!"#$ &'"()*+, -.$ /$01 234$5
675"* 89 :;51$)*
Department of Computer Science
Hunter College and The Graduate School of The City University of New York
695 Park Avenue, New York, NY 10021
[email protected]
<=51>"?1
Computer programs now play many board games as well
or better than the most expert humans. Human players,
however, learn, plan, allocate resources, and integrate multiple streams of knowledge. This paper highlights recent
achievements in game playing, describes some cognitively-oriented work, and poses three related challenge
problems for the AI community.
!"#$ &'"()*+ "5 " @3#")*
Work on games has had several traditional justifications.
Given unambiguous rules, playing a game to win is a
well-defined problem. A game’s rules create artificial
world states whose granularity is explicit. There is an
initial state, a state space with clear transitions, and a set
of readily describable goal states. Without intervening
instrumentation, games are also noise-free. For these reasons, as well as for their ability to amuse, games have
often been referred to as “toy domains.” To play the most
difficult games well, however, a program must contend
with fundamental issues in AI: knowledge representation,
search, learning, and planning.
There are two principal reasons to continue to do research on games, despite Deep Blue’s triumph (Hamilton
and Hedberg 1997). First, human fascination with game
playing is long-standing and pervasive. Anthropologists
have catalogued popular games in almost every culture.
Indeed, the same game, under various names, often appears on many continents (Bell 1969; Zaslavsky 1982).
Games intrigue us because they address important cognitive functions. In particular, the games humans like to
play are probably the ones we are good at, the ones that
capitalize on our intellectual strengths and forgive our
weaknesses. A program that plays many games well must
simulate important cognitive skills. The second reason to
continue game-playing research is that some difficult
games remain to be won, games that people play very
well but computers do not. These games clarify what our
current approach lacks. They set challenges for us to
meet, and they promise ample rewards.
This paper summarizes the role of search and knowledge in game playing, the state of the art, and recent
relevant data on expert human game players. It then
shows how cognitive skills can enhance a game-playing
program, and poses three new challenge problems for the
AI community. Although rooted in game playing, these
challenges could enhance performance in many domains.
6$">?. "*A B*3C'$A+$
In this paper, a !"#$ is a multi-agent, noise-free, discrete
space with a finite set of objects (the %&"'()! %($+$,) and a
finite, static set of rules for %&"' (agents’ serial behavior).
The rules delineate where playing pieces can reside in the
space, and when and how +-).$,.")., (the agents) can
#-v$ (transform one state into another). A %-,(.(-) is a
world state in a game; it specifies the location of the playing pieces and the agent permitted to act (the #-v$0). The
rules specify time limits for computation, a set of initial
states, and a set of .$0#()"& states in which no agent is the
mover. The rules assign to each terminal state a gametheoretic value, which can be thought of as a numerical
score for each agent. The goal of each agent is to reach a
terminal state that optimizes the game-theoretic value
from its perspective. This definition includes finite-board
games (e.g., tic-tac-toe and chess), games with imperfect
information (e.g., poker and backgammon), and games
with sequential team play (e.g., bridge), but excludes parallel activities (e.g., tennis and soccer).
A game may be represented by a !"#$ .0$$, in which
each node represents a position and each link represents
one action by one agent (called a %&')1 A +-).$,. at a game
is a finite path through a game tree from an initial state. A
contest ends at the first terminal state it reaches; it may
also be terminated by the rules because a resource limit
has been exceeded or because a position has repeatedly
occurred. The -2.+-#$ of a contest is the value of its terminal state, or the value (typically a draw) that the rules
assign to a terminated contest1
An -%.(#"& #-v$ from position % is an action that creates a position with maximal value for the mover in %. In
a terminal state, that value is determined by the rules; in a
non-terminal state, it is the best result the mover can
achieve if subsequent play to the end of the contest is always optimal. An $v"&2".(-) 32)+.(-) maps positions to
scores for each agent. A %$03$+. evaluation function pre-
ser$es order among all positions0 game1theoretic $alues5 a
heuristic one attempts to approximate them.
Gi$en a subtree whose lea$es are labeled by an e$alua1
tion function= a minimax algorithm backs those $alues up=
one ply at a time= selecting the optimal mo$e at each node
?Shannon 1B5DE. Fith a small game tree= prior to any play
one can minimax the $alues of all terminal nodes to com1
pute the game1theoretic $alue of e$ery node ?full
retrograde analysisE and cache those $alues with the op1
timal mo$es. The resultant table is a perfect e$aluation
function that can eliminate search during competition.
In a challenging game= a perfect e$aluation function is
unknown to human experts= and full retrograde analysis is
intractable= as the search space siIes in Table 1 indicate.
During play= exhaustive search ?from the current position
to only terminal statesE followed by minimax could theo1
retically identify the correct mo$e. The number of nodes
$isited during such search is dependent both on the
game0s branch factor ?a$erage number of legal mo$es
from each positionE and the depth of the subtree. Unless a
contest is near completion or few pieces remain on the
board= such a search is likely to be intractable.
Table 1: Lstimated a$erage branch factor and search
space siIe for some challenging board games.
Game
:oard
Pieces :ranch factor Space
Checkers N ! N
24
N Q 2D
5R1D2D
Chess
N!N
32
35
1D12D
Shogi
B!B
4D
ND 1 15D
1D22T
Go
1B ! 1B 3N1
25D
1D3TD
Resource conser$ation during game tree search has
been attempted in both hardware and software. Vardware
designed for a particular e$aluation function can speed
computation. Deep Blue0s custom chess1searching chips=
for example= enabled it to e$aluate 5D to 1DD billion
mo$es in three minutes= sometimes to depths o$er 3D ply.
Search algorithms can also impro$e efficiency. Some
$ariations preser$e exhausti$e search0s correctness: sa$1
ing pre$iously e$aluated positions in a transposition table=
the "1# algorithm ?Slate and Atkin 1BZZE= extensions
along promising lines of play= and extensions that include
forced mo$es ?Anantharaman= Campbell= and Vsu 1BBDE.
[ther search algorithms take conser$ati$e risks= pruning
unpromising lines early ?Berliner 1BNZE or seeking a sta1
ble heuristic e$aluation ?Beal 1BBDE. Still others grow a
best1first tree= guided by $alues estimated for the current
lea$es ?Baum and Smith 1BBZ5 \cAllester 1BNN5 ]alay
1BN55 Ri$est 1BNZE. Fhate$er its search mechanisms=
howe$er= a powerful game playing program typically
plays only a single game= because it also relies on knowl1
edge.
^nowledge can be incorporated into a game1playing
program in three standard ways. First= formulaic beha$ior
early in play ?openingsE is prerecorded in an opening
book. Larly in a contest= the program identifies the current
opening and continues it. Second= knowledge about im1
portant principles in a game ?e.g.= control of the centerE is
embedded in a heuristic e$aluation function. During play=
the typical program searches to generate a subtree rooted
at the current node= applies its heuristic e$aluation func1
tion to the lea$es of that subtree= and minimaxes those
$alues to estimate the correct mo$e. Finally= partial retro1
grade analysis may be performed offline= to calculate and
store some true game1theoretic $alues and optimal mo$es.
