Cmputer Chess Wrld champin Garry Kasparv beat Deep Thught decisively in ehibitin games in 1989 Deep Thught rated ~ 600 Deep Blue develped at IBM Thmas

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1 Cmputer Chess Within 10 years a cmputer will be wrld chess champin Herbert Simn, 197 Deep Thught develped by CMU and IBM frerunner f Deep Blue rated ~ 00 wn Wrld Cmputer Chess Champinship in 1989 Chess Ratings beginners: < 1000 grandmasters: human wrld champins: ~ 800 (Garry Kasparv: 81) current chess prgrams: > 000

2 Cmputer Chess Wrld champin Garry Kasparv beat Deep Thught decisively in ehibitin games in 1989 Deep Thught rated ~ 600 Deep Blue develped at IBM Thmas J. Watsn research center massively parallel supercmputer with special-purpse chess hardware capable f evaluating 00 millin bard psitins per secnd capable f lking ahead up t 0 plies (half-mves) in sme situatins beat Garry Kasparv in a 6-game match n May 11, 1997 final scre:. t.

3 Deep Blue

4 Cmputer Chess Deep Fritz PC with tw Intel Cre Du prcessrs capable f evaluating nly 8 millin psitins per secnd used mre sphisticated heuristics average search depth f plies in the middlegame drew an 8-game match against Vladimir Kramnik ( classical wrld champin) in 00 beat Kramnik (undisputed wrld champin) in 006, t Deep Junir develped by Israeli cmputer scientists drew a 6-game rematch against Garry Kasparv in 00 beat Deep Fritz in 007, t

5 Cmputer Chess

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8 Cmputer Chess Game tree branching factr is abut quickly leads t a cmbinatrial eplsin levels dwn, already >,000 branches Claude Shannn estimated chess game tree has ~ ndes if a cmputer culd eamine 100 trillin ndes per secnd, it wuld still take arund a ggl years ( ) t search! age f the universe is much less than years Need t select branches t eamine in an intelligent way Human chess masters ignre almst all branches and selectively fcus nly n ptentially very gd nes, using pattern-matching Chess supercmputers lk ahead many levels using brute-frce cmputatin

9 Cmputer Chess Heuristic search techniques cannt be used directly presence f ppnent cmplicates the search game tree is t large t see t the bttm Static evaluatin functin numerically evaluates the strength f a bard psitin frm the viewpint f a particular player actual values are nt as imprtant as relative bard ratings eample: number f queens, rks, knights, bishps, pawns 9q + r + k + b + p Minima algrithm determines the best mve at any pint in the game, assuming that bth players play ratinally

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19 Static Evaluatin Functin a = Number f ways t win by filling in 1 space b = Number f ways t win by filling in spaces Evaluatin functin = a + b

20 Static Evaluatin Functin a = Number f ways t win by filling in 1 space b = Number f ways t win by filling in spaces Evaluatin functin = a + b a = 1

21 Static Evaluatin Functin a = Number f ways t win by filling in 1 space b = Number f ways t win by filling in spaces Evaluatin functin = a + b a = 1 b =

22 Static Evaluatin Functin a = Number f ways t win by filling in 1 space b = Number f ways t win by filling in spaces Evaluatin functin = a + b a = 1 b = 1 + =

23 Static Evaluatin Functin a = Number f ways t win by filling in 1 space b = Number f ways t win by filling in spaces Evaluatin functin = a + b Frm 's perspective = Frm 's perspective =?

24 Static Evaluatin Functin a = Number f ways t win by filling in 1 space b = Number f ways t win by filling in spaces Evaluatin functin = a + b Frm 's perspective = Frm 's perspective = a = 0 b = 0 + =

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32 Pruning the Search Tree In practice, we dn't epand all ndes n each level at nce Ding s is inefficient and may be unnecessary Alpha-beta pruning can significantly speed up the search We can avid evaluating entire branches f the search tree If an idea is surely bad, dn't waste time analyzing just hw bad it is

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58 Pruning the Search Tree In this eample, we perfrmed 16 static evaluatins Withut alpha-beta pruning, we wuld have perfrmed 66 This represents a savings f 7% Amunt f pruning depends n the rder that ndes are epanded This eample shws the best case scenari Effective branching factr reduces frm b t b This means that alpha-beta can lk twice as far ahead as minima fr the same cst Hwever, the search is still epnential even in the best case

59 Checkers Mre manageable than chess average branching factr ~ 8 nly piece types nly squares still ~ 00 billin billin pssible bard psitins Arthur Samuel's Checkers prgram develped at IBM in 199 first successful machine learning prgram learned t play checkers better than Samuel himself used evaluatin functins, minima, and heuristics

60 Chink Checkers prgram develped by Jnathan Schaeffer and clleagues at the University f Alberta, Canada Uses minima, alpha-beta pruning, varius heuristics, and a large database cvering hundreds f billins f pening mves and endgames (all endgames with 8 pieces r less) Eamines game tree t ~ 0 ply Unlike Samuel's prgram, des nt learn Marin Tinsley: wrld champin fr 0 years, best player ever in 1990, beat Chink 7. t 6. in 199, beat Chink in Wrld Checkers Champinship (wn, lst, drew ) in 199, played Chink in 6 games, all drawn, then resigned due t ill health

61 Chink Chink has never been beaten since then...and never will be! In 007 it was prven that the current versin cannt be beaten, nly drawn Bard evaluatin is a weighted functin f: piece cunt king cunt balance f the distributin f pieces acrss the bard number f trapped kings etc. Search heuristics take int accunt the likelihd f a human player making mistakes n different pathways thrugh the game tree

62 G Still ut f reach f AI prgrams bard Average branching factr ~ 60 Search must be etremely selective Pattern recgnitin is very imprtant Best prgrams can be trunced by human players $1 millin prize fr first prgram t beat a prfessinal G player