ZPOBO)646 2129 y(S0ZQZRJ0)p 1310 2129 V 641 2133 673 5 v 425 2252 a Fp(T)m(est)i(14)f (\(T\):)h Fm(R)n(ob)n(atsch)h(v)g(Jansa)p Fp(,)f(White)g(to)g(Pla)o(y)m(,)e Fl(Qd2)j(or)g(Qe1)p Fp(.)946 2574 y(215)p eop %%Page: 216 218 216 217 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(0ZrZ0ZkZ)646 482 y(ZpZ0l0op)646 565 y(0ZbZps0Z)646 648 y(o0opZ0Z0)646 731 y(0Z0Z0ZQZ)646 814 y(ZPZPO0S0)646 897 y(PZPM0ZPO)646 980 y(Z0Z0ZRJ0)p 1310 980 V 641 984 673 5 v 464 1102 a Fp(T)m(est)15 b(15)e(\(T\):)g Fm(Fischer)i(v)g(Me)n(cking)p Fp(,)f(White)g(to)f(Pla)o(y)m(,)g Fl(Qxg7+)p Fp(.)p 641 1465 V 641 2129 5 665 v 646 1548 a Fg(rZblka0s)646 1631 y(Z0Z0mpo0)646 1714 y(pZpZ0Z0o)646 1797 y(ZpZpO0A0)646 1880 y(0Z0Z0Z0Z)646 1963 y(ZBZ0Z0Z0)646 2046 y(POPM0OPO)646 2129 y(S0ZQZRJ0)p 1310 2129 V 641 2133 673 5 v 448 2252 a Fp(T)m(est)h(16)f (\(T\):)h Fm(V)m(asilchuk)h(v)g(Bob)n(olovitch)p Fp(,)e(White)h(to)g(Pla)o(y) m(,)e Fl(Ne4)p Fp(.)946 2574 y(216)p eop %%Page: 217 219 217 218 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(rZ0l0skZ)646 482 y(Zponapop)646 565 y(pZ0o0mbZ)646 648 y(Z0ZPo0Z0)646 731 y(0ZPZPZPZ)646 814 y(Z0M0ZNZP)646 897 y(POBZQO0Z)646 980 y(S0A0ZRJ0)p 1310 980 V 641 984 673 5 v 517 1102 a Fp(T)m(est)15 b(17)e(\(L\):)h Fm(Bisch)h(v)g(Kmo)n(ch)p Fp(,)e(Blac)o(k)h(to)g(Pla)o(y)m(,)e Fl(...)22 b(h5)p Fp(.)p 641 1465 V 641 2129 5 665 v 646 1548 a Fg(rZbl0skZ)646 1631 y(opZ0opap)646 1714 y(0Zno0ZpZ)646 1797 y(Z0m0Z0Z0)646 1880 y(PZ0ZPO0Z)646 1963 y(M0O0ZNZ0)646 2046 y(0OBZ0ZPO)646 2129 y(S0A0LRJ0)p 1310 2129 V 641 2133 673 5 v 488 2252 a Fp(T)m(est)14 b(18)g(\(T\):)f Fm(Maric)i(v)g(Fischer)p Fp(,)e(Blac)o(k)h(to)g(Pla)o(y)m(,)e Fl(...)22 b(Nb3)p Fp(.)946 2574 y(217)p eop %%Page: 218 220 218 219 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(0Z0srZ0Z)646 482 y(Z0oqZ0ok)646 565 y(pZ0o0ono)646 648 y(Z0Z0Z0Z0)646 731 y(0ZQAPO0Z)646 814 y(ZPZ0Z0Z0)646 897 y(PZ0Z0ZPO)646 980 y(Z0Z0SRJ0)p 1310 980 V 641 984 673 5 v 500 1102 a Fp(T)m(est)14 b(19)f(\(T\):)h Fm(Euwe)h(v)g(Ker)n(es)p Fp(,)e(Blac)o(k)g(to)h(Pla)o(y)m(,)e Fl(...)22 b(Rxe4)p Fp(.)p 641 1465 V 641 2129 5 665 v 646 1548 a Fg(rZ0Z0j0Z)646 1631 y(obZ0apZr)646 1714 y(0o0lpZ0o)646 1797 y(Z0ZpMpZ0)646 1880 y(0Z0O0O0Z)646 1963 y(Z0M0Z0O0)646 2046 y(POPZQZ0O)646 2129 y(Z0JRS0Z0)p 1310 2129 V 641 2133 673 5 v 559 2252 a Fp(T)m(est)14 b(20)f(\(L\):)h Fm(Euwe)h(v)g(Flohr)p Fp(,)e(White)g(to)h(Pla)o(y)m(,)e Fl(g4)p Fp(.)946 2574 y(218)p eop %%Page: 219 221 219 220 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(0Z0snZ0j)646 482 y(opa0Zrop)646 565 y(0Zpoqo0Z)646 648 y(Z0Z0ZNZ0)646 731 y(0ZPZPZ0Z)646 814 y(ZPZ0Z0ZQ)646 897 y(PA0Z0OPO)646 980 y(Z0ZRS0J0)p 1310 980 V 641 984 673 5 v 454 1102 a Fp(T)m(est)14 b(21)g(\(T\):)f Fm(T)m(arr)n(asch)h(v)h(Blackburne)p Fp(,)f(White)g(to)g(Pla)o(y)m(,)e Fl(Nh6)p Fp(.)p 641 1465 V 641 2129 5 665 v 646 1548 a Fg(0ZrZ0skZ)646 1631 y(Zblnapo0)646 1714 y(0o0opm0o)646 1797 y(oPZ0Z0Z0)646 