For nodes se$eral ply from a terminal node= this is called
a closing book. Because a heuristic e$aluation function
always returns any a$ailable closing book $alues= the
larger the closing book= the more accurate the e$aluation
and the better a search engine is likely to perform. The
best programs use both search and knowledge to win at
difficult games.
!"# %&'&# () &"# *+&
,"#-.#+/ '01 -"#//
In 1BB4= Chinook became the world0s champion checker
player ?Schaeffer 1BBZE. Its opening book had ND=DDD
positions= and its 1D1gigabyte closing book had some 443
billion positions= e$ery position in which no more than
eight checkers remain on the board. In the course of its
de$elopment= it became clear that Chinook0s ultimate
prowess would be its knowledge base. As its closing book
grew= Chinook impro$ed. L$entually= with only the last N
ply sol$ed completely= Chinook defeated \arion Tinsley=
long the human world champion.
In 1BBT= Garry ^asparo$ defeated Deep Blue= but in
1BBZ he lost to a program that used the same special1
purpose hardware. In the inter$ening year= the program
had recei$ed a substantial infusion of grandmaster1le$el
knowledge. Its e$aluation function had been strengthened=
and its opening book had `a few thousand aitemsb chosen
to match aitsb stylec plus statistics on grandmasters0 open1
ing play in TDD=DDD contests. Its closing book included all
chess positions with fi$e or fewer pieces= as well as num1
ber of mo$es to completion.
Chinook and Deep Blue are examples of brute force=
the exploitation of search and knowledge on a heretofore1
unprecedented scale. Lach of them had a search engine
that explored enormous subtrees= and supported that
search with extensi$e opening and closing books. Lach
also had a carefully tuned= human1constructed= heuristic
e$aluation function= with features whose relati$e impor1
tance was well understood in the human expert
community. There are= howe$er= games whose large
branch factors preclude deep search= games where human
experts cannot pro$ide all the knowledge computers need
to win. ]rograms that play such games well ha$e learned
offline.
!ac$gammon) +t-ello) and Scra33le!
Current target6
In 1997 Logistello defeated Takeshi 5urakami, the human world Othello champion ?@uro 199AB, winning all 6
contests in the match. LogistelloEs heuristic evaluation
function is primarilG a weighted comHination of simple
patterns that appear on the Hoard, such as horiIontal or
diagonal lines. ?ParitG and stage, how far a contest has
progressed, are also included.B To produce this evaluation
function, 1.5 million weights for conLunctions of these
features were calculated with gradient descent during offline training, from analGsis of 11 million positions.
Although it uses a sophisticated search algorithm and a
large opening Hook, LogistelloEs evaluation function is the
keG to its prowess. No more than 22 moves Hefore the end
of a contest, Logistello correctlG computes the outcome.
TD-gammon, the Hest Hackgammon program HG far,
also relies on an evaluation function that was learned offline. TD-gammon narrowlG lost at the AAAI-9A Hall of
Champions to world champion 5alcolm Davis HG eight
points over 100 contests. In Hackgammon, the dice introduce a Hranch factor of T00, rendering extensive, Deep@lue-stGle search impossiHle. Instead, TD-gammon models decision making with a neural network pretrained HG
temporal difference learning on millions of offline contests Hetween two copies of the program. During
competition, TD-gammon uses its model to select a move
after a 2-to-3-plG search. Since a reworking of its douHling algorithm, Tesauro estimates that TD-gammon has a
slight advantage over the Hest human experts.
In the 199A AAAI Hall of Champions, 5aven defeated
grandmaster Adam Logan 9 contests to 5 at ScraHHle! , a
game in which contestants place one-letter tiles into a
crossword format. 5aven is the Hest ScraHHle! program,
and among the top plaGers of the game ?Sheppard 1999B.
ScraHHle! is suHLect to chance ?tiles are chosen at randomB
and includes imperfect information ?unplaGed tiles are
concealedB. 5aven uses a standard, game-specific move
generator ?Appel and XacoHson 19AAB and the @Y search
algorithm ?@erliner 1979BZ what distinguishes it from
other programs is its learned evaluation function. Indeed,
since their 1992 announcement, 5avenEs weights have
Hecome the standard for human and machine plaGers. The
current version also includes a proHaHilistic simulation of
tile selection with 3-plG lookahead.
Although these three programs search and emploG extensive knowledge, the changes that made them
champions were ultimatelG changes to their learned
evaluation functions. The creators of these programs gave
learning a headstart: the right raw material from which to
construct a powerful evaluation function. If the Hranch
factor is too large, however, even a good evaluation function maG He not He enough.
Research on Hridge and poker, card games of imperfect
information, is ongoing. One program found five errors in
the Official EncGclopedia of @ridge with a new heuristic
techni^ue ?_rank, @asin, and 5atsuHara 199AB. Loki now
plaGs poker `Hetter than the average cluH plaGera
?Schaeffer 1999B. At the same time, work on two perfect
information games indicates that neither Hrute force nor
offline learning will suffice.
Shogi is a chess-like game, with generals and lances instead of ^ueens. In addition, most shogi pieces can He
promoted to other pieces with more varied legal moves.
_urther complexitG is introduced HG the aHilitG to drop
?add to oneEs own forces anG piece previouslG captured
from the oppositionB anGwhere on the Hoard. Shogi has a
much larger Hranch factor than chess and, Hecause of
dropping, rarelG ends in a draw. Positions are rarelG quiet
?having a relativelG staHle heuristic evaluation in a small
suHtreeB. Shogi has its own annual computer tournament,
Hut no entrG has Get plaGed as well as a strong amateur.
Go presents an even greater challenge. Professional bo
plaGers develop slowlG, tGpicallG after 10 Gears of full
time studG. Amateur bo plaGers are ranked from 30 kGu
to 1 kGu, and then from 1 dan to 6 dan. Professional plaGers are ranked aHove that, from 1 to 9 dan. The Ing Cup,
estaHlished in 19A6, promises approximatelG c1.A million
for the first program to defeat TaiwanEs three Hest 1T-to16 Gear-old plaGers Hefore 2000. Such a program would
He ranked aHout 3 dan professional, a level hundreds of
people attain. The Hest bo-plaGing program, however,
now ranks onlG aHout T kGu. The bo-programming communitG generallG acknowledges that the Ing Cup will
expire without Heing won.
Heuristics are essential for games of incomplete information, which are NP-hard ?@lair, 5utchler, and Liu
1993B. TheG are also necessarG to plaG shogi and bo well,
Hut the re^uisite knowledge is inaccessiHle. @ecause their
endgames are likelG to have a larger Hranch factor and at
least as manG plaGing pieces, the generation of a useful
closing Hook is intractaHle. dnowledge for a heuristic
evaluation function is also proHlematic. In shogi, unlike
chess, there is not even human consensus on the relative
strength of the individual pieces ?@eal and Smith 199AB.