1880 y(NZPZPZ0Z)646 1963 y(O0ZBZNZP)646 2046 y(0A0ZQOPZ)646 2129 y(S0ZRZ0J0)p 1310 2129 V 641 2133 673 5 v 442 2252 a Fp(T)m(est)i(22)f (\(T\):)h Fm(Najdorf)g(v)h(R)n(eshevsky)p Fp(,)f(Blac)o(k)g(to)g(Pla)o(y)m(,) e Fl(...)22 b(Bxe4)p Fp(.)946 2574 y(219)p eop %%Page: 220 222 220 221 bop 641 315 673 5 v 641 980 5 665 v 646 399 a Fg(rZblkZ0s)646 482 y(opZ0apop)646 565 y(0ZpZ0Z0Z)646 648 y(Z0ZpO0Z0)646 731 y(PZ0L0O0Z)646 814 y(Z0M0A0Z0)646 897 y(0OPZ0ZPO)646 980 y(S0Z0ZRJ0)p 1310 980 V 641 984 673 5 v 512 1102 a Fp(T)m(est)14 b(23)g(\(L\):)f Fm(Jansa)j(v)f(Kavalek)p Fp(,)e(Blac)o(k)h(to)g(Pla)o(y)m(,)e Fl(...)22 b(f6)p Fp(.)p 641 1465 V 641 2129 5 665 v 646 1548 a Fg(rZ0lnsnj)646 1631 y(o0ZbZ0a0)646 1714 y(0o0o0Zpo)646 1797 y(Z0oPopZ0)646 1880 y(0OPZPZ0Z)646 1963 y(ORMBA0Z0)646 2046 y(0Z0LNOPO)646 2129 y(Z0Z0ZRJ0)p 1310 2129 V 641 2133 673 5 v 563 2252 a Fp(T)m(est)15 b(24)e(\(L\):)h Fm(Szab)n(o)h(v)g(Ivkov)p Fp(,)f(White)g(to)g(Pla)o(y)m(,)e Fl(f4)p Fp(.)946 2574 y(220)p eop %%Page: 221 223 221 222 bop 262 654 a Fn(App)s(endix)33 b(E)262 897 y Fo(T)-10 b(est)39 b(Games)h(Pla)m(y)m(ed)262 1148 y Fp(This)19 b(app)q(endix)h(con)o (tains)f(the)i(test)g(games)d(pla)o(y)o(ed)h(b)o(y)h(HIAR)o(CS)f(5.0.)35 b(The)20 b(matc)o(h)262 1198 y(scores)15 b(w)o(ere)g(as)f(follo)o(ws:)p 324 1416 977 2 v 323 1466 2 50 v 349 1451 a Fm(Players)p 724 1466 V 267 w(1)p 795 1466 V 50 w(2)p 866 1466 V 50 w(3)p 937 1466 V 50 w(4)p 1008 1466 V 50 w(5)p 1079 1466 V 53 w(6)p 1156 1466 V 53 w(T)m(otal)p 1299 1466 V 324 1468 977 2 v 323 1518 2 51 v 349 1503 a Fp(HIAR)o(CS)f(5.0)p 724 1518 V 174 w(1)p 795 1518 V 50 w(1)p 866 1518 V 50 w(1)p 937 1518 V 50 w(1)p 1008 1518 V 50 w(1)p 1079 1518 V 1110 1487 a Fk(1)p 1110 1494 17 2 v 1110 1517 a(2)p 1156 1518 2 51 v 1205 1503 a Fp(5)1231 1487 y Fk(1)p 1230 1494 17 2 v 1230 1517 a(2)p 1299 1518 2 51 v 324 1520 977 2 v 323 1570 2 51 v 349 1555 a Fp(Mephisto)h(Exclusiv)o(e)p 724 1570 V 50 w(0)p 795 1570 V 50 w(0)p 866 1570 V 50 w(0)p 937 1570 V 50 w(0)p 1008 1570 V 50 w(0)p 1079 1570 V 1110 1538 a Fk(1)p 1110 1545 17 2 v 1110 1569 a(2)p 1156 1570 2 51 v 1220 1538 a(1)p 1220 1545 17 2 v 1220 1569 a(2)p 1299 1570 2 51 v 324 1571 977 2 v 324 1790 589 2 v 323 1839 2 50 v 349 1825 a Fm(Players)p 627 1839 V 169 w(1)p 698 1839 V 50 w(2)p 769 1839 V 50 w(T)m(otal)p 912 1839 V 324 1841 589 2 v 323 1891 2 50 v 349 1876 a Fp(HIAR)o(CS)f(5.0)p 627 1891 V 77 w(1)p 698 1891 V 50 w(0)p 769 1891 V 86 w(1)p 912 1891 V 324 1893 589 2 v 323 1942 2 50 v 349 1927 a(Mark)h(Uniac)o(k)o(e)p 627 1942 V 50 w(0)p 698 1942 V 50 w(1)p 769 1942 V 86 w(1)p 912 1942 V 324 1944 589 2 v 324 2163 826 2 v 323 2212 2 50 v 349 2197 a Fm(Players)p 716 2212 V 261 w(1)p 792 2212 V 53 w(2)p 863 2212 V 50 w(3)p 934 2212 V 50 w(4)p 1005 2212 V 50 w(T)m(otal)p 1148 2212 V 324 2214 826 2 v 323 2264 2 51 v 349 2249 a Fp(HIAR)o(CS)f(5.0,)g (3)g(ply)p 716 2264 V 747 2233 a Fk(1)p 747 2240 17 2 v 747 2263 a(2)p 792 2264 2 51 v 818 2249 a Fp(0)p 863 2264 V 50 w(0)p 934 2264 V 50 w(1)p 1005 2264 V 73 w(1)1080 2233 y Fk(1)p 1080 2240 17 2 v 1080 2263 a(2)p 1148 2264 2 51 v 324 2266 826 2 v 323 2316 2 51 v 349 2301 a Fp(NOKNO)o(W,)h(6)f(ply)p 716 2316 V 747 2284 a Fk(1)p 747 2291 17 2 v 747 2315 a(2)p 792 2316 2 51 v 818 2301 a Fp(1)p 863 2316 V 50 w(1)p 934 2316 V 50 w(0)p 1005 2316 V 73 w(2)1080 2284 y Fk(1)p 1080 2291 17 2 v 1080 2315 a(2)p 1148 2316 2 51 v 324 2317 826 2 v 946 2574 a Fp(221)p eop %%Page: 222 224 222 223 bop 262 307 a Fr(E.1)69 b(HIAR)n(CS)22 b(5.0)i(v)n(ersus)f(Mephisto)g (Exclusiv)n(e)262 442 y Fu(E.1.1)55 b(Game)17 b(1)321 604 y Fp(White)77 b(:)18 b Fl(Mephisto)13 b(Exclusiv)o(e)321 654 y Fp(Blac)o(k)88 b(:)18 b Fl(HIAR)o(CS)d(5.0)321 703 y Fp(Op)q(ening)36 b(:)18 b(Kings)13 b(Gam)o(bit)f(Accepted)415 803 y(1.)62 b(e4)102 b(e5)552 b(31.)40 b(Qc2)71 b(Qf4)415 853 y(2.)62 b(f4)107 b(ef)560 b(32.)40 b(Nf2)77 b(g3)415 903 y(3.)62 b(Nf3)76 b(d6)547 b(33.)40 b(Nd3)67 b(gh+)14 b(\(mate)f(in)g(5\))415 952 y(4.)62 b(Bc4)73 b(Be6)523 b(34.)40 b(Kh1)66 b(Rxf1+)415 1002 y(5.)c(Bxe6)51 b(fe)560 b(35.)40 b(Rxf1)55 b(Qxf1+)415 1052 y(6.)62 b(d4)97 b(Qf6)525 b(36.)40 b(Kxh2)k(Qg1+)415 1102 y(7.)62 b(o-o)85 b(Nc6)521 b(37.)40 b(Kh3)66 b(Qg3+)14 b(mate)415 1152 y(8.)62 b(Nc3)71 b(Nge7)618 b(0)35 b Ff(\000)54 b Fp(1)415 1201 y(9.)62 b(Nb5)k(o-o-o)415 1251 y(10.)41 b(a4)99 b(a6)415 1301 y(11.)41 b(Nc3)71 b(e5)415 1351 y(12.)41 b(d5)97 b(Nb4)415 1401 y(13.)41 b(Bd2)68 b(Qg6)415 1451 y(14.)41 b(Nh4)66 b(Qh6)415 1500 y(15.)41 b(Qg4+)35 b(Kb8)415 1550 y(16.)41 b(Rac1)50 b(g5)415 1600 y(17.)41 b(Nf3)76 b(Rg8)415 1650 y(18.)41 b(Nd1)66 b(a5)415 1700 y(19.)41 b(Bxb4)46 b(ab)415 1749 y(20.)41 b(a5)99 b(Qg6)415 1799 y(21.)41 b(Nd2)66 b(Bg7)415 1849 y(22.)41 b(c4)102 b(h5)415 1899 y(23.)41 b(Qf3)75 b(g4)415 1949 y(24.)41 b(Qe2)70 b(f3)415 1998 y(25.)41 b(Qf2)75 b(Bh6)415 2048 y(26.)41 b(Ne3)71 b(fg)415 2098 y(27.)41 b(Kxg2)k(Rdf8)415 2148 y(28.)c(Qe2)70 b(Rf3)415 2198 y(29.)41 b(Nd1)66 b(Bxd2)415 2248 y(30.)41 b(Qxd2)i(Qxe4)946 2574 y(222)p eop %%Page: 223 225 223 224 bop 262 307 a Fu(E.1.2)55 b(Game)17 b(2)321 469 y Fp(White)77 b(:)18 b Fl(HIAR)o(CS)d(5.0)321 519 y Fp(Blac)o(k)88 b(:)18 b Fl(Mephisto)13 b(Exclusiv)o(e)321 569 y Fp(Op)q(ening)36 b(:)18 b(Bogo{Indian)415 668 y(1.)62 b(d4)97 b(Nf6)526 b(31.)40 b(Rc8)72 b(Rdd8)415 718 y(2.)62 b(c4)102 b(e6)552 b(32.)40 b(Rc6)72 b(Qh6)415 768 y(3.)62 b(Nf3)76 b(Bb4)518 b(33.)40 b(Qe2)71 b(Rf6)415 818 y(4.)62 b(Bd2)68 b(Bxd2)496 b(34.)40 b(h3)98 b(Qg5)415 868 y(5.)62 b(Qxd2)43 b(o-o)535 b(35.)40 b(Qb5)66 b(Qh4)415 917 y(6.)c(Nc3)71 b(d5)547 b(36.)40 b(Rxb6)45 b(Nxb6)415 967 y(7.)62 b(e3)102 b(Ne4)521 b(37.)40 b(Qxb6)k(Rc8)415 1017 y(8.)62 b(Nxe4)49 b(de)550 b(38.)40 b(Rxa5)47 b(Rc1+)415 1067 y(9.)62 b(Ng1)68 b(Nc6)521 b(39.)40 b(Kh2)66 b(Rc2)415 1117 y(10.)41 b(Ne2)71 b(Rb8)516 b(40.)40 b(Ra8)69 b(Kf7)415 1166 y(11.)41 