In bo, the rules distinguish no stone ?plaGing pieceB from
anG other of the same colorZ a stoneEs significance is determined HG the position. There are, moreover, thousands
of possiHle bo features whose interactions are not well
understood. To excel at their current targets, game plaGing
programs will need something more.
Cogniti8e Science and 9ame Pla;ing
Cognitive scientists seeking the source of human prowess
have studied expert game plaGers for more than a centurG.
!"e$ &'(e !"#$#%#&'( &)'*+,)-.&+ o0 .eo.1e+2 3e)4'1 ,om6
me*&')$ d8)-*g '*d '0&e) .1'$: ;og*-&-3e +,-e*&-+&+ '1+o
8+e "-g"1$ ',,8)'&e de3-,e+ &o &)',( e<.e)&+2 e$e mo3e6
me*&+: !oge&"e)= .)o&o,o1+ '*d e$e mo3eme*& d'&'
+8gge+& "ow e<.e)&+ .1'$:
Perception and cognition
?e8)o+,-e*&-+&+ "'3e -de*&-0-ed d-+&-*,& )eg-o*+ -* &"e "86
m'* 4)'-* 0o) 3-+8'1 .e),e.&-o* '*d 0o) "-g"61e3e1
)e'+o*-*g: @* .eo.1e= &"e)e -+ e3-de*,e &"'& .e),e.&8'1
+'1-e*,e ,8e+ 08*,&-o*'1 +-g*-0-,'*,e= &"e)e4$ d-)e,&-*g
"8m'* '&&e*&-o* A!3e)+($ BCDCE: !"-+ -+ ,o))o4o)'&ed 4$
&-med -m'ge+ o0 ' ,"e++ .1'$e)2+ 4)'-* d8)-*g de,-+-o*
m'(-*g A?-,"e11-= F)'0m'*= G-e&)-*-= H1w'$= ;')&o*= '*d
I-1e&-," BCCJE: Ge),e.&-o* '..e')+ &o 4eg-* 0-)+&= 0o16
1owed +omew"'& 1'&e) A'*d &"e* -* .')'11e1 w-&"E
)e'+o*-*g '*d &"e-) -*&eg)'&-o*: @*deed= .)o&o,o1+ o* g'me
.1'$e)+ )eg81')1$ "-g"1-g"& '!)$*)& %#,-*$*#-( ' .)o,e++
w"e)e4$ .eo.1e '&&e*d &o 3-+8'1 0e'&8)e+= de&e)m-*e &"e-)
+-g*-0-,'*,e= '*d &"e* 3'18e &"em ',,o)d-*g1$: !"-+ -+
w"$ .eo.1e .1'$ 4e&&e) w-&"o8& 41-*d0o1d+ K 3-+-o* *o&
o*1$ 0o,8+e+ &"e-) '&&e*&-o*= 48& -+ '1+o '* -*&eg)'1 .')& o0
de,-+-o* m'(-*g:
F-3e* &"e 1-*( 4e&wee* &"em= '&&e*&-o* &o .e),e.&8'11$
+'1-e*& 0e'&8)e+ ,o81d ,8e 1e')*-*g '4o8& 08*,&-o*
A!3e)+($ BCCLE: M"e* ' .e)+o* *eed+ &o 1e')* '* e3'18'6
&-o* 08*,&-o* 0o) .1'$-*g &"e g'me+ ,o*+-de)ed "e)e= +"e
)e,e-3e+ +&)o*g 3-+8'1 ,8e+ 0o) &"e -m.o)&'*& 0e'&8)e+N &"e
1o,'&-o* o0 .1'$-*g .-e,e+ '*d &"e +"'.e+ &"e$ 0o)m o* &"e
4o')d: Oow m-g"& &"e+e ,8e+ 4e -*&eg)'&ed w-&" "-g"6
1e3e1 )e'+o*-*gP
H .o+-&-o* ,'* 4e de+,)-4ed -* &e)m+ o0 !)$$."-'= )e1'6
&-o*+ 4e&wee* .1'$-*g .-e,e+: M"e* e')1$ )e+81&+ 0o8*d *o
me'+8)'41e d-00e)e*,e -* e<.e)&+2 '*d 'm'&e8)+2 +e'),"
Ade F)oo& BCQRE= ;"'+e '*d S-mo* .)o.o+ed &"'& ,"e++
e<.e)&-+e 1'$ -* &"e ',T8-+-&-o* '*d '..1-,'&-o* o0 8*o)6
de)ed +.'&-'1 .'&&e)*+ &"e$ ,'11ed %/0-1'2 U<.e)& g'me
.1'$e)+= &"e$ &"eo)-Ved= (*ew m'*$ -m.o)&'*& .'&&e)*+=
)e,og*-Ved &"em T8-,(1$= '*d '++o,-'&ed ' mo3e +e1e,&-o*
me,"'*-+m w-&" &"em: We&&e) .1'$e)+ wo81d +-m.1$ (*ow
mo)e ,"8*(+= '*d .)o.o+e mo3e+ '..)o.)-'&e &o &"em.
X-+,)e&e ,"8*(+ we)e *o& de&e,&ed -* Fo AYe-&m'*
BCZQE= "owe3e)= *o) w'+ .'&&e)* )e,og*-&-o* '1o*e '41e &o
',,o8*& 0o) d-00e)e*,e+ de&e,&ed mo)e )e,e*&1$ -* &"e w'$
4e&&e) ,"e++ .1'$e)+ +e')," AFo4e& BCCDE: Io)eo3e)= e<6
&e*+-3e +&8d-e+ -*d-,'&e &"'& e<.e)& Fo .1'$e)+ 8+e *o&
o*1$ +&'&-, .'&&e)*+ 48& '1+o d$*'m-, o*e+ A[o+"-('w'
'*d S'-&o BCCZE: M-&" o*1$ o*e (-*d o0 .-e,e 0o) e',"
,o*&e+&'*&= Fo '..e')+ &o )eT8-)e ' d-00e)e*& (-*d o0 1oo(6
-*g= o*e &"'& d$*'m-,'11$ -*3e+&+ +&o*e+ w-&" m81&-.1e
)o1e+= -*&e)1e'3-*g .e),e.&-o* w-&" ,og*-&-o* AW8)me-+&e)=
S'-&o= [o+"-('w'= '*d M-1e+ BCCZE: G)o0e++-o*'1 Fo
.1'$e)+ 0o,8+ed o* 1oo('"e'd '*d \good +"'.e=] '* '46
+&)',& -m'ge o0 ,e)&'-* .')&+ o0 &"e ,8))e*& .o+-&-o*= '*
-m'ge &"'& 1oo('"e'd m'*-.81'&e+ '*d )e0o)m81'&e+
A[o+"-('w' '*d S'-&o BCCZE: Fo e<.e)&+ -* &"o+e e<.e)-6
me*&+ 1oo(ed '& o*1$ ' +m'11 .')& o0 &"e 4o')d= 4e&wee*
+&o*e+= '+ -0 *'))ow-*g &"e-) o.&-o*+= '*d o* )e,'11 o0&e*
'&&)-48&ed ' .1'8+-41e me'*-*g &o ' mo3e: @* )e+.o*+e=
+e3e)'1 &"eo)-e+ &"'& '**o&'&e .'&&e)*+ "'3e 4ee* .)o6
.o+ed= -*,18d-*g 1')ge)= 0)'me61-(e +&)8,&8)e+ ,'11ed
$.3!&)$.' AFo4e& '*d S-mo* BCCQE '*d mo)e 01e<-41e=
mo)e e1'4o)'&e +&)8,&8)e+ ,'11ed /45"*6 !)$$."-'