b(Ng3)68 b(f5)557 b(41.)40 b(Ra7)69 b(Kg6)415 1216 y(12.)41 b(Be2)73 b(b6)547 b(42.)40 b(Re7)72 b(Rxf2)415 1266 y(13.)41 b(o-o)85 b(Bb7)518 b(43.)40 b(Rxe6)50 b(Kf7)415 1316 y(14.)41 b(Rac1)50 b(Ne5)521 b(44.)40 b(d5)98 b(Qh6)415 1366 y(15.)41 b(Qc2)70 b(Nc6)521 b(45.)40 b(Kg1)68 b(Rd2)415 1416 y(16.)41 b(c5)102 b(Nb4)516 b(46.)40 b(Nxf5)55 b(Rd1+)415 1465 y(17.)41 b(Qb3)65 b(Nd5)516 b(47.)40 b(Kh2)66 b(Rxe6)415 1515 y(18.)41 b(c6)102 b(Ba8)520 b(48.)40 b(Qb7+)34 b(Kf8)415 1565 y(19.)41 b(Qa4)67 b(a5)549 b(49.)40 b(Qb4+)34 b(Kf7)415 1615 y(20.)41 b(Qb3)65 b(Qh4)515 b(50.)40 b(Nxh6+)13 b(Rxh6)415 1665 y(21.)41 b(Rfd1)53 b(Rb)q(d8)492 b(51.)40 b(Qxe4)49 b(Rd2)415 1714 y(22.)41 b(a4)99 b(Rd6)516 b(52.)40 b(b4)98 b(Rg6)415 1764 y(23.)41 b(Bb5)68 b(Nb4)516 b(53.)40 b(a5)100 b(Ra2)415 1814 y(24.)41 b(Rd2)66 b(Bxc6)501 b(54.)40 b(d6)98 b(Rxd6)415 1864 y(25.)41 b(Bxc6)51 b(Nxc6)499 b(55.)40 b(Qc4+)f(Re6)415 1914 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b(Qd4)515 b(38.)40 b(Qa3)68 b(Ke6)415 1067 y(9.)62 b(Nc3)71 b(Qb4)515 b(39.)40 b(Qxb2)k(Bxb2)415 1117 y(10.)d(Qf5)75 b(Bd6)518 b(40.)40 b(h7)98 b(f5)415 1166 y(11.)41 b(Qg5)67 b(o-o)535 b(41.)40 b(Resigns)415 1216 y(12.)h(Rb1)66 b(Rfe8)626 b(0)35 b Ff(\000)54 b Fp(1)415 1266 y(13.)41 b(a3)99 b(Qc5)415 1316 y(14.)41 b(Be3)73 b(Qa5)415 1366 y(15.)41 b(b4)97 b(h6)415 1416 y(16.)41 b(Qg3)67 b(Qxa3)415 1465 y(17.)41 b(Rb3)66 b(Qxb3)415 1515 y(18.)41 b(cb)100 b(Bxb4)415 1565 y(19.)41 b(Na2)68 b(Bf8)415 1615 y(20.)41 b(f4)107 b(ef)415 1665 y(21.)41 b(Bxf4)56 b(Bc5+)415 1714 y(22.)41 b(Kh1)65 b(Nh5)415 1764 y(23.)41 b(Qg4)67 b(Nxf4)415 1814 y(24.)41 b(Rxf4)54 b(Bd6)415 1864 y(25.)41 b(Rf6)76 b(h5)415 1914 y(26.)41 b(Qxh5)i(gf)415 1963 y(27.)e(h4)97 b(Rad8)415 2013 y(28.)41 b(Nc3)71 b(Be5)415 2063 y(29.)41 b(Qg4)67 b(Kf8)415 2113 y(30.)41 b(d4)97 b(Rxd4)946 2574 y(224)p eop %%Page: 225 227 225 226 bop 262 307 a Fu(E.1.4)55 b(Game)17 b(4)321 469 y Fp(White)77 b(:)18 b Fl(HIAR)o(CS)d(5.0)321 519 y Fp(Blac)o(k)88 b(:)18 b Fl(Mephisto)13 b(Exclusiv)o(e)321 569 y Fp(Op)q(ening)36 b(:)18 b(Catalan)415 668 y(1.)62 b(d4)97 b(Nf6)526 b(31.)40 b(Kg2)68 b(Nb4)415 718 y(2.)62 b(c4)102 b(e6)552 b(32.)40 b(Rxa5)47 b(Na6)415 768 y(3.)62 b(g3)99 b(d5)547 b(33.)40 b(Rad5)46 b(g6)415 818 y(4.)62 b(Bg2)70 b(dc)550 b(34.)40 b(a4)100 b(Nb8)415 868 y(5.)62 b(Nf3)76 b(Nb)q(d7)492 b(35.)40 b(Rf7)77 b(Na6)415 917 y(6.)62 b(Nc3)71 b(Bb4)518 b(36.)40 b(Rd7)67 b(Re6)415 967 y(7.)62 b(Bd2)68 b(o-o)535 b(37.)40 b(Rxh7+)13 b(Resigns)415 1017 y(8.)62 b(o-o)85 b(Be7)617 b(\(mate)13 b(in)h(3\))415 1067 y(9.)62 b(Bf4)78 b(c5)670 b(1)35 b Ff(\000)54 b Fp(0)415 1117 y(10.)41 b(e3)102 b(cd)415 1166 y(11.)41 b(Qxd4)i(Qb6)415 1216 y(12.)e(Rb1)66 b(Qxd4)415 1266 y(13.)41 b(Nxd4)j(Nc5)415 1316 y(14.)d(Bc7)73 b(Bd7)415 1366 y(15.)41 b(Rfd1)53 b(Ng4)415 1416 y(16.)41 b(h3)97 b(Rfc8)415 1465 y(17.)41 b(Ndb5)i(Bxb5)415 1515 y(18.)e(Nxb5)j(Nh6)415 1565 y(19.)d(Bd6)68 b(Bxd6)415 1615 y(20.)41 b(Nxd6)j(Rcb8)415 1665 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y(20.)h(f4)107 b(Ng6)636 b(0)35 b Ff(\000)54 b Fp(1)415 1799 y(21.)41 b(Qf2)75 b(Qc7)415 1849 y(22.)41 b(Nde2)48 b(Rc4)415 1899 y(23.)41 b(Rxd8)j(Qxd8)415 1949 y(24.)d(Rd1)66 b(Qc7)415 1998 y(25.)41 b(Rd4)66 b(Rxd4)415 2048 y(26.)41 b(Qxd4)i(Nxf4)415 2098 y(27.)e(Nxf4)54 b(e5)415 2148 y(28.)41 b(Qd2)65 b(ef)415 2198 y(29.)41 b(a3)99 b(Kf8)415 2248 y(30.)41 b(Nd5)66 b(Nxd5)946 2574 y(228)p eop %%Page: 229 231 229 230 bop 262 307 a Fu(E.2.2)55 b(Game)17 b(2)321 469 y Fp(White)77 b(:)18 b Fl(HIAR)o(CS)d(5.0)321 519 y Fp(Blac)o(k)88 b(:)18 b Fl(Mark)e(Uniac)o(k)o(e)321 569 y Fp(Op)q(ening)36 b(:)18 b(Pirc)c(Defence)415 668 y(1.)62 b(e4)102 b(d6)547 b(31.)40 b(b3)98 b(Nb6)415 718 y(2.)62 b(d4)97 b(Nf6)526 b(32.)40 b(h4)98 b(a5)415 768 y(3.)62 b(Nc3)71 b(g6)549 b(33.)40 b(h5)98 b(Na6)415 818 y(4.)62 b(f4)107 b(Bg7)520 b(34.)40 b(hg)98 b(hg)415 868 y(5.)62 b(Nf3)76 b(o-o)535 b(35.)40 b(Rh1+)35 b(Kg7)415 917 y(6.)62 b(Be3)73 b(Ng4)518 b(36.)40 b(Kc1)71 b(a4)415 967 y(7.)62 b(Bd2)68 b(c5)552 b(37.)40 b(ba)98 b(Nxa4)415 1017 y(8.)62 b(dc)100 b(dc)550 b(38.)40 b(Qc2)71 b(Qc6)415 1067 y(9.)62 b(e5)102 b(a6)549 b(39.)40 b(Rh3)67 b(ba)415 1117 y(10.)41 b(h3)97 b(Nh6)516 b(40.)40 b(Nxa3)47 b(Nb4)415 1166 y(11.)41 b(Be3)73 b(Qa5)517 b(41.)40 b(Rxd8)45 b(Nxc2)415 1216 y(12.)c(Qd5)65 b(Nd7)516 b(42.)40 b(Rxe8)50 b(Qxe8)415 1266 y(13.)41 b(g4)99 b(Kh8)515 b(43.)40 b(Kxc2)49 b(Qc6)415 1316 y(14.)41 b(o-o-o)50 b(e6)552 b(44.)40 b(Bd2)69 b(Qe4+)415 1366 y(15.)41 b(Qd6)65 b(Re8)521 b(45.)40 b(Kb3)66 b(Qe2)415 1416 y(16.)41 b(Ng5)68 b(Bf8)528 b(46.)40 b(Kc2)71 b(Qxg4)415 1465 y(17.)41 b(Qd2)65 b(Be7)523 b(47.)40 b(Rb3)67 b(Qf5+)415 1515 y(18.)41 b(Nge4)50 b(b5)547 b(48.)40 b(Kc1)71 b(Qe4)415 1565 y(19.)41 b(Nd6)66 b(Bxd6)496 b(49.)40 b(Kd1)66 b(Qd4)415 1615 y(20.)41 b(Qxd6)i(Bb7)518 b(50.)40 b(Kc2)71 b(g5)415 1665 y(21.)41 b(Rh2)66 b(Rad8)495 b(51.)40 b(Rg3)69 b(Kf8)415 1714 y(22.)41 b(Bg2)70 b(Bxg2)498 b(52.)40 b(fg)108 b(Qxe5)415 1764 y(23.)41 b(Rxg2)46 b(b4)547 b(53.)40 b(Rd3)67 b(Qe4)415 1814 y(24.)41 b(Nb1)66 b(Ng8)518 b(54.)40 b(Be3)74 b(Nb2)415 1864 y(25.)41 b(a3)99 b(Ne7)521 b(55.)40 b(Kxb2)k(Qxd3)415 1914 y(26.)d(c4)102 b(Nc8)521 b(56.)40 b(Bxc5+)20 b(Kg7)415 1963 y(27.)41 b(Qc6)70 b(Ncb6)498 b(57.)40 b(Be7)74 b(Kg6)415 2013 y(28.)41 b(Qe4)70 b(Nb8)516 b(58.)40 b(Bf6)79 b(e5)415 2063 y(29.)41 b(Rgg1)47 b(Na4)518 b(59.)40 b(Be7)74 b(e4)415 2113 y(30.)41 b(Kc2)70 b(Qc7)520 b(60.)40 b(Nc2)72 b(Qxc4)946 2574 y(229)p eop %%Page: 230 232 230 231 bop 415 357 a Fp(61.)41 b(Bf6)78 b(Qd3)415 407 y(62.)41 b(Nb4)66 b(Qd2+)415 457 y(63.)41 b(Nc2)71 b(e3)415 506 y(64.)41 b(Bc3)73 b(Qd3)415 556 y(65.)41 b(Bd4)68 b(e2)415 606 y(66.)41 b(Bf6)78 b(Qd2)415 656 y(67.)41 b(Kb1)65 b(e1\(Q\)+)415 706 y(68.)41 b(Nxe1)49 b(Qxe1+)415 756 y(69.)41 b(Kc2)70 b(Qf2+)415 805 y(70.)41 b(Kd3)65 b(Qf4)415 