A[o+"-('w' '*d S'-&o BCCZE: M"-,"e3e) &"eo)$ .)o3e+
,o))e,&= 3-+-o* -+ ,e)&'-* &o .1'$ '* -*&eg)'1 )o1e:
Less search and 2no3ledge
U<.e)& "8m'* g'me .1'$e)+ "'3e 0'+& ',,e++ &o 1')ge
+&o)e+ o0 ,')e0811$ o)g'*-Ved= g'me6+.e,-0-, (*ow1edge
w"-," &"e$ 8+e 4o&" &o 0o,8+ &"e-) '&&e*&-o* '*d &o g8-de
+e'),": ;om.')ed &o ,"'m.-o* .)og)'m+= "owe3e)= "86
m'* e<.e)&+ "'3e 0') +m'11e) o.e*-*g '*d ,1o+-*g 4oo(+:
!"e-) .'&&e)*6o)-e*&ed )e.)e+e*&'&-o* 0o) &"-+ d'&' '..e')+
&o 4e 'd'.&ed &o ' +.e,-0-, g'me AU-+e*+&'d& '*d ^')ee3
BCZRE '*d &'-1o)ed o*1$ &o .o+-&-o*+ &"'& ,'* ')-+e d8)-*g
.1'$ A;"'+e '*d S-mo* BCZ_E:
;om.')ed &o ,"'m.-o* .)og)'m+= "8m'* e<.e)&+ '1+o
,o*+-de) 0ewe) '1&e)*'&-3e+ '*d +e')," 1e++ dee.1$: ;"e++
e<.e)&+ ,o*+-de) o*1$ ' 0ew mo3e+= '*d )')e1$ +e'),"
mo)e &"'* D o) C .1$ AFo4e& BCCDE: Fo e<.e)&+ .e)0o)m
)e1'&-3e1$ +m'11 +e'),"e+= w-&" '3e)'ge de.&" J '*d
m'<-m8m 4)'*," 0',&o) _ A[o+"-('w' '*d S'-&o BCCZE:
O8m'* e<.e)&+ 0o,8+ &"e-) '&&e*&-o* o* %)-6*6)$. 3#7.'
A&"o+e wo)&"$ o0 +e')," &o e3'18'&e &"em 08)&"e)E mo)e
T8-,(1$ &"'* *o3-,e+: U$e mo3eme*& +&8d-e+ ,o*0-)m &"-+
-* 4o&" ,"e++ '*d FoN e<.e)&+ 1oo( '& 3e)$ 0ew .o-*&+
w"e* &"e$ +o13e ' &e+& .)o41em Ade F)oo& BCQR` Fo4e&
BCCD` [o+"-('w' '*d S'-&o BCCZE: !"e Fo .1'$e)+2 +.eed
-+ .')&-,81')1$ )em')('41eN -* L:aKL:_ +e,o*d+ &"e e<6
.e)&2+ e$e 0-<'&e+ o* &"e ,o))e,& mo3e: H,,om.'*$-*g
.)o&o,o1+ +8gge+& &"'& &"e +e1e,&-o* o0 ,'*d-d'&e mo3e+
-*3o13e+ 4o&" -*0e)e*,e '*d .'&&e)* )e,og*-&-o*:
Alternative cognitive mechanisms
!"e)e -+ -*,)e'+-*g e3-de*,e= 0)om ' 3')-e&$ o0 dom'-*+=
&"'& .eo.1e ')$*'8*%.= &"'& -+= m'(e ' de,-+-o* &"'& -+ good
e*o8g": S'&-+0-,-*g o0&e* -*&eg)'&e+ ' 3')-e&$ o0 +&)'&eg-e+
&o ',,om.1-+" .)o41em +o13-*g AW-+w'+= Fo1dm'*= b-+"e)=
W"83'= '*d F1ewwe BCCR` ;)ow1e$ '*d S-eg1e) BCC_`
Y'&&e)m'* '*d U.+&e-* BCCRE: S'&-+0-,-*g m'$ '1+o -*6
,18de &"e '4-1-&$ &o )e'+o* 0)om -*,om.1e&e o) -*,o*+-+&e*&
-*0o)m'&-o*:
Geo.1e de3e1o. e<.e)&-+e o3e) &-me= &")o8g" +&8d$ '*d
,om.e&-&-o*` &"e$ do *o& 4eg-* ' *ew g'me '+ e<.e)&+
AU)-,++o*= ^)'m.e= '*d !e+,"6Ycme) BCC_` Oo1d-*g
BCDRE: X8)-*g de3e1o.me*&= .eo.1e 1e')*= .')&-,81')1$
0)om &"e-) m-+&'(e+= w"e)e'+ ' de&e)m-*-+&-, .)og)'m
m'(e+ &"e +'me e))o) )e.e'&ed1$: H1&"o8g" !X6g'mmo*=
dog-+&e11o= '*d I'3e* "'3e 1e')*ed e3'18'&-o* 08*,&-o*+=
&"e$ do *o& 1e')* 0)om &"e-) m-+&'(e+ d8)-*g ,om.e&-&-o*=
t"e wa' (eo(*e wo+*d. .or do (eo(*e re0+ire mi**ions of
contests to ac"ie7e ex(ert stat+s. T"e initia* *earning
c+r7e in ;o, for exam(*e, can =e 7er' ra(id > a ? @'+
ran@ can =e reac"ed in se7era* mont"s ASaito and Cos"iD
@awa EFFGH. In addition, as (eo(*e "a7e more ex(erience
wit" a tas@, t"eir s(eed at it genera**' im(ro7es. In conD
trast, (rograms w"ose e7a*+ation f+nction f+nctions re*'
+(on more @now*edge t'(ica**' re0+ire more time at eac"
searc" node, res+*ting in s"a**ower searc" t"at can deD
grade (erformance AAnant"araman, Cam(=e**, and Ls+
EFF0N O+ro EFFPH.
Protoco*s a*so (ro7ide extensi7e e7idence of "ig"D*e7e*
*ang+age conce(ts +sed to form+*ate s+=goa*s, and of
(*anning to reac" t"ose s+=goa*s. ;ame (*a'ing ex(erts
s+mmariRe some of t"eir @now*edge t"is wa'. T"e' +se
!"#!$#% As"ortDterm (*ansH and %!&"!'($'% A*ongDterm (*ansH
to ma@e decisions and to ex(*ain t"eir =e"a7ior to eac"
ot"er. T"is is (artic+*ar*' accessi=*e from (rotoco*s on
masters (*a'ing So+dan ;o, w"ere eac" side is (*a'ed in
a se(arate room =' a free*' comm+nicating team of two
(*a'ers ACos"i@awa, SoTima, and Saito EFFPH. T"e (rotoD
co*s demonstrate t"at U=ot" sides c*ear*' +nderstand t"eir
o((onentVs intention and t"eir +nderstandings agree comD
(*ete*'W ASaito and Cos"i@awa EFFGH. S+c" e7idence
moti7ated t"e annotation of tem(*ates and "'=rid (atterns
wit" 7aria=i*iRed (*ans and strategies.