855 y(71.)41 b(Ke2)70 b(Qxf6)415 905 y(72.)41 b(gf)107 b(Kxf6)415 955 y(73.)41 b(Kf2)75 b(Kf5)415 1005 y(74.)41 b(Kf3)75 b(f6)415 1054 y(75.)41 b(Kg3)67 b(Ke4)415 1104 y(76.)41 b(Kf2)75 b(Kf4)415 1154 y(77.)41 b(Kg2)67 b(Ke3)415 1204 y(78.)41 b(Kg3)67 b(f5)415 1254 y(79.)41 b(Kg2)67 b(f4)415 1303 y(80.)41 b(Kf1)75 b(Kf3)415 1353 y(81.)41 b(Ke1)70 b(Kg2)415 1403 y(82.)41 b(Resigns)533 1453 y(0)35 b Ff(\000)54 b Fp(1)946 2574 y(230)p eop %%Page: 231 233 231 232 bop 262 307 a Fr(E.3)69 b(HIAR)n(CS)22 b(5.0)i(v)n(ersus)f(NOKNO)n(W) 262 442 y Fu(E.3.1)55 b(Game)17 b(1)321 604 y Fp(White)77 b(:)18 b Fl(NOKNO)o(W,)f(6)e(ply)321 654 y Fp(Blac)o(k)88 b(:)18 b Fl(HIAR)o(CS)d(5.0,)i(3)e(ply)321 703 y Fp(Op)q(ening)36 b(:)18 b(Queens)d(Gam)o(bit)c(Declined)415 803 y(1.)62 b(d4)97 b(d5)547 b(31.)40 b(Qa7)68 b(Qxe5)415 853 y(2.)62 b(c4)102 b(e6)552 b(32.)40 b(Rb1)67 b(Qe4)415 903 y(3.)62 b(Nc3)71 b(Nf6)526 b(33.)40 b(a5)100 b(Rc2)415 952 y(4.)62 b(Bg5)70 b(Be7)523 b(34.)40 b(a6)100 b(ba)415 1002 y(5.)62 b(e3)102 b(o-o)535 b(35.)40 b(Qxa6)46 b(Kh7)415 1052 y(6.)62 b(Nf3)76 b(h6)547 b(36.)40 b(Qd6)66 b(Rc6)415 1102 y(7.)c(Bxf6)56 b(Bxf6)506 b(37.)40 b(Qd1)66 b(Rcc7)415 1152 y(8.)c(Qb3)j(c6)552 b(38.)40 b(Rb6)67 b(Rcd7)415 1201 y(9.)62 b(Rd1)k(Nd7)516 b(39.)40 b(Rd6)67 b(Qf5)415 1251 y(10.)41 b(Bd3)68 b(g6)549 b(40.)40 b(Rxd7)45 b(Rxd7)415 1301 y(11.)c(cd)100 b(ed)550 b(41.)40 b(Qe2)71 b(Qc5)415 1351 y(12.)41 b(e4)102 b(de)550 b(42.)40 b(Kg2)68 b(Qd5+)415 1401 y(13.)41 b(Nxe4)49 b(Nb6)516 b(43.)40 b(f3)108 b(Qd4)415 1451 y(14.)41 b(Nxf6)54 b(Qxf6)503 b(44.)40 b(f4)108 b(Qc3)415 1500 y(15.)41 b(Be4)73 b(Bf5)528 b(45.)40 b(Kh3)66 b(Qd2)415 1550 y(16.)41 b(Bxf5)56 b(Qxf5)503 b(46.)40 b(Qxd2)k(Rxd2)415 1600 y(17.)d(o-o)85 b(Rde8)498 b(47.)40 b(Rh1)67 b(Kg7)415 1650 y(18.)41 b(Ne5)71 b(Kg7)517 b(48.)40 b(Kg4)68 b(Kf6)415 1700 y(19.)41 b(Qa3)67 b(f6)557 b(49.)40 b(Kf3)76 b(Rc2)415 1749 y(20.)41 b(Qxa7)k(fe)560 b(50.)40 b(Ke4)71 b(Re2+)415 1799 y(21.)41 b(Qxb6)i(Rf7)526 b(51.)40 b(Kd3)66 b(Rb2)415 1849 y(22.)41 b(Qc5)70 b(Qf4)525 b(52.)40 b(Kc3)71 b(Rf2)415 1899 y(23.)41 b(a4)99 b(Ree7)503 b(53.)40 b(Kd4)66 b(Rd2+)415 1949 y(24.)41 b(b4)97 b(Ree8)503 b(54.)40 b(Kc4)71 b(Rc2+)415 1998 y(25.)41 b(b5)97 b(Rf6)526 b(55.)40 b(Kd5)66 b(Rd2+)415 2048 y(26.)41 b(Qa7)67 b(Re7)521 b(56.)40 b(Kc6)71 b(g5)415 2098 y(27.)41 b(b)q(c)99 b(Rxc6)499 b(57.)40 b(fg+)76 b(Kxg5)415 2148 y(28.)41 b(Qb8)65 b(Rc4)521 b(58.)40 b(h3)98 b(Rc2+)415 2198 y(29.)41 b(g3)99 b(Qf5)525 b(59.)40 b(Kd5)66 b(Rg2)415 2248 y(30.)41 b(de)100 b(Rc8)521 b(60.)40 b(g4)100 b(Kh4)946 2574 y(231)p eop %%Page: 232 234 232 233 bop 415 357 a Fp(61.)41 b(Ke4)70 b(Rg3)415 407 y(62.)41 b(Kf4)75 b(Rxh3)415 457 y(63.)41 b(Rg1)68 b(Rd3)415 506 y(64.)41 b(Kf5)75 b(Rd5+)415 556 y(65.)41 b(Kf6)75 b(Rd2)415 606 y(66.)41 b(Ke5)70 b(Kg5)415 656 y(67.)41 b(Rh1)66 b(Re2+)415 706 y(68.)41 b(Kd5)65 b(Re3)415 756 y(69.)41 b(Rh5+)34 b(Kxg4)415 805 y(70.)41 b(Rxh6)510 855 y(Dra)o(wn)538 889 y Fk(1)p 538 896 17 2 v 538 919 a(2)595 905 y Ff(\000)680 889 y Fk(1)p 680 896 V 680 919 a(2)946 2574 y Fp(232)p eop %%Page: 233 235 233 234 bop 262 307 a Fu(E.3.2)55 b(Game)17 b(2)321 469 y Fp(White)77 b(:)18 b Fl(HIAR)o(CS)d(5.0,)i(3)e(ply)321 519 y Fp(Blac)o(k)88 b(:)18 b Fl(NOKNO)o(W,)f(6)e(ply)321 569 y Fp(Op)q(ening)36 b(:)18 b(Ruy)13 b(Lop)q(ez)415 668 y(1.)62 b(e4)102 b(e5)415 718 y(2.)62 b(Nf3)76 b(Nc6)415 768 y(3.)62 b(Bb5)68 b(a6)415 818 y(4.)62 b(Ba4)70 b(Nf6)415 868 y(5.)62 b(o-o)85 b(Be7)415 917 y(6.)62 b(Re1)71 b(b5)415 967 y(7.)62 b(Bb3)68 b(d6)415 1017 y(8.)62 b(c3)102 b(o-o)415 1067 y(9.)62 b(h3)97 b(Bb7)415 1117 y(10.)41 b(d4)97 b(Re8)415 1166 y(11.)41 b(Ng5)68 b(Rf8)415 1216 y(12.)41 b(f4)107 b(ed)415 1266 y(13.)41 b(cd)100 b(h6)415 1316 y(14.)41 b(Nf3)76 b(d5)415 1366 y(15.)41 b(ed)100 b(Na5)415 1416 y(16.)41 b(Bc2)73 b(Bxd5)415 1465 y(17.)41 b(Nc3)71 b(Bxf3)415 1515 y(18.)41 b(gf)107 b(c5)415 1565 y(19.)41 b(Be3)73 b(Nc4)415 1615 y(20.)41 b(dc)100 b(Nxe3)415 1665 y(21.)41 b(Rxe3)49 b(Bxc5)415 1714 y(22.)41 b(Qe1)70 b(Qd4)415 1764 y(23.)41 b(Nd1)66 b(Nd5)415 1814 y(24.)41 b(Resigns)533 1864 y(0)35 b Ff(\000)54 b Fp(1)946 2574 y(233)p eop %%Page: 234 236 234 235 bop 262 307 a Fu(E.3.3)55 b(Game)17 b(3)321 469 y Fp(White)77 b(:)18 b Fl(NOKNO)o(W,)f(6)e(ply)321 519 y Fp(Blac)o(k)88 b(:)18 b Fl(HIAR)o(CS)d(5.0,)i(3)e(ply)321 569 y Fp(Op)q(ening)36 b(:)18 b(Reti)13 b(\(irregular\))415 668 y(1.)62 b(Nf3)76 b(d5)547 b(31.)40 b(Ra1)69 b(Nb4)415 718 y(2.)62 b(Na3)68 b(Nc6)521 b(32.)40 b(Rxa7)47 b(b6)415 768 y(3.)62 b(c4)102 b(e5)552 b(33.)40 b(Rc7)72 b(c5+)415 818 y(4.)62 b(cd)100 b(Qxd5)493 b(34.)40 b(Kc4)71 b(Nc2)415 868 y(5.)62 b(d3)97 b(Bb4+)486 b(35.)40 b(Rb7)67 b(Nd4)415 917 y(6.)62 b(Bd2)68 b(Bg4)520 b(36.)40 b(f4)108 b(Ne6)415 967 y(7.)62 b(Bxb4)46 b(Bxf3)506 b(37.)40 b(Rxb6)45 b(g6)415 1017 y(8.)62 b(ef)110 b(Nxb4)494 b(38.)40 b(f3)108 b(Ke7)415 1067 y(9.)62 b(Nc4)71 b(Nf6)526 b(39.)40 b(Kd5)66 b(h5)415 1117 y(10.)41 b(Qe2)70 b(o-o)535 b(40.)40 b(Ke4)71 b(Ng7)415 1166 y(11.)41 b(Nxe5)49 b(Nxd3+)462 b(41.)40 b(Ke5)71 b(Nf5)415 1216 y(12.)41 b(Qxd3)i(Qxe5+)466 b(42.)40 b(Rb7)67 b(Ke8)415 1266 y(13.)41 b(Qe2)70 b(Qc5)520 b(43.)40 b(Kf6)76 b(Nxh4)415 1316 y(14.)41 b(Qd2)65 b(Rfe8+)476 b(44.)40 b(Re7+)g(Kd8)415 1366 y(15.)h(Be2)73 b(Rad8)495 b(45.)40 b(Rxf7)55 b(Nxf3)415 1416 y(16.)41 b(Qc1)70 b(Qb5)515 b(46.)40 b(Kxg6)46 b(Nd4)415 1465 y(17.)41 b(Qc2)70 b(Rxe2+)467 b(47.)40 b(Rb7)67 b(h4)415 1515 y(18.)41 b(Qxe2)48 b(Re8)521 b(48.)40 b(Kg5)68 b(Kc8)415 1565 y(19.)41 b(Qxe8+)16 b(Qxe8+)466 b(49.)40 b(Rh7)67 b(Nxb3)415 1615 y(20.)41 b(Kd2)65 b(Qe5)520 b(50.)40 b(Kxh4)k(c4)415 1665 y(21.)d(b3)97 b(Qg5+)485 b(51.)40 b(Kg5)68 b(Nd4)415 1714 y(22.)41 b(Ke2)70 b(Qxg2)495 b(52.)40 b(Kf6)76 b(c3)415 1764 y(23.)41 b(h4)97 b(Nd5)516 b(53.)40 b(Rh5)67 b(Kb7)415 1814 y(24.)41 b(Rag1)47 b(Nc3+)489 b(54.)40 b(Rc5)72 