!"#$nin' )o +#)is-ic"
)*+,' is a (rogram w"ose cogniti7e orientation ena=*es it
to (*a' a =road 7ariet' of games s+r(rising*' we**. Xi@e
(eo(*e, =+t +n*i@e t"e (rograms descri=ed t"+s far, Lo'*e
can (*a' an' twoD(erson, (erfect information, finiteD=oard
game, gi7en t"e r+*es AY(stein, ;e*fand, and Xoc@ EFFPH.
To date it "as *earned on*ine, d+ring com(etition, to (*a'
EP games ex(ert*' in rea* time. T"e games, on twoD and
t"reeDdimensiona* =oards of 7ario+s s"a(es, are drawn
from ant"ro(o*og' texts, and are intended to ca(t+re
(ro=*ems t"at intrig+e (eo(*e. A*t"o+g" t"eir game trees
are re*ati7e*' sma** At"e *argest "as on*' se7era* =i**ion
statesH, t"e s(eed wit" w"ic" Lo'*e masters t"em, and its
trans(arenc', ma@e t"e a((roac" of interest "ere.
Lo'*e =egins an' new game as a no7ice, =+t it @nows
w"at to *earn. As it (*a's, it grad+a**' ac0+ires .%'/.,
01*2,'3(', (ro=a=*' correct and (ossi=*' a((*ica=*e inD
formation from t"e contests it "as ex(erienced. Yac" @ind
of +sef+* @now*edge is (res(ecified, wit" its own re(reD
sentation and a (roced+re to *earn it. An o(ening, for
exam(*e, mig"t =e *earned as a tree =' rote.
Lo'*e a*so =egins wit" a set of mo7eDse*ection rationD
a*es ca**ed 435$%*&%6 ;i7en t"e ac0+ired +sef+* @now*edge
for a game and a (osition from it, an Ad7isor can recomD
mend or ca+tion against an' n+m=er of mo7es ='
generating #*77'1!%. Ad7isors are s+=Tect to reso+rce
*imits, =+t not to an' +niform decision (rocess or re(reD
sentation.
Ad7isors are categoriRed into t"ree tiers. T"ose in tier E
re*' on s"a**ow searc" and *earned gameDt"eoretic 7a*+es
to (ro7ide (erfect g+idance on a sing*e mo7e, mandating
its se*ection or a7oidance. TierDE Ad7isors ma@e eas'
decisions 0+ic@*', and (re7ent o=7io+s =*+nders. Zictor',
for exam(*e, ma@es an immediate*' winning mo7e. A**
ot"er Ad7isors are "e+ristic, eit"er =eca+se t"e' de(end
+(on ind+ced +sef+* @now*edge or =eca+se t"eir reasonD
ing met"od is a((roximate*' correct. [ateria*, for
exam(*e, enco+rages (iece ca(t+re in tier \. TierD2 Ad7iD
sors ad7ocate a se0+ence of mo7es Aa 8,"1H, w"i*e tierD\
Ad7isors ad7ocate a sing*e mo7e.
Comments are com=ined to se*ect a mo7e, as s"own in
^ig+re E. Ad7isors are cons+*ted seria**' in tiers E and 2,
w"ere t"e first Ad7isor a=*e to determine t"e next mo7e
does so. In tier \ Ad7isors are cons+*ted in (ara**e*, and a
weig"ted com=ination of t"eir comment strengt"s se*ects
t"e =est mo7e. _eig"ts are =ot" gameDde(endent and
stageDde(endent, and are *earned.
`n a few sim(*e games, Lo'*e "as =een cogniti7e*'
7a*idated, t"at is, its *earning and decision ma@ing "a7e
=een s"own simi*ar to t"at of (eo(*e Aaatterman and Y(D
stein EFF?H. Indeed, t"e (rogram intentiona**' "as man'
of t"e "a**mar@s of "+man ex(ert (*a'b
c Lo'*e satisfices. _"i*e it decides in rea* time, it to*erD
ates incom(*ete and incorrect information, entertains a
7ariet' of conf*icting rationa*es sim+*taneo+s*', and deD
grades gracef+**' in +nfami*iar sit+ations.
ac?uired use.ul k-o2led5e
positio-
le5al
moves
Aictor9
Tier 1' (eactio- .rom
per.ect k-o2led5e
<o-!t
Bose
<ecisio- =
9es
e@ecute
decisio-
-o
CkD1
Tier 2' 7la--i-5
tri55ered b9 situatioreco5-itio-
Cm
<ecisio- =
9es
-o
Tier 3' Heuristic
reactio-s
Material
C9ber
Greedom
Aoti-5
9$(.&' :; A sc"ematic for Lo'*eds mo7e se*ection.
! #$%&' &'()*+ ,-./0&%1 23 -+-(&&% (/4.'5'+ .3+ '67')3.+' .*
&'++ 34(* 899 /$*3'+3+1
! #$%&' .+ 3)(*+7()'*31 23 /(* '67&(.* .3+ :$5'+ 34)$-;4 (
*(3-)(& &(*;-(;' .*3')7)'3(3.$* $< .3+ =>5.+$)+? /$::'*3+1
! #$%&' .*3';)(3'+ 5.+-(& 7')/'73.$* @.34 4.;4A&'5'& )'(A
+$*.*;1 23+ (&&$@(*/' <$) :-&3.7&' )'7)'+'*3(3.$*+B .*
-+'<-& 0*$@&'>;' (*> .* =>5.+$)+B +-77$)3+ 34.+1 C4' /-)A
)'*3 7$+.3.$*B <$) '6(:7&'B /(* D' +.:-&3(*'$-+&%
)'7)'+'*3'> (+ ( &.+3B (* ())(%B ( D.7()3.3' ;)(74B ( +'3 $<
<.6'>A+4(7' 7(33')*+B (*> ( +'3 $< 7.'/'A>'&.*'(3'> 3')).3$A
).'+1
! #$%&' &.*0+ 7')/'73.$* @.34 <-*/3.$*1 23 &'()*+ 5.+-(&&%A
D(+'>B 4.;4A&'5'&B ;(:'A>'7'*>'*3 /$*/'73+ (+ ;(:'A
+7'/.<./ =>5.+$)+ <$) 3.') E1 F$) '6(:7&'B .3 /(* &'()* 34(3
34' /$*+$&.>(3.$* $< 3')).3$)% .+ (>5.+(D&' .* ( ;(:'B >'A
3'):.*' 4$@ 34(3 3')).3$)% +4$-&> D' >':()/(3'>B (*>
/)'(3' (*> -+' (* =>5.+$) 3$ '*/$-)(;' 34(3 D'4(5.$)1
! #$%&' 7&(*+1 23 (/,-.)'+ D$34 +7'/.<./ (*> 3(/3./(& :$5'
+',-'*/'+ (+ 3.')AG =>5.+$)+1
! #$%&' -+'+ 4.;4A&'5'& /$*/'73+1 H$:'B +-/4 (+ D&$/0.*;
( @.**.*; :$5'B ()' ;(:'A.*>'7'*>'*3B (*> 7)'+7'/.<.'>
.* 3.') 81 I34')B ;(:'A>'7'*>'*3 $*'+ ()' &'()*'> <)$:
7')/'73-(& /-'+B (+ >'+/).D'> (D$5'1
!ew %&me (l&*+ng ./&llenges
J'+-&3+ @.34 #$%&' +-;;'+3 @(%+ .* @4./4 ( 7)$;)(:
:.;43 D' :$)' &.0' ( 4-:(* /4(:7.$*1 #$%&'?+ 7'*/4(*3
<$) -+'<-& 0*$@&'>;' (*> :-&3.7&' 4'-).+3./ $7.*.$*+ .+
&.0'&% 3$ 7)$5' 4'&7<-& .* (>>)'++.*; 34' <$&&$@.*; /4(&A
&'*;' 7)$D&':+1 K(/4 .*/)'(+'+ @.34 >.<<./-&3%B $< /$-)+'B
(//$)>.*; 3$ 34' 3();'3 ;(:'1
(ro3lem 4: 6odel & contest&nt
H3)(3';./ (*> 3(/3./(& >'/.+.$*+ ()' $<3'* (<<'/3'> D% 34'
*(3-)' $< $*'?+ 7)$D&': +$&5.*; '*5.)$*:'*31 =* .:7$)A
3(*3 <(/3$) .* ;(:' 7&(%.*; >'/.+.$*+B <$) '6(:7&'B +4$-&>
D' 34' *(3-)' $< $*'?+ $77$*'*31 C4' <.)+3 /4(&&'*;' 7)$DA
&': .+ 3$ /$*+3)-/3 ( :$>'& $< ( 7()3./-&() /$*3'+3(*3 .* (
3@$A7')+$* ;(:'1 L.5'* ( +-.3' $< /$*3'+3+ 7&(%'> D% (
+.*;&' 7')+$* $) 7)$;)(: (;(.*+3 5().$-+ /$:7'3.3$)+B 34'
7)$;)(: +4$-&> 7)$>-/' *(3-)(& &(*;-(;' 34(3 /4()(/3')A
.M'+ 34' $77$*'*3?+ /-))'*3 7&(% .* ( /$*3'+3 N'1;1B OP&(/0
.+*Q3 .*3')'+3'> .* /(+4.*; .* 4.+ .*.3.(3.5' @.34 8R111P6>ST
G9 /6>S U6>S @4'* V4.3' 4(+ '6/'&&'*3 7&(% <$) 34'
7(@*WX1 23 +4$-&> (&+$ .>'*3.<% ;'*')(& +3)'*;34+B @'(0A
*'++'+B (*> 7)'>.&'/3.$*+B +-/4 (+ O2* 34' $7'*.*;B
Y(+7()$5 7&(%+ D&(/0 &.0' @4.3'BW OY()7$5 +3).5'+ 3$ .:A
7)$5' 4.+ 7$+.3.$* &.33&' D% &.33&'B :(*'-5').*; +-D3&%B
:(0.*; 4.+ 34)'(3+BW O#' .+ always (33(/0.*;B $<3'* <)$:
>.)'/3.$*+ 4.+ $77$*'*3+ 4(>*?3 /$*+.>')'>B 7&(%.*;
:$5'+ 34(3 4(5' +-D3&' :-&3.7&' 34)'(3+BW (*> OZ$- /(*
3'&& <)$: [4.+ $77$*'*3+?\ :$5'+ 34'% ()' +/()'>1 C4'.)
(33(/0+ ()' @.&> (*> 4$7'&'++ $) '&+' 5')% 3.:.>1W
NV(.3M0.* 8RR9X1
H$:' ;)$-*>D)'(0.*; @$)0 $* 34.+ 4(+ D''* >$*' .*
7$0') NP.&&.*;+B ](77B H/4('<<')B (*> HM(<)$* 8RR^X (*>
L$ N2+$M(0. (*> Y(3+-*$ 8RR_X1 C4' ;'*')(3.$* (*>
(*(&%+.+ $< +-::()% +3(3.+3./+ @$-&> D' ( )'(+$*(D&' @(%
3$ /$*3.*-'1 ]&(* >'3'/3.$* .+ )',-.)'>B (+ @'&& (+ +$:'
)'7)'+'*3(3.$* <$) 5$&.3.$*B (;;)'++.$*B (*> ).+01 Y*$@&A
'>;' (D$-3 ':$3.$*+ (*> 34' (D.&.3% 3$ ;'*')(3' :'3(74$)+
+4$-&> 7)$5' 4'&7<-&1
(ro3lem :: Annot&te & contest
]'$7&' (**$3(3' ( /4'++ /$*3'+3 D$34 :$5' D% :$5' N'1;1B
OF() <)$: &$+.*; ( 3':7$B P&(/0 4(+ )'(&&% ;(.*'> 3.:'
+.*/' 34' 0*.;43 +3$$> D'33') $* >S 34(* DEWX (*> @.34
3(/3./+ (*> +3)(3';% N'1;1B O3)% 3$ 7&(% >GA>SB D).*; 34'
0*.;43 $* D8 3$ 'GB (*> <$&&$@ -7 @.34 `<EA'aB 7&(%.*; $*
34' >()0 +,-()'+1WX =**$3(3.$*+ /$*3(.* /$::'*3()% (*>
$<3'* >.(;)(:+1 H.*/' 8RREB 34' 2*3')*(3.$*(& b$:7-3')
b4'++ =++$/.(3.$* 4(+ (@()>'> (* (**-(& 7).M' 3$ 34'
7)$;)(: 34(3 D'+3 (**$3(3'+ (* .*7-3 /4'++ /$*3'+3 .* )'(&
3.:'B D-3 '*3).'+ ()' <'@ (*> ,-.3' :(/4.*'A&.0'
NPc$)*++$* (*> d()+&(*> 8RR^X1 ])$;)(:+ ()' '*/$-)(;'>
3$ 7)$7$+' 5().(3.$*+B .*/&->' @).33'* /$::'*3+B (*> 7)$A
5.>' '67&(*(3$)% >.(;)(:+1
C4' +'/$*> /4(&&'*;' 7)$D&': .+ 3$ (**$3(3' ( /$*3'+3
+$ @'&& 34(3 7'$7&' /(**$3 >.+3.*;-.+4 .3 <)$: ( 4-:(*A
;'*')(3'>B 7$7-&()&% 7-D&.+4'> (**$3(3.$*B +(% <)$: The
New +ork Times. = +$&-3.$* :-+3 ;'*')(3' D$34 *(3-)(&
&(*;-(;' (*> (77)$7).(3' >.(;)(:+1 23 @.&& (&+$ )',-.)'
4.;4A&'5'& /$*/'73+ (77)$7).(3' 3$ 34' ;(:'B /$*3'63A
+'*+.3.5' 7')+7'/3.5'+B (*> 34' .*>-/3.$* $< ( :$>'& <$)
'(/4 /$*3'+3(*3 (+ (* (;'*3 @.34 .*3'*3.$*+ (*> 34' (D.&.3%
3$ >'/'.5'1
(ro3lem <: =e&c/ & g&me
I*' :'(+-)' $< 4-:(* '67')3.+' .+ 34' (D.&.3% 3$ /$*5'%
0*$@&'>;'1 C4' 34.)> /4(&&'*;' 7)$D&': .+ 3$ 4(5' (*
'67')3 ;(:' 7&(%.*; 7)$;)(: N34' instructorX 3'(/4 .3+
+0.&& 3$ ( 7')+$* $) (*$34') 7)$;)(: N34' studentX1 C$ >$
34.+ @'&&B 34' .*+3)-/3$) :-+3 <.)+3 (*(&%M' (*> )'7)'+'*3 .3+
$@* 0*$@&'>;'1 `'63B 34' .*+3)-/3$) @$-&> :$>'& 34'
+3->'*3?+ 0*$@&'>;'B >.(;*$+' .3+ @'(0*'++'+B (*> <$):-A
&(3' ( /-))./-&-:1 2*+3)-/3.$* /$-&> D' 7)'+'*3'> (+
7$+.3.$*+B &.*'+ $< 7&(%B $) '*3.)' /$*3'+3+B (&& /$-/4'> .*
(77)$7).(3' *(3-)(& &(*;-(;'1 =* (*(&%+.+ $< 34' +3->'*3?+
&'()*.*; +3%&' .+ &.0'&% 3$ 7)$5' 4'&7<-&1 I*/' 34' +3->'*3
/$*+.+3'*3&% 7&(%+ (+ @'&& (+ 34' 3'(/4')B 34' 7)$D&': @.&&
D' +$&5'>1
.oncl>s+on
b4(:7.$* 7)$;)(:+ 34-+ <() &(/0 /$;*.3.5' <'(3-)'+ $<3'*
/.3'> (+ 4(&&:()0+ $< 4-:(* .*3'&&.;'*/'e $*&.*' &'()*.*;B
7&(**.*;B (*> 34' (D.&.3% 3$ /$::-*./(3' 0*$@&'>;'1
C4')' .+ ( ;)$@.*; .*3')'+3B 4$@'5')B .* )'(/3.5'B 4.')()A
/4./(& +(3.+<./')+ &.0' #$%&'B (*> .* 34' 0.*> $< (;'*3
interaction and modeling targeted by the challenge problems posed here (Dobson and Forbus 1999). We can look
forward, therefore, to programs that narrow their options,
learn from their mistakes, model other agents, explain
their rationales, and teach us to play better.
Ackno&ledgments
This work was supported in part by NSF grant
E9423085. Thanks to Michael Buro, Murray Campbell,
Takuya Kojima, Jonathan Schaeffer, Brian Sheppard,
Gerry Tesauro, and Atsushi Yoshikawa for generously
sharing their substantial expertise. Discussions with Hans
Berliner, Ian Frank, Jack Gelfand, Esther Lock, and Donald Michie have inspired and informed much of this work.
References
Anantharaman, T., Campbell, M. S. and Hsu, F.-h. 1990.
Singular Extensions: Adding Selectivity to Brute-Force
Searching. !"#$%$&$'( *+#,(($-,+&,, 43(1): 99-110.
Appel, A. W. and Jacobson, G. J. 1988. The World[s Fastest Scrabble Program. ./001+$&'#$/+2 /% #3, !.4,
31(5): 572-578.
Baum, E. B. and Smith, W. D. 1997. A Bayesian Approach to Relevance in Game Playing. !"#$%$&$'(
*+#,(($-,+&,, 97: 195-242.
Beal, D. and Smith, M. 1998. First results from Using
Temporal Difference learning in Shogi. In 5"/&,,6$+-2
/% #3, 7$"2# *+#,"+'#$/+'( ./+%,",+&, /+ ./081#,"2 '+6
9'0,2. Tsukuba, Japan.
Beal, D. F. 1990. A Generalised `uiescence Search Algorithm. !"#$%$&$'( *+#,(($-,+&,, 43(1): 85-98.
Bell, R. C. 1969. :/'"6 '+6 ;'<(, 9'0,2 %"/0 4'+=
.$>$($?'#$/+2. London: Oxford University Press.
Berliner, H. J. 1979. The BcTree Search Algorithm: A
Best-First Proof Procedure. !"#$%$&$'( *+#,(($-,+&,, 12(1):
23-40.
Berliner, H. J. 1987. Some Innovations Introduced by
HITECH. *.!! @/1"+'(, 18(2): 71-76.
Billings, D., Papp, D., Schaeffer, J. and Szafron, D. 1998.
Opponent Modeling in Poker. In 5"/&,,6$+-2 /% #3, 7$%A
#,,+#3 B'#$/+'( ./+%,",+&, /+ !"#$%$&$'( *+#,(($-,+&,C
493-499. Madison: AAAI Press.
Biswas, G., Goldman, S., Fisher, D., Bhuva, B. and
Glewwe, G. 1995. Assessing Design Activity in Complex CMOS Circuit Design. In P. Nichols, S. Chipman,
e R. Brennan (Ed.), ./-+$#$>,(= D$'-+/2#$& !22,220,+#C
Hillsdale, NJ: Lawrence Erlbaum.
Bjornsson, Y. and Marsland, T. 1998. Fritz 5.0 Wins the
1997 Herschberg Best-Annotation Award. *..! @/1"A
+'(, 20(1): 65-66.
Blair, J., Mutchler, D. and Liu, C. 1993. Games with Imperfect Information. In 5"/&,,6$+-2 /% #3, 7'((
E=08/2$10 /+ 9'0,2F 5('++$+- '+6 G,'"+$+-C 59-67.
Burmeister, J., Saito, Y., Yoshikawa, A. and Wiles, J.
1997. Memory Performance of Master Go Players. In
5"/&,,6$+-2 /% #3, *@.!* H/"I23/8 /+ J2$+- 9'0,2 '2
'+ KL8,"$0,+#'( ;,2#<,6 %/" !* M,2,'"&3.
Buro, M. 1998. From Simple Features to Sophisticated
Evaluation Functions. In 5"/&,,6$+-2 /% #3, N2# *+#,"+'A
#$/+'( ./+%,",+&, /+ ./081#,"2 '+6 9'0,2. Tsukuba.
Chase, W. G. and Simon, H. A. 1973. The Mind[s Eye in
Chess. In W. G. Chase (Ed.), O$21'( *+%/"0'#$/+ 5"/&A
,22$+-C 215-281. New York: Academic Press.
Crowley, K. and Siegler, R. S. 1993. Flexible Strategy
Use in Young Children[s Tic-Tac-Toe. ./-+$#$>, E&$A
,+&,, 17(4): 531-561.
de Groot, A. 1965. ;3/1-3# '+6 .3/$&, $+ .3,22. The
Hague: Mouton.
Dobson, D. and Forbus, K. (1999). 5"/&,,6$+-2 /% #3,
!!!* NPPP E8"$+- E=08/2$10 /+ !"#$%$&$'( *+#,(($-,+&,
'+6 ./081#," 9'0,2.
Eisenstadt, M. and Kareev, Y. 1975. Aspects of Human
Problem Solving: The Use of Internal Representations.
In D. A. Norman, e D. E. Rumelhart (Ed.), KL8(/"'#$/+2
$+ ./-+$#$/+C 308-346. San Francisco: Freeman.
Epstein, S. L., Gelfand, J. and Lock, E. T. 1998. Learning
Game-Specific Spatially-Oriented Heuristics. ./+A
2#"'$+#2, 3(2-3): 239-253.
Ericsson, K. A., Krampe, R. T. and Tesch-Rfmer, C.
1993. The Role of Deliberate Practice in the Acquisition
of Expert Performance. 52=&3/(/-$&'( M,>$,Q, 100(3):
363-406.
Frank, I., Basin, D. and Matsubara, H. 1998. Finding Optimal Strategies for Incomplete Information Games. In
5"/&,,6$+-2 /% #3, 7$%#,,+#3 B'#$/+'( ./+%,",+&, /+ !"A
#$%$&$'( *+#,(($-,+&,C 500-507. Madison: AAAI Press.
Gobet, F. 1998. Chess Players[ Thinking Revisited. EQ$22
@/1"+'( /% 52=&3/(/-=, 57(1): 18-32.
Gobet, F. and Simon, H. 1996. Templates in Chess memory: A Mechanism for Recalling Several Boards.
./-+$#$>, 52=&3/(/-=, 31: 1-40.
Hamilton, C. M. and Hedberg, S. 1997. Modern Masters
of an Ancient Game. !* 4'-'?$+,, 18(4): 11-12.
Holding, D. 1985. ;3, 52=&3/(/-= /% .3,22 EI$((.
Hillsdale, NJ: Lawrence Erlbaum.
Isozaki, H. and Katsuno, J. 1996. A Semantic Characterization of an Algorithm for Estimating Others[ Beliefs
from Observation. In 5"/&,,6$+-2 /% #3, ;3$"#,,+#3 B'A
#$/+'( ./+%,",+&, /+ !"#$%$&$'( *+#,(($-,+&,C 543-549.
MIT Press.
McAllester, D. A. 1988. Conspiracy Numbers for MinMax Search. !"#$%$&$'( *+#,(($-,+&,, 35(3): 287-310.
Nichelli, P., Grafman, J., Pietrini, P., Alway, D., Carton,
J. and Miletich, R. 1994. Brain Activity in Chess Playing. B'#1",, 369: 191.
Palay, A. J. 1985. E,'"&3$+- Q$#3 5"/<'<$($#$,2. Pitman.
Ratterman, M. J. and Epstein, S. L. 1995. Skilled like a
Person: A Comparison of Human and Computer Game
Playing. In 5"/&,,6$+-2 /% #3, E,>,+#,,+#3 !++1'( ./+A
%,",+&, /% #3, ./-+$#$>, E&$,+&, E/&$,#=C 709-714.
Pittsburgh: Lawrence Erlbaum Associates.
Reitman, J. S. 1976. Skilled Perception in Go: Deducing
Memory Structures from Inter-Response Times. ./-+$A
#$>, 52=&3/(/-=, 8: 36-356.
Ri#est' R. L. 19-.. /ame Tree Searching 9: ;in<;a=
Appro=imation. !"#$%$&$'( *+#,(($-,+&,' A4C1DE ..-96.
Saito' H. and HoshikaKa' A. 199.. /o as a Test9ed for
Cogniti#e Science StNdies. In ."/&,,0$+-1 /% #2, *34!*5
67 8/"912/: /+ ;1$+- <'=,1 '1 '+ >?:,"$=,+#'( @,1#5
A,0 %/" !* B,1,'"&2.
Schaeffer' P. 199.. C+, 3D=: !2,'0E 42'((,+-$+- FD='+
GD:",='&H $+ 42,&9,"1. QeK HorkE Springer-Rerlag.
Schaeffer' P. C1999D. Personal commNnication.
Shannon' C. E. 1950. Programming a CompNter for Pla:ing Chess. 41C256DE 2.5.
Sheppard' Y. C1999D. Personal commNnication.
Slate' Z. P. and Atkin' L. R. 19... C[ESS 4.5 - The
QorthKestern \ni#ersit: Chess Program. In P. Fre:
CEd.D' 42,11 G9$(( $+ I'+ '+0 I'&2$+,J YerlinE Springer.
TesaNro' /. 1995. Temporal Zifference Learning and TZ/ammon. 4!4I' A-CADE 5--6-.
T#ersk:' Y. 19-9. Parts' Partonomies' and Ta=onomies.
K,L,(/:=,+#'( .1H&2/(/-H' 25C6DE 9-A-995.
T#ersk:' Y. 1990. Where Partonomies and Ta=onomies
;eet. In S. L. Tsohat_idis CEd.D' I,'+$+-1 '+0 ."/#/5
#H:,1 5 G#D0$,1 $+ M$+-D$1#$& 4'#,-/"$N'#$/+J AA4-A44.
LondonE RoNtledge.
Wait_kin' F. C1990D. O'1:'"/L. The QeK Hork Times
;aga_ineE 2--A0' 60-64' -6--..
HoshikaKa' A.' `oaima' T. and Saito' H. 199-. Relation
9etKeen the Wa: of \sing Terms and the Skill - from
Anal:sis of Protocols of the /ame of /o. In ."/&,,0$+-1
/% #2, P$"1# *+#,"+'#$/+'( 4/+%,",+&, /+ 4/=:D#,"1 '+0
<'=,1J 211-22.. TsNkN9a.
HoshikaKa' A. and Saito' H. 199.. [:9rid Pattern
`noKledgeE /o Pla:ersb `noKledge Representation for
Sol#ing TsNme-/o Pro9lems. In ."/&,,0$+-1 /% #2,
G/D#2 O/",'+ *+#,"+'#$/+'( 4/+%,",+&, /+ 4/-+$#$L,
G&$,+&,.
casla#sk:' C. 19-2. @$& @'& @/, '+0 C#2," @2",,5$+5'5
B/Q <'=,1J %"/= !+&$,+# >-H:# #/ #2, I/0,"+ 4/=5
:D#,". QeK HorkE CroKell.
FOR SLIDES
For slides: 2The real art in chess is to evaluate the factors because they are so different. What is more
important, one pawn or the open lineE WhatFs more important, the weak position of your king or some initiative
on the queensideEJ 2At the highest level, chess is a talent
to control unrelated things.J 2Some positions are so complex that you cannot calculate even two moves ahead.J
Karpov continued: He avoids weaknesses and waits for
his opponent to make mistakes. He works to neutralize
threats and gain control of certain squares and files, so
that with his superior technique he will be able to win in
the end game.