b(c2)415 1864 y(25.)41 b(Ke3)70 b(Qxh1)493 b(55.)40 b(Ke5)71 b(Nc6+)415 1914 y(26.)41 b(Rxh1)j(c6)552 b(56.)40 b(Kd6)66 b(Nb4)415 1963 y(27.)41 b(Kd4)65 b(Nb5+)484 b(57.)40 b(f5)108 b(c1\(Q\))415 2013 y(28.)41 b(Kc5)70 b(Nc3)521 b(58.)40 b(Rxc1)50 b(Resigns)415 2063 y(29.)41 b(Re1)71 b(Kf8)643 b(1)35 b Ff(\000)54 b Fp(0)415 2113 y(30.)41 b(Kd4)65 b(Nxa2)946 2574 y(234)p eop %%Page: 235 237 235 236 bop 262 307 a Fu(E.3.4)55 b(Game)17 b(4)321 469 y Fp(White)77 b(:)18 b Fl(HIAR)o(CS)d(5.0,)i(3)e(ply)321 519 y Fp(Blac)o(k)88 b(:)18 b Fl(NOKNO)o(W,)f(6)e(ply)321 569 y Fp(Op)q(ening)36 b(:)18 b(Alekhines)c(Defence)415 668 y(1.)62 b(e4)102 b(Nf6)526 b(31.)40 b(Rb6)67 b(Rac8)415 718 y(2.)62 b(e5)102 b(Nd5)516 b(32.)40 b(Rd4)67 b(Bc6)415 768 y(3.)62 b(d4)97 b(e6)552 b(33.)40 b(Ra6)69 b(a4)415 818 y(4.)62 b(c4)102 b(Bb4+)486 b(34.)40 b(Ra5)69 b(g6)415 868 y(5.)62 b(Bd2)68 b(Bxd2+)464 b(35.)40 b(h5)98 b(Ke6)415 917 y(6.)62 b(Qxd2)43 b(Ne7)521 b(36.)40 b(hg)98 b(hg)415 967 y(7.)62 b(Nc3)71 b(Nb)q(c6)497 b(37.)40 b(Nh4)67 b(Rg7)415 1017 y(8.)62 b(Nf3)76 b(d6)547 b(38.)40 b(f4)108 b(Ra8)415 1067 y(9.)62 b(o-o-o)50 b(o-o)535 b(39.)40 b(Rc5)72 b(Ra6)415 1117 y(10.)41 b(Bd3)68 b(Nf5)526 b(40.)40 b(Rd2)67 b(Be4)415 1166 y(11.)41 b(Bxf5)56 b(ef)560 b(41.)40 b(Nf3)77 b(Rg8)415 1216 y(12.)41 b(ed)100 b(cd)550 b(42.)40 b(Nd4+)35 b(Ke7)415 1266 y(13.)41 b(Rde1)48 b(b6)547 b(43.)40 b(Rc7+)g(Ke8)415 1316 y(14.)h(Nd5)66 b(Be6)523 b(44.)40 b(Nb5)67 b(Ra8)415 1366 y(15.)41 b(Ne3)71 b(Bd7)518 b(45.)40 b(Nd6+)35 b(Kd8)415 1416 y(16.)41 b(h4)97 b(a5)549 b(46.)40 b(Rf7)77 b(Bc6)415 1465 y(17.)41 b(Nd5)66 b(Be6)523 b(47.)40 b(Nxf5+)23 b(Ke8)415 1515 y(18.)41 b(Nxb6)j(Qxb6)493 b(48.)40 b(Nd6+)35 b(Kd8)415 1565 y(19.)41 b(d5)97 b(Qc5)520 b(49.)40 b(Nb5+)35 b(Ke8)415 1615 y(20.)41 b(b3)97 b(Bd7)518 b(50.)40 b(Rxf6)55 b(Bxb5)415 1665 y(21.)41 b(dc)100 b(Bxc6)501 b(51.)40 b(cb)101 b(Ke7)415 1714 y(22.)41 b(Re7)71 b(d5)547 b(52.)40 b(Rfd6)54 b(Rgf8)415 1764 y(23.)41 b(Re5)71 b(Qa3+)485 b(53.)40 b(g3)100 b(Rf6)415 1814 y(24.)41 b(Qb2)65 b(Qxb2+)461 b(54.)40 b(Rd7+)35 b(Ke8)415 1864 y(25.)41 b(Kxb2)i(dc)550 b(55.)40 b(Kb4)66 b(Re6)415 1914 y(26.)41 b(b)q(c)99 b(Be4)523 b(56.)40 b(R7d6)46 b(Ke7)415 1963 y(27.)41 b(Rd1)66 b(f6)557 b(57.)40 b(Rxe6+)18 b(Kxe6)415 2013 y(28.)41 b(Re7)71 b(Rf7)526 b(58.)40 b(b6)98 b(Rb8)415 2063 y(29.)41 b(Re6)71 b(Rc7)521 b(59.)40 b(Kc5)71 b(Rc8+)415 2113 y(30.)41 b(Kc3)70 b(Kf7)525 b(60.)40 b(Kb5)66 b(a3)946 2574 y(235)p eop %%Page: 236 238 236 237 bop 415 357 a Fp(61.)41 b(Rd3)66 b(Ra8)415 407 y(62.)41 b(b7)97 b(Rb8)415 457 y(63.)41 b(Kb6)65 b(Rg8)415 506 y(64.)41 b(Rxa3)46 b(Rd8)415 556 y(65.)41 b(Re3+)e(Kf6)415 606 y(66.)i(Kc7)70 b(Rf8)415 656 y(67.)41 b(b8\(Q\))33 b(Rxb8)415 706 y(68.)41 b(Kxb8)i(g5)415 756 y(69.)e(fg+)75 b(Kxg5)415 805 y(70.)41 b(a4)99 b(Resigns)533 855 y(1)35 b Ff(\000)54 b Fp(0)946 2574 y(236)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF