T ENRI N
NG-R, 1E 9C9O7 ,G3N( 4IT),IO
T H IN K I N G A N D R P
EA
AT
SO
2 9N1 –A3 N
1 3D S E A R C H
291
A P a tte rn -re co g n itio n T h e o ry o f S ea rch in E x p e r t
P ro b le m S o lv in g
F e rn a n d G o b e t
U n iv e rs ity o f N o ttin g h a m , U K
U n d e r s t a n d i n g h o w lo o k - a h e a d s e a rc h a n d p a tt e r n re c o g n it i o n i n t e r a c t i s o n e o f
t h e i m p o rt a n t r e s e a r c h q u e s t i o n s i n th e s t u d y o f e x p e r t p r o b l e m s o lv i n g . T h i s p a p e r
e x a m i n e s t h e im p l ic a t i o n s o f t h e t e m p la t e t h e o r y ( G o b e t & S im o n , 1 9 9 6 a ) , a r e c e n t
t h e o r y o f e x p e r t m e m o r y , o n t h e t h e o r y o f p ro b l e m so l v i n g i n c h e s s . T e m p l a te s a r e
“ c h u n k s ” ( C h a s e & S i m o n , 1 9 7 3 ) t h a t h a v e e v o l v e d in t o m o r e c o m p l e x d a t a
s t ru c t u r e s a n d t h a t p o ss e s s s l o t s a l l o w i n g v a l u e s t o b e e n c o d e d r a p id l y . T e m p la t e s
m a y f a c i li t a t e s e a r c h i n t h r e e w a y s : (a ) b y a ll o w in g i n f o r m a t i o n to b e s t o re d i n t o
L T M r a p i d l y ; ( b ) b y a l lo w i n g a s e a r c h i n t h e t e m p l a t e s p a c e i n a d d i t io n t o a s e a r c h
in th e m o v e sp a c e ; a n d (c ) b y c o m p e n sa tin g lo ss in th e “ m in d ’s e y e ” d u e to
i n t e r f e r e n c e a n d d e c a y . A c o m p u te r m o d e l i m p l e m e n t i n g th e m a in i d e a s o f t h e
t h e o r y is p re s e n t e d , a n d s i m u l a t io n s o f i t s s e a rc h b e h a v io u r a r e d i s c u s s e d . T h e
t e m p l a t e t h e o ry a c c o u n t s f o r th e s li g h t s k i l l d if f e r e n c e i n a v e r a g e d e p t h o f s e a r c h
f o u n d in c h e s s p l a y e r s , a s w e l l a s f o r o t h e r e m p ir i c a l d a t a .
IN T R O D U C T IO N
H o w m u c h o f e x p e r t p ro b le m -so lv in g b e h a v io u r is e x p la in e d b y re a l-tim e se a rc h
th ro u g h th e ta sk p ro b le m s p a c e , a n d h o w m u c h is e x p la in e d b y p a tte rn
re c o g n itio n ? E v e r sin c e th e s e m in a l w o rk o f D e G ro o t (1 9 4 6 /1 9 7 8 ), th is q u e stio n
h a s b e e n a re c u rrin g th e m e in th e stu d y o f e x p e rtise (s e e C h a rn e ss , 1 9 9 1 ;
H o ld in g , 1 9 8 5 ) .
T h e s tu d y o f c h e ss p la y e rs, o rig in a te d in its m o d e r n fo rm b y D e G ro o t (1 9 4 6 ),
h a s b e e n a p ro d u c tiv e su b fie ld o f th e p s y c h o lo g y o f e x p e rtise . C h e s s is a ta s k
w h e re p e rc e p tio n , m e m o ry , k n o w le d g e o rg a n is a tio n , a n d se a rc h in te ra c t in a
c o m p le x , d y n a m ic w a y . T h e a d v a n ta g e s it o ffe rs in c lu d e : a q u a n tita tiv e sc a le f o r
m e a s u rin g sk ill, a la rg e d a ta b a se o f g a m e s , a n d e c o lo g ic a l v a lid ity (N e is se r,
1 9 7 6 ) o f th e d o m a in . I n a d d itio n , n u m e r o u s e m p ir ic a l d a ta h a v e b e e n c o lle c te d ,
a n d s e v e ra l p s y c h o lo g ic a l th e o rie s o f c h e ss sk ill h a v e b e e n p ro p o s e d .
R e q u e s t s fo r r e p ri n ts s h o u ld b e s e n t t o F e rn a n d G o b e t , D e p a rt m e n t o f P s y c h o l o g y , U n iv e r s i ty o f
N o t t in g h a m , N o ttin g h a m N G 7 2 R D , U K . E m a i l : f rg @ p s y c .n o t t.a c .u k
I a m g ra t e fu l t o F r a n k R itte r a n d t o a n a n o n y m o u s r e v i e w e r fo r h e l p fu l c o m m e n t s o n th i s p a p e r.
© 1 9 9 7 P s y c h o l o g y P r e s s L td
292
GOBET
T h e g o a l o f th is p a p e r is to e x te n d th e te m p la te th e o r y (G o b e t & S im o n ,
1 9 9 6 a ), w h ic h w a s o rig in a lly in te n d e d a s a th e o r y o f c h e s s p la y e rs ’ p e rc e p tio n
a n d m e m o ry , to th e re a lm o f p ro b le m s o lv in g . In th e first p a rt, I b rie fly re v ie w
p re v io u s th e o r ie s o f p ro b le m s o lv in g in c h e ss. T h e n , I p ro p o se e le m e n ts o f a
c o m p re h e n siv e th e o ry o f c h e s s p ro b le m s o lv in g th a t is c o m p a tib le w ith e m p iric a l
d a ta o n m e m o ry a n d p e rc e p tio n re s e a rc h . A sp e c ts o f th is th e o ry a re im p le m e n te d
in a c o m p u te r p ro g r a m , S E A R C H , w h ic h is d e s c rib e d in th e th ird p a rt o f th e
p a p e r, in c o n ju n c tio n w ith re s u lts o f s im u la tio n s. F in a lly , I c o n s id e r h o w th e
p ro p o s e d th e o ry g e n e ra lis e s to o th e r d o m a in s o f e x p e rtise .
C H E S S P R O B L E M S O L V IN G :
T H E O R IE S A N D D A T A
D e G r o o t ’s C la s s ic R e s u lts
T h e b a sic fin d in g o f D e G ro o t’s s tu d y (1 9 4 6 /1 9 7 8 ) w a s th a t th e re w e re n o
im p o rta n t d if fe r e n c e s in th e m a c ro s tr u c tu re o f se a rc h b e tw e e n w o rld -c la ss
g ra n d m a ste rs a n d s tro n g a m a te u rs , e x c e p t th a t th e b e s t p la y e rs fo u n d b e tte r
m o v e s a n d w e re s o m e w h a t f a s te r to re a c h a d e c isio n . O n a v e ra g e , p la y e rs fro m
b o th s k ill le v e ls se a rc h e d e q u a lly d e e p , v isite d th e sa m e n u m b e r o f p o sitio n s in
th e ir s e a rc h , a n d p r o p o se d th e sa m e n u m b e r o f c a n d id a te m o v e s . D e G ro o t
c o n c lu d e d th a t th e k e y to e x p e rtise is n o t a s u p e rio rity in “ sp e e d o f th in k in g ” o r in
a m o re ra tio n a l w a y o f o rg a n is in g o n e ’s th o u g h t, b u t s p e c ific k n o w le d g e a b o u t
v a rio u s a sp e c ts o f th e ta s k d o m a in . D e G ro o t n o te d th a t th e se a r c h b e h a v io u r
sh o w n b y h is p la y e rs w a s c o m p a tib le w ith S e lz ’s (1 9 2 2 ) th e o r y o f p ro d u c tiv e
th in k in g , b u t h e d id n o t o ffe r a d e ta ile d m o d e l o f c h e ss th in k in g .
S im o n ’s T h e o r y a n d C o m p u te r P r o g r a m s
o f C h e s s P la y in g
A d e ta ile d a c c o u n t o f c h e s s th in k in g w a s la te r o f fe re d b y C h a s e a n d S im o n
(1 9 7 3 ). T h e ir th e o ry , k n o w n a s th e c h u n k in g th e o ry (C T ), p ro p o s e d th a t a t th e
c o re o f e x p e rtis e lie s th e a b ility to re c o g n ise im p o rta n t p ro b le m fe a tu re s ra p id ly .
T h e s e fe a tu re s , in te rn a lly sto re d a s c h u n k s, a c t a s a c c e ss p o in ts to se m a n tic lo n g te rm m e m o ry (L T M ) a n d a s th e c o n d itio n s o f p ro d u c tio n s , w h o se a c tio n s m a y b e
c a r rie d o u t in te r n a lly o r e x te r n a lly . T h is p ro d u c tio n - sy s te m a c c o u n t w a s lin k e d
to a ss u m p tio n s a b o u t in fo rm a tio n -p ro c e ss in g m e c h a n ism s, d e sc rib in g , f o r
e x a m p le , h o w a n o b je c t is so rte d th r o u g h a d isc rim in a tio n n e t in o rd e r to re a c h a
n o d e in L T M . I t a lso in c lu d e d p a ra m e te rs s p e c ify in g le a rn in g a n d a c c e ss in g
tim e s (e .g . a b o u t e ig h t s e c o n d s to le a rn a n e w c h u n k ), a s w e ll a s s tric t c a p a c ity
lim its (e .g . S T M lim ite d to se v e n c h u n k s) . In th e c a s e o f c h e s s e x p e rtise ,
p e rc e p tio n m e c h a n ism s in C T a llo w re c o g n itio n o f p a tte rn s o f p ie c e s o n th e
b o a rd . T h e s e p a tte rn s su g g e s t m o v e s , w h ic h a r e u se d to u p d a te th e in te rn a l
re p re se n ta tio n o f th e b o a rd in w h a t th e y c a ll th e m in d ’s e y e . (T h e m in d ’s e y e is a
re la tio n a l s y ste m th a t c a n b e s u b je c te d to v is u o -sp a tia l m e n ta l o p e ra tio n s a n d th a t
P A T T E R N -R E C O G N IT IO N A N D S E A R C H
293
sto re s p e rc e p tu a l s tru c tu re s , b o th fr o m e x te rn a l in p u ts a n d fro m m e m o ry s to re s .)
P a tte rn -re c o g n itio n m e c h a n is m s a p p ly re c u rs iv e ly in th e in te r n a l re p re se n ta tio n
o f p o s itio n s in th e m in d ’s e y e . T e rm in a tio n o f se a rc h in a b ra n c h is o b ta in e d b y
e v a lu a tin g w h e th e r c e rta in g o a ls a re a b o v e o r b e lo w a th re s h o ld , w h o s e v a lu e
m a y c h a n g e a s a f u n c tio n o f p la y e rs ’ e x p e c ta tio n le v e l o f th e p o sitio n .
V a rio u s c o m p u te r p r o g ra m s o f p r o b le m s o lv in g in c h e ss w e re d e v e lo p e d b y
S im o n
a n d h is
c o lle a g u e s , b u t n o n e
o f th e m
d ire c tly
in c o rp o ra te d
th e
re c o g n itio n – a s so c ia tio n m e c h a n ism o f th e c h u n k in g th e o ry . T h e p ro g ra m s
w ritte n b y N e w e ll, S h a w , a n d S im o n (1 9 6 3 ), a n d B a y lo r a n d S im o n (1 9 6 6 )
im p le m e n te d th e id e a o f s e le c tiv e se a rc h m a d e p o ss ib le b y th e u se o f h e u ristic s.
N e w e ll a n d S im o n ’s m o d e l (1 9 6 5 ; se e a lso W a g n e r & S c u rra h , 1 9 7 1 ) fo rm u la te d
six p rin c ip le s th a t d ic ta te th e g e n e ra tio n o f m o v e s o r e p iso d e s , u s in g m a in ly th e
e v a lu a tio n o b ta in e d a t th e e n d o f a b ra n c h .
H o ld in g ’s S E E K T h e o r y
H o ld in g (1 9 8 5 , 1 9 9 2 ) c ritic is e d C T , a n d p ro p o s e d in ste a d th e S E E K (S E a rc h ,
E v a lu a tio n , a n d K n o w le d g e ) th e o ry , a th e o ry th a t w a s h o w e v e r o n ly lo o se ly
fra m e d a n d d id n o t re a c h th e th e o re tic a l d e ta il o f C T . T h e m a in th ru st o f S E E K
w a s to su g g e s t th a t m a ste ry in c h e s s d e p e n d s p rim a rily in th in k in g a h e a d , a n d n o t
in p a tte rn re c o g n itio n . N o te th a t a ll th re e c o m p o n e n ts o f th e S E E K th e o ry a re
p re se n t in C T a n d th a t it is re a lly th e w e ig h t g iv e n to e a c h o f th e s e c o m p o n e n ts
th a t d iff e re n tia te th e tw o th e o r ie s .
S a a r ilu o m a ’s A p p e rc e p tio n a n d
R e s t r u c tu r a tio n T h e o r y
R e c e n tly , S a a rilu o m a (1 9 9 0 , 1 9 9 2 ) p r o p o se d th a t p la y e rs , w h ile try in g to fin d a
m o v e in a p o sitio n , a c c e ss g o a l p o s itio n s b y p a tte r n re c o g n itio n ( S a a r ilu o m a u s e s
th e o ld te rm “ a p p e rc e p tio n ” ). T h e y th e n try to c lo se th e p a th fro m th e p ro b le m
p o sitio n to th e g o a l p o sitio n . W h e n it is n o t p o ss ib le to c lo se th e p a th , th e p ro b le m
sp a c e is re stru c tu re d . T h u s, p ro c e sse s le a d in g to a M a s te r’s c h o o sin g a m o v e m a y
b e d e sc rib e d a s a s e q u e n c e o f a p p e rc e p tio n – r e s tru c tu r a tio n c y c le s , w h ic h m a k e it
p o s sib le to fin d so lu tio n s w ith o n ly a lim ite d s e a rc h in th e p ro b le m s p a c e .
S a a rilu o m a ’s th e o ry , a d m itte d ly s till a t its e a rly sta g e o f d e v e lo p m e n t, is n o t
q u ite sa tisfa c to ry : it is u n c le a r w h a t d iffe re n tia te s it fro m N e w e ll a n d S im o n ’s
(1 9 7 2 ) m e a n s– e n d s a n a ly s is, a n d it d o e s n o t m a k e p ro v is io n fo r w h a t h a p p e n s
w h e n p la y e rs d o n o t h a v e a g o a l p o sitio n in m in d .
E r ic s s o n a n d K in t s c h ’s L o n g -t e r m W o r k in g
M e m o ry T h e o ry
E ric s so n a n d K in tsc h ( 1 9 9 5 ) p ro p o s e , w ith in th e fr a m e w o rk o f th e ir lo n g -te r m
w o r k in g m e m o ry th e o ry (L T W M T ), th a t sk ille d p la y e rs h a v e c o n s tr u c te d a n
h ie ra rc h ic a l re tr ie v a l stru c tu re , n o t u n lik e th e stru c tu re c re a te d b y S F a n d D D ,
294
GOBET
tw o m n e m o n is ts sp e c ia lise d in th e d ig it- sp a n ta s k (C h a s e & E ric s so n , 1 9 8 2 ).
T h is p o w e rfu l m e m o ry stru c tu re , is o m o rp h ic to th e 6 4 s q u a r e s o f th e c h e ss b o a rd ,
a llo w s p la y e rs to u p d a te in f o rm a tio n ra p id ly d u rin g se a rc h . T h e th e o r y a ls o
p ro p o s e s th a t c h e ss p la y e rs c a n c re a te n e w L T M a s so c ia tio n s ra p id ly , a lth o u g h
n o p a ra m e te r is g iv e n to s p e c ify th is s p e e d o f e n c o d in g .
I h a v e sh o w n e ls e w h e r e (G o b e t, 1 9 9 6 ) th a t L T W M T , in a d d itio n to b e in g
v a g u e a n d le a v in g m a n y d e ta ils u n s p e c ifie d , g e n e ra te s p re d ic tio n s th a t d o n o t
a g re e w ith th e e x p e rim e n ta l d a ta o n c h e s s p e rc e p tio n a n d m e m o ry . In a d d itio n ,
th e m e m o ry m e c h a n ism s p ro p o s e d b y L T W M T (re tr ie v a l stru c tu re a n d ra p id
e la b o r a tio n o f L T M stru c tu re s) s e e m a t o d d s w ith th e fo llo w in g a sp e c t o f c h e ss
p la y e r s’ se a r c h b e h a v io u r. It is c o m m o n f o r c h e ss p la y e r s to re v is it a n o d e d u rin g
th e ir a n a ly s is o f th e p o sitio n . H o w e v e r, in ste a d o f a c c e ssin g th is n o d e d ire c tly , a s
su g g e s te d b y L T W M T ’s v e ry p o w e rf u l m e c h a n is m s fo r s to rin g p o sitio n s ra p id ly
a n d a c c u ra te ly , p la y e r s a c c e s s th e ta rg e t p o sitio n b y g e n e ra tin g a s e q u e n c e o f
in d iv id u a l m o v e s fro m th e g iv e n p ro b le m p o s itio n (c f. D e G ro o t, 1 9 4 6 ). T h is
b e h a v io u r su g g e sts th a t p la y e rs m a y n o t sto re p o sitio n s a s q u ic k ly a s p ro p o s e d b y
LTW M T.
T H E T E M P L A T E T H E O R Y A N D IT S A P P L IC A T IO N
T O P R O B L E M S O L V IN G
In itia lly , th e te m p la te th e o ry (T T ) w a s d e v e lo p e d to re m o v e so m e w e a k n e ss e s in
th e c h u n k in g th e o ry w ith r e s p e c t to d a ta fro m m e m o r y re se a rc h (G o b e t & S im o n ,
1 9 9 6 a ). C o n tra ry to C T ’s p re d ic tio n s, b a s e d o n a lim ite d S T M c a p a c ity , c h e ss
p la y e r s’ m e m o ry is re s ista n t to re tro a c tiv e in te rfe re n c e ( C h a rn e s s, 1 9 7 6 ) a n d
c h e ss p la y e rs c a n re c a ll s e v e ra l b rie f ly p re s e n te d p o sitio n s w ith re a so n a b le
a c c u ra c y (C o o k e , A tla s, L a n e , & B e rg e r, 1 9 9 3 ; G o b e t & S im o n , 1 9 9 6 a ).
L ik e C T , T T p ro p o s e s th a t c h u n k s a re a c c e ss e d b y tra v e rsin g a d isc rim in a tio n
n e t. C h u n k s a re lin k e d to o th e r in fo rm a tio n s to r e d in L T M , s u c h a s m o v e s , p la n s,
ta c tic a l m o tiv e s , a n d s o o n . In a d d itio n , c h u n k s th a t o fte n o c c u r in a p la y e r’s
e x p e r ie n c e c a n e v o lv e in to m o re c o m p le x d a ta s tru c tu re s (te m p la te s ), w h ic h h a v e
slo ts a llo w in g v a ria b le s to b e e n c o d e d , fo r e x a m p le , to sp e c ify th e sq u a re
o c c u p ie d b y a p ie c e . A c c o rd in g to T T , th is e n c o d in g o c c u rs ra p id ly (a b o u t o n e
se c o n d p e r s lo t). In a d d itio n to slo ts, te m p la te s c o n ta in a c o r e , w h ic h is m a d e u p
o f (v a ria b le -fre e ) c h u n k s . A lto g e th e r, te m p la te s a re a s su m e d to sto re a t le a s t
a b o u t 1 0 p ie c e s. F in a lly , te m p la te s m a y b e lin k e d to o th e r te m p la te s . T T a ls o
p ro p o s e s th a t in fo r m a tio n sto re d in th e m in d ’s e y e , a s tr u c tu re s im ila r to th a t
p ro p o s e d b y C T , d e c a y s ra p id ly , a n d th a t it n e e d s to b e u p d a te d e ith e r b y in p u ts
fro m th e e x te rn a l w o rld o r b y in p u ts fro m m e m o ry s tr u c tu re s .
T T re m o v e s th e d iffic u lty o f C T w ith in te rfe re n c e p h e n o m e n a , fir st b e c a u s e it
h y p o th e sis e s s o m e fa st L T M e n c o d in g (th ro u g h te m p la te s lo ts), a n d se c o n d
b e c a u s e te m p la te s c o n ta in m o r e in fo rm a tio n th a n th e c h u n k s p ro p o s e d b y C T
(C T a ssu m e d th a t c h u n k s c o n ta in a t m o s t fiv e o r s ix p ie c e s). F in a lly , T T k e e p s
295
P A T T E R N -R E C O G N IT IO N A N D S E A R C H
th e p o w e r o f C T to e x p la in th e r a p id re c o g n itio n o f p o sitio n s sh o w n b y m a ste rs,
a s th e s a m e d isc rim in a tio n m e c h a n ism s a r e p re s e n t (G o b e t, 1 9 9 6 ).
S e a r c h M e c h a n is m s
T T a n d C T p ro p o se th a t se a rc h is c a rrie d o u t in a fo rw a r d fa sh io n , b y re c u rsiv e
a p p lic a tio n o f p a tte rn re c o g n itio n p r o c e s se s in th e in te rn a l re p r e s e n ta tio n . In th e
re m a in d e r o f th is se c tio n , I w ill fle sh o u t th is m e c h a n is m w ith a d d itio n a l sp e c ific a tio n s . I w ill a lso sh o w h o w c h u n k s a n d te m p la te s m a y b e u se d to te rm in a te
se a rc h , a n d h o w te m p la te s m a y b e u se d to c a rry o u t s e a rc h a t a le v e l m o re
a b stra c t th a n th e m o v e le v e l.
M o v e G e n e ra tio n .
A s m e n tio n e d e a rlie r, p a tte r n r e c o g n itio n is a p p lie d
re c u rsiv e ly in T T . If a c h u n k — o r a te m p la te , a s te m p la te s a r e a s p e c ia l c a s e o f
c h u n k s— is re c o g n is e d , it m a y g iv e a c c e s s to a m o v e (o r a se q u e n c e o f m o v e s ) o r
to a n h e u ris tic fo r se le c tin g th e n e x t m o v e . E x a m p le s o f s u c h h e u ristic s a re :
“ O c c u p y o p e n lin e s ” , o r “ C o u n te r-a tta c k in th e c e n tre w h e n a tta c k e d o n th e
K in g ’s sid e ” . In th is c a s e , th e m o v e (s ) is (a re ) c a rrie d o u t in th e m in d ’s e y e . If n o
m o v e re su lts fro m p a tte rn re c o g n itio n , o n e o f tw o o p e ra tio n s m a y b e a p p lie d .
E ith e r th e re is a n e w a tte m p t to g e n e ra te a m o v e b y a c c e ss in g a d iffe re n t c h u n k ,
o r w e a k e r h e u ristic s a re a p p lie d .
U p d a te
T e m p la te .
of
In te rn a l
R e p re se n ta tio n
and
S to r a g e
of
In fo rm a tio n
in to
W h e n a m o v e o r a se q u e n c e o f m o v e s is c a rrie d o u t in th e m in d ’s
e y e , th e in te rn a l re p re s e n ta tio n is u p d a te d , a n d , w h e n a te m p la te h a s b e e n
a c c e ss e d , slo ts a re u p d a te d a s w e ll. S lo ts m a y sto re in fo r m a tio n a b o u t th e
lo c a tio n o f p ie c e s , stra te g ic in fo r m a tio n , e v a lu a tio n o f th e p o sitio n o r p a rt o f it,
a n d s o o n . N o te th a t th is in fo rm a tio n fa c ilita te s s e a rc h , b e c a u se p o s sib le fo r g e ttin g th ro u g h d e c a y in th e m in d ’s e y e m a y b e b a c k e d -u p b y in fo rm a tio n s to re d
in s lo ts.
E v a lu a tio n o f N o d e s .
E v a lu a tio n o f a p o sitio n is n o t c a r rie d o u t a f te r e a c h
m o v e b u t o n ly a t th e te rm in a l p o sitio n s. E v a lu a tio n is e ith e r r e trie v e d , w h e n
p o s sib le , fro m c h u n k s th a t h a v e b e e n re c o g n ise d , o r c o m p u te d w h e n th e p la y e r
d e c id e s to te rm in a te s e a rc h (s e e n e x t p a ra g ra p h ). D e G ro o t’s (1 9 4 6 ) p ro to c o ls
in d ic a te th a t p la y e rs e v a lu a te o n ly te rm in a l p o s itio n s a n d th a t th e ir e v a lu a tio n s
a re ra th e r s im p le , ta k in g in to a c c o u n t a s in g le fe a tu r e , su c h a s m o b ility o r c o n tro l
o f th e c e n tre , a n d stro n g ly su g g e s t th a t e v a lu a tio n s a re n o t c o m p u te d b y
c o n jo in in g s e v e r a l fe a tu re s .
E n d in g
S ea rch
of an
E p iso d e .
A
c ritic a l q u e s tio n , g iv e n
a
lim ite d
in fo rm a tio n - p ro c e s sin g c a p a c ity , is w h e n to s to p se a rc h in g a n e p iso d e (i.e . a
se q u e n c e o f m o v e s g e n e ra te d fro m a b a s e m o v e ). I p r o p o se th a t th e fo llo w in g
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GOBET
c o n d itio n s c a n h a lt th e se a rc h o f a n e p iso d e . T o b e g in w ith , th e p ro b a b ility o f
m a k in g a n e rro r is to o h ig h . P s y c h o lo g ic a lly , th is p ro b a b ility is a fu n c tio n o f th e
fo rg e ttin g a n d in te r fe r e n c e r a te s in th e m in d ’ s e y e . P h e n o m e n o lo g ic a lly , p la y e rs
p ro b a b ly a s se ss th is p ro b a b ility b y ta k in g in to a c c o u n t th e d e p th o f se a rc h
re a c h e d a n d b y e s tim a tin g th e ir fa m ilia rity w ith th e p o s itio n .
A n o th e r re a so n to h a lt s e a rc h o c c u r s w h e n th e le v e l o f e x p e c ta tio n fo r th e
p o s itio n is m e t o r w h e n a f e a tu re o f th e p o s itio n (e .g . sa fe ty o f th e K in g ) w a s
e v a lu a te d to b e lo w e r th a n its a d m iss ib le v a lu e (N e w e ll & S im o n , 1 9 7 2 ). T h is
le v e l o f e x p e c ta tio n is p ro v id e d b y a c h u n k e n c o u n te re d d u rin g e a rlie r s e a rc h o r
b y e x p lic it e v a lu a tio n o f th e p o s itio n , a n d w a s s to re d e ith e r in S T M o r , w h e n
a v a ila b le , in a te m p la te slo t. A fin a l h a ltin g c o n d itio n is th a t a d e c isiv e e v e n t
o c c u rre d s u c h a s m a te , im p o rta n t m a te ria l g a in o r lo ss , o r fu lfilm e n t o f a k e y
g o a l.
S e le c tin g th e N e x t B a s e -m o v e .
N o w c o n s id e r th e q u e stio n o f w h ic h b a se -
m o v e to se a rc h n e x t w h e n a le a f n o d e h a s b e e n re a c h e d . A n y o f six m e c h a n is m s
m a y b e e n g a g e d . F irst, if th e le a f w a s e v a lu a te d w ith a h ig h risk o f e r ro r, th e s a m e
se q u e n c e o f m o v e s is se a rc h e d a g a in in o rd e r to o b ta in a m o re re lia b le e stim a te .
S e c o n d , th e sa m e s e q u e n c e o f m o v e s m a y b e se a rc h e d a g a in to m a k e s u re th a t it
h a s b e e n sto re d in L T M . T h ir d , if a te m p la te h a s b e e n re c o g n is e d , a m e ta -se a rc h
(s e e la te r) is c a rr ie d o u t. F o u rth , th e re is a b ia s to g iv e p re fe re n c e to n o rm a l b a s e -
m o v e s e a rly in se a rc h , a n d to u n u su a l b a s e -m o v e s la te r (N e w e ll & S im o n , 1 9 7 2 ,
p .7 2 3 ) . F ifth , a m o v e re a c h e d a t a n y le v e l o f d e p th in s e a rc h in g a lin e m a y b e trie d
a s a c a n d id a te m o v e in th e n e x t lin e . S ix th , if th e e v a lu a tio n o f a n e p iso d e g iv e s a
fa v o u ra b le re su lt, its a n a ly s is is c o n tin u e d ; if th e e v a lu a tio n is u n fa v o u r a b le a
d iffe re n t b a se -m o v e is ta k e n u p (N e w e ll & S im o n , 1 9 7 2 ) .
M e ta -s e a rc h w ith T e m p la te s (A b stra c t P la n n in g ).
S e a rc h m a y b e c a rrie d o u t
n o t o n ly a t th e m o v e le v e l, b u t a lso a t th e te m p la te le v e l. P la y e rs s o m e tim e s
d e v e lo p a tre e se a rc h b y g e n e r a tin g k e y p o sitio n s (te m p la te s ) in s te a d o f
d e v e lo p in g a tre e se a r c h b y g e n e ra tin g m o v e s (e .g . D e G ro o t, 1 9 7 8 , p .1 5 3 ). P a th s
b e tw e e n k e y p o sitio n s c o n s is t o f m a c r o -o p e ra to r s o r in u n s p e c ifie d o p e ra to r s,
w h ic h w ill b e fille d in a t a la te r sta g e o f se a rc h , if th e le a f p o sitio n s a re ju d g e d
fa v o u ra b le . T h is ty p e o f se a r c h is c o n tin g e n t to th e p re s e n c e , in p la y e rs ’ L T M , o f
te m p la te s su ffic ie n tly c lo se to th e p o s itio n a t h a n d . K o e d in g e r a n d A n d e rs o n
(1 9 9 0 ) h a v e p r o p o se d a sim ila r id e a w ith re sp e c t to g e o m e try . T h is m e ta -se a rc h
m e c h a n ism is a ls o sim ila r to th e “ a p p e rc e p tio n ” m e c h a n is m su g g e s te d b y
S a a rilu o m a (1 9 9 0 , 1 9 9 2 ) .
T h e o r e t ic a l Im p o r ta n c e o f T e m p la te s
O b v io u s ly , m a n y o f th e p r o c e s se s ju st d e s c rib e d c a n b e im p le m e n te d w ith in th e
e a r lie r C T w ith o u t h y p o th e sisin g th e p re se n c e o f te m p la te s . T e m p la te s a re ,
h o w e v e r, im p o rta n t fo r s o m e o f th e k e y c o g n itiv e p ro c e s se s in c h e ss , b e c a u se
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(a ) slo ts a llo w in fo rm a tio n a b o u t s tra te g ic o r ta c tic a l th e m e s, a s w e ll a s a b o u t
e v a lu a tio n o f th e p o sitio n , to b e e n c o d e d in L T M r a p id ly ; (b ) lin k s b e tw e e n
te m p la te s a llo w fo r “ m e ta -se a rc h ” ; (c ) in fo r m a tio n s to re d b o th in th e c o re a n d in
th e slo ts o f th e te m p la te c o m p e n sa te s fo r d e c a y a n d in te rfe re n c e in th e m in d ’s
e y e , a s it m a y b e u se d to re in sta te fa d in g in fo rm a tio n . T h is c o m p e n sa tio n
m e c h a n ism is p a r tic u la rly u se fu l w h e n p e rc e p tu a l in fo rm a tio n fro m th e e x te rn a l
b o a rd is u n re lia b le , fo r e x a m p le b e c a u s e se v e ra l m o v e s h a v e b e e n c a rr ie d o u t in
th e m in d ’s e y e .
E m p ir ic a l D a ta S u p p o r tin g t h e T T A c c o u n t o f S e a rc h
a n d P a tte r n R e c o g n itio n
In th is se c tio n , T T is q u a lita tiv e ly a p p lie d to s o m e o f th e k e y d a ta f ro m e m p ir ic a l
stu d ie s o f c h e s s p ro b le m s o lv in g . Q u a n tita tiv e a s se ss m e n t w ill b e th e to p ic o f
th e fo llo w in g se c tio n . I h a v e sh o w n e ls e w h e re (G o b e t, 1 9 9 6 ) th a t th e p re d ic tio n s
o f T T a re w e ll su p p o rte d b y e m p ir ic a l d a ta fro m re se a rc h o n m e m o r y a n d
p e rc e p tio n .
In c re a sin g th e n u m b e r o f c h u n k s a n d te m p la te s h a s tw o o p p o site e f fe c ts w ith
re sp e c t to se a rc h (G o b e t, in p r e s s). O n th e o n e h a n d , d e e p s e a rc h is fa c ilita te d , a s
c o m p a re d w ith th e m o re c o m p u ta tio n a lly e x p e n s iv e w e a k m e th o d s, b e c a u se
p a tte rn re c o g n itio n is a ra p id p ro c e s s a n d b e c a u s e se q u e n c e s o f m o v e s m a y b e
le a rn e d a n d su g g e ste d b y c h u n k s. O n th e o th e r h a n d , th e n e e d f o r d e e p se a rc h
o fte n d isa p p e a r s b e c a u s e e v a lu a tio n s su g g e ste d b y p a tte rn re c o g n itio n m a y b e
m o re re lia b le th a n e v a lu a tio n s c o m p u te d b y w e a k m e th o d s . T h e s e tw o o p p o site
e ffe c ts c a n e x p la in w h y th e sk ill d iffe re n c e s in a v e ra g e d e p th o f se a rc h a re sm a ll.
P a tte rn re c o g n itio n a llo w s stro n g p la y e rs to b e h ig h ly s e le c tiv e in th e ir s e a rc h .
T h is c a n b e s e e n b o th in th e ra p id w a y M a s te rs z e ro in to th e k e y a s p e c ts o f a
p o s itio n (D e G ro o t, 1 9 4 6 ), a n d in th e w a y e y e m o v e m e n ts d iffe r a s a fu n c tio n o f
sk ill d u rin g th e firs t s e c o n d s o f th e p e rc e p tio n o f a p o sitio n (D e G ro o t & G o b e t,
1 9 9 6 ). A d d itio n a l e v id e n c e is p ro v id e d b y S a a rilu o m a (1 9 9 0 ) , w h o h a s sh o w n
th a t p la y e rs c h o o se ste re o ty p e d so lu tio n s in p ro b le m s w h e re fa ste r (in th e
n u m b e r o f m o v e s to r e a c h m a te ) b u t u n c o m m o n so lu tio n s a re p re s e n t. T h e se d a ta
a d d s u p p o rt to T T , b e c a u se p a tte rn re c o g n itio n lie s a t its c o re .
F u r th e r s tro n g e v id e n c e fo r th e r o le o f p a tte rn re c o g n itio n is th a t M a s te rs c a n
p la y s e v e ra l o p p o n e n ts s im u lta n e o u sly a t a s tre n g th c lo se to th a t in o n e -a g a in s to n e p la y . It is in te re stin g th a t, in s im u lta n e o u s g a m e s, th e y te n d to p la y “ n o rm a l”
m o v e s a n d re ly o n o p p o n e n ts ’ e rro rs (G o b e t & S im o n , 1 9 9 6 c ). N o rm a l m o v e s
m a y c o rre sp o n d to th e ty p e o f m o v e s su g g e ste d b y c h u n k s a n d te m p la te s .
A fe a tu re o f c h e s s e x p e rtise c a p tu re d u n iq u e ly b y T T is th e h ig h le v e ls a t
w h ic h c h e s s p la y e rs o rg a n is e th e ir k n o w le d g e . D e G ro o t (1 9 4 6 ) p ro p o s e d th a t
p la y e r s o r g a n is e p o sitio n s a ro u n d la rg e “ c o m p le x e s” , b ig g e r th a n th e c h u n k s th a t
w e re la te r p ro p o se d b y C h a se a n d S im o n (1 9 7 3 ). D e G ro o t a lso su g g e s te d , a s d id
C o o k e e t a l. (1 9 9 3 ), th a t p la y e rs re p re s e n t in fo rm a tio n a t a c o n c e p tu a l le v e l. In
p a rtic u la r, D e G ro o t (1 9 4 6 ) p ro p o se d th a t M a ste rs’ d e sc rip tio n s o f g a m e s a re
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c e n tr e d a ro u n d k e y p o sitio n s o f th e g a m e . T T o ffe rs th e o r e tic a l s tru c tu r e s
(te m p la te s) th a t c o u ld a c c o u n t fo r p la y e rs ’ la r g e c o m p le x e s , h ig h - le v e l re p re se n ta tio n s, a n d k e y p o sitio n s. T T a ls o o ff e rs m e c h a n ism s , b a s e d o n f re q u e n c y o f
o c c u rre n c e s , e x p la in in g h o w th e s e h ig h - le v e l re p re se n ta tio n s a re d e v e lo p e d , a n d
m e c h a n ism s, b a se d o n d isc rim in a tio n p ro c e sse s , e x p la in in g h o w th e y c o u ld b e
a c c e ss e d ra p id ly .
T T is a lso c o m p a tib le w ith re su lts fro m e x p e r im e n ts u s in g p o s itio n s fo r w h ic h
a c c e ss to k n o w le d g e is d iffic u lt. In H o ld in g a n d R e y n o ld s ’ (1 9 8 2 ) e x p e rim e n t,
c h e ss s k ill d id n o t c o rr e la te w ith th e re c a ll o f s e m i-ra n d o m p o s itio n s sh o w n fo r a
fe w se c o n d s, b u t e ff e c tiv e n e s s o f th e s e a rc h f o r th e b e st m o v e in th e s e p o s itio n s
d id c o rr e la te w ith s k ill. T T o f fe r s a n e x p la n a tio n fo r th e fa c t th a t th e re w a s a
stro n g c o rre la tio n b e tw e e n sk ill le v e l a n d q u a lity o f m o v e p ro p o se d . P la y e rs
re c u rsiv e ly g e n e ra te a m o v e th ro u g h w e a k m e th o d s w h e n n o c h u n k is
re c o g n ise d , u n til o n e o f th e h a ltin g c o n d itio n s (m e n tio n e d e a rlie r ) a p p lie s . T h e n ,
g iv e n th e ir la rg e r d a ta b a se o f c h u n k s, stro n g p la y e rs a re m o re lik e ly th a n w e a k
p la y e r s to fin d a u s e fu l p a tte rn in p o sitio n s th a t h a v e b e e n n e w ly u p d a te d in th e
m in d ’s e y e , a n d th e re fo re a re m o re lik e ly to f in d g o o d m o v e s in th e ir se a rc h .
I m e n tio n e d e a rlie r th a t E ric ss o n a n d K in ts c h (1 9 9 5 ) p ro p o s e d m e c h a n ism s
(re trie v a l stru c tu re a n d e la b o ra tio n s o f L T M sc h e m a s ) th a t e n c o d e in fo r m a tio n
q u ic k ly a n d re lia b ly . B y c o n tra st, th e e n c o d in g c a p a c ity o f te m p la te s is r e la tiv e ly
w e a k . In p a rtic u la r, T T p re d ic ts th a t th e sa m e te m p la te m a y s o m e tim e s b e u se d to
e n c o d e s e v e ra l sim ila r p o sitio n s, th u s in c re a s in g th e ris k o f in te rf e re n c e a s se a rc h
p ro g re s se s. A s a c o n se q u e n c e , a n d c o n tra r y to L T W M T ’s p re d ic tio n s, p la y e rs
sh o u ld o fte n re v isit p o sitio n s b y g e n e ra tin g m o v e s in s te a d o f a c c e ss in g th e m
d ire c tly fro m m e m o ry . T h is is w h a t p la y e rs— e v e n m a ste rs — d o (D e G ro o t,
1 9 4 6 ). F in a lly , T T m a y h a v e s o m e th in g to sa y a b o u t e rro rs in c h e ss . K ro g iu s
(1 9 7 6 ) m e n tio n s th a t e r ro rs o f te n o c c u r w h e n a m o v e h a s c a u s e d im p o rta n t
c h a n g e s in th e p o s itio n . T h is m a y b e d u e to p la y e rs’ in a b ility to re c o g n ise th a t a
p re v io u sly a d e q u a te te m p la te h a s b e c o m e in a d e q u a te .
In s u m m a ry , T T o ffe rs a g o o d q u a lita tiv e a c c o u n t o f s e v e r a l im p o rta n t c h e ss
p h e n o m e n a . It is n o w tim e to tu rn to m o re o b je c tiv e , q u a n tita tiv e te sts o f th e
th e o r y .
A C O M P U T E R M O D E L O F S E A R C H IN C H E S S
In th e re m a in d e r o f th is p a p e r, I p re s e n t a c o m p u te r m o d e l c a lle d S E A R C H ,
w h ic h im p le m e n ts T T in so m e d e ta il. I firs t d e s c rib e th e im p le m e n ta tio n o f
S E A R C H , m a k in g c le a r w h a t a s p e c ts o f T T h a v e b e e n in c lu d e d , a n d th e n d isc u ss
its b e h a v io u r w ith r e s p e c t to h u m a n d a ta .
O v e r v ie w o f M o d e l
F u ll im p le m e n ta tio n o f T T a s a c h e ss- p la y in g c o m p u te r p ro g ra m w o u ld b e a
m a jo r ta sk — th is d iffic u lty is d e m o n stra te d b y th e fa c t th a t n o c o m p le te c o m p u te r
m o d e l o f c h e s s c o g n itio n , in c lu d in g p e rc e p tio n , m e m o ry , a n d p ro b le m so lv in g ,
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h a s e v e r b e e n d e v e lo p e d . I p u rs u e d a lim ite d a im : a c o m p u te r m o d e l th a t c o n ta in s
so m e o f th e im p o rta n t p a r a m e te rs o f T T a n d th a t c o m p u te s k e y b e h a v io u ra l
v a ria b le s . T h is m o d e l d o e s n o t c o n stitu te a c o m p le te im p le m e n ta tio n o f th e
th e o ry (it d o e s n o t s e a rc h o r e v a lu a te c h e ss p o sitio n s) , b u t is d e ta ile d e n o u g h to
o ffe r a g o o d te st o f so m e a s p e c ts o f T T . It is s o b e rin g to n o tic e th a t e v e n th is
p a rtia l im p le m e n ta tio n o f th e th e o ry is q u ite c o m p le x a n d re q u ire s m a n y
p a ra m e te rs. T h is is th e p ric e o f a v o id in g th e v a g u e n e s s o f v e rb a l th e o ris in g .
T h e M a in P r o b le m -s o lv in g L o o p
T h e m a in in te re st o f th e m o d e l is in th e in te ra c tio n b e tw e e n p a tte rn re c o g n itio n
a n d s e a rc h . T h e m o d e l g e n e ra te s in d e p e n d e n t e p is o d e s fo llo w in g se v e ra l ru le s
fo r g e n e r a tin g m o v e s a n d c h o o sin g sto p c o n d itio n s . C o m p a tib le w ith m o s t
h u m a n p ro to c o ls , th e p ro g ra m c o n sid e rs o n ly o n e b ra n c h w ith in a n e p is o d e (th u s,
th e re is n o b ra n c h in g p o in t w ith in a n e p iso d e ). A s illu stra te d in F ig . 1 , th e m o d e l
is c lo se to th e d e s c rip tio n o f T T g iv e n e a rlie r in th is p a p e r. T h e v a rio u s c o n d itio n s
a n d o p e ra tio n s in S E A R C H a re re p re se n te d a s p ro b a b ilitie s o r p ro b a b ility
d istrib u tio n s , a n d n o t a s a c tu a l c h e ss m o v e s, e v a lu a tio n s , o r s y m b o lic s tru c tu r e s
in S T M o r in th e m in d ’s e y e .
A tra c e o f S E A R C H is sh o w n in F ig . 2 . T h e a n a ly s is w ill c e n tre o n th e
fo llo w in g v a ria b le s a s a fu n c tio n o f th e n u m b e r o f c h u n k s : ra te o f g e n e ra tin g a
m o v e ; le v e l o f fu z z in e ss in th e m in d ’s e y e w h e n a n e p is o d e is e n d e d ; m e a n d e p th
o f s e a rc h ; m e th o d s u se d fo r g e n e ra tin g a m o v e ; a n d m e th o d s u se d fo r s to p p in g a n
e p is o d e .
T h e c o n c e p t o f te m p la te is im p le m e n te d in tw o w a y s : (a ) b y h ig h e r
p ro b a b ilitie s o f fin d in g (s e q u e n c e s o f) m o v e s a n d e v a lu a tio n s th a n w ith p la in
c h u n k s, a n d (b ) b y a d e c re a se in th e le v e l o f fu z z in e ss, m a d e p o s sib le b y th e L T M
re p re se n ta tio n o f th e c o re o f th e p o sitio n a n d o f slo ts .
T h e le v e l o f re lia b ility o f th e in fo rm a tio n in th e m in d ’s e y e is c a p tu re d b y a
“ fu z z in e s s” p a ra m e te r, e x p re ss e d in a rb itr a ry u n its. T h re e m a in c o g n itiv e
fe a tu re s a r e c a p tu re d b y th is p a ra m e te r: w o rk in g m e m o r y c a p a c ity , a b ility to
m a in ta in a v is u o -s p a tia l im a g e , a n d su b je c tiv e e s tim a te o f th e r is k o f m a k in g a n
e rro r. T h e fu z z in e s s p a ra m e te r is th e n a s su m e d to o rig in a te b o th fro m th e
h a rd w a re a n d th e so ftw a re o f th e sy s te m . It m a y v a ry d u r in g th e life tim e o f a
p la y e r , b e c a u se o f b io lo g ic a l m a tu ra tio n o r a g e in g , a n d m a y b e a ffe c te d b y
e x p e rim e n ta l m a n ip u la tio n s . T h e re a re th re e re a so n s w h y S E A R C H e n d s a
se a rc h : th e le v e l o f fu z z in e s s is to o h ig h , a n e v a lu a tio n is p ro p o se d , o r n o m o v e is
p ro p o s e d . T h e id e a o f e x p e c ta tio n le v e l is n o t e x p lic itly p re se n t in th e m o d e l, b u t
it is im p lic it in th e p ro b a b ility v a lu e s o f f in d in g fe a tu re s e n d in g th e s e a rc h o f a n
e p iso d e , e ith e r b y p a tte rn re c o g n itio n o r b y th e a p p lic a tio n o f h e u ristic s.
S e le c tio n o f th e n e x t b a se -m o v e (a k e y c o n c e rn o f N e w e ll & S im o n , 1 9 6 5 , a n d
W a g n e r & S c u rra h , 1 9 7 1 ) is n o t a d d r e s se d b y S E A R C H , w h ic h in g e n e ra l la c k s
th e s e m a n tic in fo rm a tio n n e c e s sa ry fo r su c h a se le c tio n . F in a lly , m e ta -se a rc h
w ith te m p la te s is n o t d ire c tly im p le m e n te d in S E A R C H , b u t it is im p lic itly
300
GOBET
F IG . 1 .
300
F l o w c h a rt o f S E A R C H .
P A T T E R N -R E C O G N IT IO N A N D S E A R C H
F IG . 2 .
301
E x a m p l e s o f e p is o d e s g e n e ra t e d b y S E A R C H .
301
302
GOBET
re p re se n te d b y th e re la tiv e ly h ig h p r o b a b ility o f fin d in g (s e q u e n c e s o f) m o v e s
a n d e v a lu a tio n s w ith te m p la te s , a s c o m p a re d w ith c h u n k s.
T h e M o d e l’s P a r a m e te r s
S E A R C H h a s m a n y p a ra m e te rs a n d it is , o f c o u rs e , n e c e s sa ry to se t u p a f e w o f
th e m w ith in d e p e n d e n t d a ta in o rd e r to re d u c e th e n u m b e r o f d e g re e s o f fre e d o m
in th e m o d e l. W h e n p o ss ib le I h a v e u s e d sim u la tio n s w ith th e C H R E S T (D e
G ro o t & G o b e t, 1 9 9 6 ; G o b e t, 1 9 9 3 ) a n d C H U M P (G o b e t & Ja n s e n , 1 9 9 4 )
p ro g r a m s to se t p a ra m e te r v a lu e s . C H R E S T is a p ro g ra m im p le m e n tin g a s p e c ts
o f T T a n d s im u la tin g n u m e ro u s e x p e r im e n ts o n p e rc e p tio n a n d m e m o ry in c h e s s,
a n d C H U M P is a p ro g ra m p la y in g ( w e a k ) c h e ss b y p u re p a tte rn re c o g n itio n .
N u m b e r o f C h u n k s a n d T e m p la te s.
T a b le 1 sh o w s th e v a lu e s th a t w ill b e
u s e d w ith th e S E A R C H m o d e l fo r th e se p a ra m e te rs. T o c h o o se th e v a lu e s re la te d
to th e n u m b e r o f c h u n k s a n d te m p la te s , th e c u rre n t v e rsio n o f C H R E S T h a s b e e n
e m p lo y e d . T h e p ro b a b ility o f fin d in g a te m p la te w a s e stim a te d b y r u n n in g
C H R E S T o n 5 0 p o s itio n s ra n d o m ly ta k e n fro m M a s te rs ’ g a m e s. T h e first lin e (0
c h u n k ) w a s a d d e d to g e t p re d ic tio n s a t th e n o v ic e le v e l. W ith n e ts o f 1 0 0 ,0 0 0 ,
1 2 0 ,0 0 0 , a n d 1 5 0 ,0 0 0 c h u n k s, th e p a ra m e te rs w e r e e stim a te d w ith th e b e s t-fittin g
fu n c tio n s a v a ila b le (th e “ n o v ic e ” v a lu e s w e re n o t u se d ). T h e n u m b e r o f te m p la te s
is ro u g h ly a lin e a r fu n c tio n o f th e n u m b e r o f c h u n k s (r 2 = .9 7 ). T h e p ro b a b ility
o f fin d in g a te m p la te is a p p ro x im a te ly a lo g -fu n c tio n o f th e n u m b e r o f c h u n k s
(r 2 = .9 4 ) .
H e u r is tic s , C h u n k s, T e m p la te s a n d T h e ir R e la tio n to th e P ro b a b ility o f
F in d in g M o v e s a n d E v a lu a tio n s .
T a b le 2 g iv e s th e v a lu e s u s e d in th e
sim u la tio n s fo r th e p a ra m e te rs re la te d to h e u ristic s, c h u n k s, a n d te m p la te s.
H e u ris tic s in c lu d e sim p le se a rc h te c h n iq u e s (e .g . “ ta k e a p ie c e b a c k ” o r “ c h e c k
th e K in g ” ) a s w e ll a s m o re a b stra c t ru le s (e .g . “ o c c u p y th e c e n tre ” ). T h e ir m a in
c h a ra c te ristic , in c o m p a riso n w ith c h u n k s a n d te m p la te s , is th a t th e y a re g e n e ra l
a n d re q u ire so m e c o n sc io u s c o m p u ta tio n in o rd e r to p ro d u c e a m o v e . T h e
a ss u m p tio n u n d e rly in g T a b le 2 is th a t th e p a r a m e te rs re la te d to h e u ristic s sta y
ro u g h ly c o n sta n t, w h ile th e o th e r p a r a m e te rs v a ry a s a lo g a rith m ic fu n c tio n o f th e
n u m b e r o f c h u n k s in th e n e t. (A lo g a rith m ic fu n c tio n h a s b e e n c h o se n to in d ic a te
th a t c h u n k s y ie ld a d im in ish in g re tu rn a s th e ir n u m b e r in c re a se s.) T h e
a ss u m p tio n th a t th e n u m b e r o f h e u ristic s is c o n sta n t a c ro s s s k ill le v e ls se e m s
re a so n a b le (p e rh a p s w ith th e e x c e p tio n o f th e n o v ic e le v e l), a s m o s t c h e ss
M a ste rs ’ k n o w le d g e is v e ry sp e c ific to c e rta in a sp e c ts o f th e g a m e (D e G ro o t,
1 9 4 6 ).
T h e fo llo w in g c o n s id e ra tio n s w e re m a d e in se ttin g th e v a lu e s g iv e n in
T a b le 2 . It w a s d e e m e d p la u sib le th a t th e p ro b a b ility o f fin d in g so m e h e u ristic in
a p o s itio n b e h ig h (.9 5 ), a s w e ll a s th e p ro b a b ility o f fin d in g s o m e c h u n k . F in a lly ,
P A T T E R N -R E C O G N IT IO N A N D S E A R C H
303
TA BLE 1
T h e V a lu e s o f th e 1 4 N e ts U s e d in th e S im u la tio n s
P r o b a b i lit y o f
N um ber of chunks
N u m b e r o f te m p la t e s
r e c o g n i s i n g a t le a s t
P r o p o r t io n o f
o n e t e m p l a te g i v e n a
tem p la tes
p o sitio n
0
0
.0 0 0
.0 0 0
2680
5
.0 0 2
.1 8 0
1002
0
5003
.0 0 0
36
10011
100
30001
493
20003
.0 0 7
1142
80010
2285
72044
.4 6 0
.0 2 3
.4 0 0
.0 3 0
.4 8 0
.0 2 9
.5 4 0
.0 2 8
3357
150000
.3 6 0
.0 1 9
2765
120000
.3 0 0
.0 1 6
2136
100000
.2 4 0
.0 1 3
774
50006
.1 4 0
.0 1 0
265
40005
.0 0 0
.5 1 0
.0 2 8
4245
.5 4 0
.0 2 8
.5 6 0
T h e v a l u e s b e lo w 1 0 0 ,0 0 0 c h u n k s w e r e t a k e n f ro m s i m u la t i o n s w ith C H R E S T , th e o t h e rs
e x t ra p o l a te d . S e e t e x t f o r d e t a ils .
TA BLE 2
H e u r is t ic s , C h u n k s , T e m p la te s , a n d T h e ir R e la tio n to th e P ro b a b ility o f F in d in g
M o v e s a n d E v a lu ta tio n s
T ype
H e u r is tic s
C hu nks
T e m p la tes
P ro b a b i lity o f e v o k in g a n
.9 5
g (n _ c h u n k s , .9 5 ) a
P ro b a b i lit y o f f in d i n g a m o v e
.5 0
g (n _ c h u n k s , .5 0 )
g (n _ c h u n k s , .9 0 )
.1 5
g (n _ c h u n k s , .0 5 )
g (n _ c h u n k s , .5 0 )
h e u ri s t ic , a c h u n k , o r a t e m p l a te
g i v e n t h a t a n h e u r is tic , a c h u n k ,
o r a te m p la t e h a s b e e n e v o k e d
P ro b a b i lity o f f in d i n g a n e v a l u a tio n
g i v e n t h a t a n h e u ri s t ic , a c h u n k , o r
s e e T a b le 1
a tem p late h as b een ev o k ed
a
T h e fu n c tio n g i s d e f in e d a s :
g (n _ c h u n k s , p ro b ) = p ro b * 0 .2 * l o g 1 0 (n _ c h u n k s ), i f n _ c h u n k s > 0
and
g (n _ c h u n k s , p ro b ) = 0 , i f n _ c h u n k s = 0 ,
w h e re n _ c h u n k s i s th e n u m b e r o f c h u n k s in a g i v e n n e t, a n d p r o b i s a c o n s t a n t .
303
304
GOBET
th e p ro b a b ility o f re c o g n isin g a te m p la te in a p o sitio n is sm a lle r a n d is g iv e n in
T a b le 1 .
T h e p ro b a b ility o f fin d in g a m o v e g iv e n a h e u ristic is s e t to .5 0 , in d ic a tin g th a t
h e u ristic s m a y fa il to p ro d u c e a m o v e h a lf o f th e tim e . T h is is b e c a u se so m e
h e u ristic s m a y n o t y ie ld a m o v e a n d b e c a u se so m e p ro p o se d m o v e s m a y b e
ille g a l. T h e p ro b a b ility o f f in d in g a m o v e g iv e n a te m p la te is h ig h , p a rtly
re fle c tin g th e ric h s e m a n tic k n o w le d g e a n d th e in te r-te m p la te lin k s a s su m e d to
c h a ra c te rise te m p la te s . F o r th e p ro b a b ility o f fin d in g a m o v e , g iv e n th a t a c h u n k
h a s b e e n re c o g n is e d , I u se d th e p a ra m e te r p ro b in th e f u n c tio n g (s e e T a b le 2 ) so
th a t it a p p ro x im a te s th e d a ta p ro d u c e d b y th e C H U M P p r o g ra m (G o b e t & Ja n se n ,
1 9 9 4 ). E v a lu a tio n s a re su p p o s e d to b e h a rd e r to le a rn a n d , th e re fo re , h a rd e r to u se
th a n m o v e s . H e n c e , th e ir p ro b a b ilitie s a re lo w e r th a n th e c o r re s p o n d in g p ro b a b ilitie s w ith m o v e s . A g a in , fo llo w in g d ir e c tly fro m th e th e o ry , te m p la te s o ffe r
th e b e st so u rc e o f e v a lu a tio n s.
W ith re sp e c t to th e n u m b e r o f se q u e n tia l m o v e s p ro p o s e d , c o u n te d in p lie s
(i.e . m o v e s fo r W h ite o r B la c k ) , it is a s su m e d th a t h e u ristic s g iv e a c c e ss to o n ly
o n e m o v e , w h ile c h u n k s a n d te m p la te s y ie ld se q u e n c e s o f m o v e s w h o se n u m b e r
fo llo w s a g e o m e tric p ro b a b ility d is trib u tio n (th e c h o ic e o f th is d is tr ib u tio n w a s
in sp ire d b y sta tis tic s ta k e n fro m C H U M P ). T h e lo n g e s t s e q u e n c e ( c a ll it k ) h a s a
fre q u e n c y o f 1 , th e s e c o n d -lo n g e st a fre q u e n c y o f 2 , th e th ird -lo n g e st a fre q u e n c y
o f 4 , a n d so o n u n til th e sh o rte st se q u e n c e , w h o s e le n g th is 1 m o v e a n d w h o se
fre q u e n c y is 2 (k – 1 ) . T h e m a x im u m se q u e n c e o f m o v e s w a s se t to 1 8 . F in a lly ,
S E A R C H a tte m p ts to g e n e ra te a m o v e b y p a tte rn re c o g n itio n ( c h u n k o r te m p la te )
fo u r tim e s b e fo re u sin g a n h e u ristic .
T im e a n d F u zzin e ss P a ra m e te rs .
T h e tim e p a ra m e te r s fo r th e re sp e c tiv e
o p e ra tio n s w e re s e t u sin g p la u sib le v a lu e s (se e T a b le 3 ) . M o v e g e n e ra tio n b y
p a tte rn re c o g n itio n (c h u n k o r te m p la te ) is a s su m e d to b e v e ry sh o rt (a fe w
h u n d re d m illis e c o n d s); n o tim e c o st is u se d in th e m o d e l. T h e tim e fo r c o m p u tin g
a m o v e -g e n e ra tin g h e u ristic w a s s e t to th e ra th e r lo n g 2 0 s e c o n d s — g e n e ra tin g a
m o v e w ith o u t u sin g p a tte rn r e c o g n itio n re q u ire s p u ttin g to g e th e r v a rio u s ty p e s o f
in fo rm a tio n a n d a s k s fo r m a n y c h e c k in g p ro c e d u r e s . T h e tim e fo r c a rry in g o u t
o n e m o v e (o n c e g e n e r a te d ) in th e m in d ’s e y e w a s s e t to tw o s e c o n d s . T h is is
c o m p a tib le w ith S a a rilu o m a ’s (1 9 8 9 ) d a ta , w h ic h sh o w th a t a b lin d fo ld e d M a ste r
c a n fo llo w a g a m e d ic ta te d a t tw o se c o n d s a m o v e . F in a lly , th e tim e fo r c a rry in g
o u t a n e v a lu a tio n b y h e u ris tic is s e t to 1 0 s e c o n d s . T h is ra th e r s h o rt tim e m a y b e
ju stifie d b y th e fa c t th a t p la y e rs ty p ic a lly c o n s id e r o n ly o n e (s u b je c tiv e ) a sp e c t o f
th e p o sitio n (D e G ro o t, 1 9 4 6 ) a n d th a t m a n y e v a lu a tio n s c a n b e g ro u n d e d o n th e
b a sis o f c le a r m a te ria l lo ss e s.
T h e fu z z in e ss le v e l o f th e s y ste m is e x p re ss e d in a rb itra ry u n its. It s ta rts w ith
th e v a lu e z e ro , a n d it is in c re a se d w h e n a m o v e is c a rrie d o u t in th e m in d ’s e y e
a n d w h e n tim e is s p e n t a p p ly in g a n h e u ris tic . W h e n a te m p la te is fo u n d , th e
P A T T E R N -R E C O G N IT IO N A N D S E A R C H
305
TA BLE 3
T im e a n d “ F u z z in e s s ” P a r a m e t e r s U s e d in th e
S im u la t io n s
T im e fo r c a r ry i n g o u t a m o v e
2
s
10
s
T im e fo r c o m p u t in g m o v e -g e n e r a tin g h e u r is tic
20
U p p e r l i m it o f fu z z i n e s s
50
T im e fo r c o m p u t in g e v a lu a t io n
In c r e a s e o f fu z z in e s s p e r m o v e
In c re a s e o f f u z z i n e s s p e r s e c o n d
D e c re a s e i n fu z z i n e s s d u e t o te m p l a t e
s
1
2
5
fu z z in e s s le v e l is d e c re a se d , a s p a rt o f th e in fo rm a tio n m a y b e sto re d in L T M
d ire c tly , fre e in g c a p a c ity in w o rk in g m e m o ry a n d in th e m in d ’s e y e .
S im u la t io n s w it h t h e “ C a n o n ic a l M o d e l ”
T h e sim u la tio n s d e sc rib e d in th is s e c tio n a re stra ig h tfo rw a rd . U s in g th e
p a ra m e te r v a lu e s d is c u sse d e a rlie r, I le t th e p ro g ra m s e a rc h 1 0 0 0 e p is o d e s fo r
e a c h n e t s iz e . S u m m a ry v a lu e s fo r m e a n d e p th o f se a rc h , tim e , ra tio d e p th /tim e ,
a n d fu z z in e s s, a s w e ll a s fo r g e n e ra tio n a n d s to p c o n d itio n s w e re c o m p u te d f o r
e a c h n e t siz e .
M e a n D e p th o f S e a r c h , R a te o f S e a rc h , a n d F u z zin e ss .
A c c o rd in g to
S E A R C H , m e a n d e p th o f s e a rc h fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f
c h u n k s (se e F ig . 3 a ) . If w e a s su m e a c o n sta n t ra te o f le a rn in g n e w c h u n k s, a s is
c o m m o n p ra c tic e in so m e c o g n itiv e a rc h ite c tu r e s (c f. N e w e ll, 1 9 9 0 ), a n d if w e
a ss u m e th a t s k ille d p la y e rs h a v e sp e n t m o re p r a c tic e a n d stu d y tim e th a n
u n s k ille d p la y e rs, th e n m e a n d e p th fo llo w s a p o w e r fu n c tio n o f s k ill a s w e ll. T h is
p re d ic tio n , w h ic h is a t v a r ia n c e w ith H o ld in g ’s p re d ic tio n (1 9 8 5 , p .1 8 2 ) o f a
lin e a r in c re a s e , is p a rtly c o n siste n t w ith C h a rn e ss ’s (1 9 8 1 ) p ro p o s a l th a t d e p th o f
se a rc h is n o t lin e a rly re la te d to s k ill, b u t th a t th e re is a c e ilin g a t h ig h s k ill le v e ls.
T h e re su lt is a ls o c o m p a tib le w ith th e w e a k lin e a r re la tio n fo u n d in e m p ir ic a l
stu d ie s (C h a rn e ss , 1 9 8 1 ; G o b e t, in p re ss ) b e tw e e n m e a n d e p th o f se a rc h a n d sk ill
le v e l, b e c a u se re stric te d ra n g e s o f th e c u rv e c a n b e a p p ro x im a te d b y a lin e a r
fu n c tio n . T h e a b so lu te v a lu e s a re a ls o q u ite r e a so n a b le : th e y ris e f ro m lo w d e p th s
(le ss th a n 1 p ly ) w ith n o c h u n k s (c o r re s p o n d in g to th e n o v ic e le v e l) to a ro u n d 2 .5
p lie s w ith a sm a ll n e t ( 1 0 0 0 c h u n k s ), a n d th e n to a ro u n d 4 p lie s w ith e x p e rt le v e l
(a ro u n d 3 0 ,0 0 0 c h u n k s , a s e s tim a te d b y s im u la tio n s o n th e re c a ll ta s k ). T h e y th e n
slo w ly (s a v e fo r a f e w ra n d o m v a ria tio n s ) in c re a se to m o re th a n 5 p lie s w ith n e t
la rg e r th a n 1 0 0 ,0 0 0 c h u n k s , w h ic h c o rre sp o n d s to G ra n d m a ste r le v e l. H o ld in g
(1 9 8 5 ) c o m p u te d m e a n d e p th o f se a rc h f o r d e G ro o t’s (1 9 4 6 ) d a ta a n d fo u n d th a t
306
GOBET
E x p e rts a n d G ra n d m a s te rs h a d re s p e c tiv e ly a n a v e ra g e d e p th o f se a rc h o f 4 .8 a n d
5 .3 . T h e re g r e s sio n e q u a tio n d e riv e d f ro m C h a rn e ss ’s (1 9 8 1 ) d a ta y ie ld a n
a v e ra g e d e p th o f se a rc h o f a b o u t 2 .3 p lie s a t th e 1 3 0 0 E L O 1 le v e l, o f 4 .1 a t th e
E x p e rt le v e l (2 0 0 0 E L O ), a n d o f 5 .7 a t th e G ra n d m a s te r le v e l. U n fo rtu n a te ly , n o
stu d y te ste d p la y e rs ra n g in g fro m n o v ic e s to G r a n d m a ste rs, a n d S E A R C H ’s
p re d ic tio n o f a p o w e r la w o f p ra c tic e c a n n o t b e te ste d (y e t). I w ill re p o rt la te r
sim u la tio n s a d d re ssin g d a ta c o lle c te d b y S a a rilu o m a (1 9 9 0 ), w h e re In te r n a tio n a l
M a ste rs a n d G ra n d m a s te rs te n d e d to s e a rc h le s s th a n M a s te rs.
T h e ra te o f s e a rc h a lso fo llo w s a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (se e
F ig . 3 b ) . D e G ro o t (1 9 4 6 ), C h a rn e s s (1 9 8 1 ), a n d G o b e t (in p r e s s) a ll f o u n d th a t
stro n g p la y e r s te n d e d to s e a rc h fa ste r. F o r e x a m p le , G o b e t (in p re s s) fo u n d th a t
h is M a ste rs, E x p e rts, C la ss A , a n d C la s s B p la y e rs re sp e c tiv e ly se a r c h e d 4 .8 , 4 .1 ,
3 .2 , a n d 3 .4 n o d e s p e r m in u te . S E A R C H ’s v a lu e s a re h ig h e r, b u t still p la u s ib le .
F o r e x a m p le , W a g n e r a n d S c u rra h ’s (1 9 7 1 ) E x p e rt g e n e ra te d a b o u t 1 0 m o v e s p e r
m in u te . N o te a lso th a t a ll th e e x p e rim e n ts m e n tio n e d e a rlie r h a v e u se d v e rb a l
p ro to c o ls, w h ic h m a y h a v e s lo w e d d o w n th e ra te o f se a rc h (c f. E ric ss o n &
S im o n , 1 9 8 0 ). F in a lly , th e ra te o f se a r c h m a y h a v e b e e n u n d e re s tim a te d in th e
lite ra tu re , b e c a u se th e r a te o f g e n e ra tin g n o d e s p e r m in u te is ty p ic a lly c o m p u te d
b y d iv id in g th e n u m b e r o f n o d e s b y th e to ta l tim e . H o w e v e r, to ta l tim e in c lu d e s
tim e n o t sp e n t in s e a rc h ( fo r e x a m p le , w h a t D e G ro o t c a lls th e “ firs t p h a se ” ) .
T h e p la u sib ility o f th e sim u la tio n s o f th e la s t v a ria b le , th e le v e l o f f u z z in e ss a t
w h ic h a se a rc h is e n d e d , is m o re d if fic u lt to ju d g e , b e c a u se little is k n o w n a b o u t
th e r o le o f fu z z in e s s in c h e s s th in k in g . A g a in , S E A R C H p ro p o se s th a t th is
v a ria b le is a p o w e r fu n c tio n o f th e n u m b e r o f c h u n k s (s e e F ig . 3 c ). W ith la rg e r
n e ts, e p iso d e s te n d to b e e n d e d w ith lo w e r le v e ls o f fu z z in e s s. T h is su g g e s ts th a t,
in g e n e ra l, s tr o n g p la y e rs s h o u ld b e m o r e c o n fid e n t in th e ir c a lc u la tio n s , a s th e y
a re n o t a t th e e d g e o f th e ir p o s sib ilitie s. N o te th a t th e ra te o f c h a n g e is ra th e r h ig h
fo r th is p o w e r la w , w h ic h s u g g e sts th a t it sh o u ld b e p o ss ib le to d e te c t it
e x p e rim e n ta lly .
G e n e ra tio n o f M o v e s .
H o w is m o v e g e n e ra tio n a f fe c te d b y sk ill le v e l? A s
sh o w n in F ig . 4 a , S E A R C H m a k e s c le a r p re d ic tio n s . W ith sm a ll n u m b e rs o f
c h u n k s, th e tim e -c o n s u m in g p r o c e s s o f g e n e ra tin g m o v e s b y h e u ristic s is
e m p lo y e d . T h is p ro c e ss is so o n d o m in a te d b y g e n e ra tin g m o v e s b y c h u n k s,
w h ic h is in tu r n d o m in a te d b y te m p la te g e n e r a tio n .
1
T h e E L O ra t in g i s a n i n te r v a l s c a l e t h a t ra n k s c o m p e t itio n c h e s s p la y e rs . I ts s t a n d a rd d e v ia t io n
(2 0 0 p o i n ts ) is o f te n i n te r p re t e d a s a m e a s u r e o f s k i ll c la s s in c h e s s . G r a n d m a s te r s a re n o rm a lly ra t e d
a b o v e 2 5 0 0 , In t e rn a t io n a l M a s te r s a b o v e 2 4 0 0 , M a s t e r s a b o v e 2 2 0 0 , a n d E x p e rt s a b o v e 2 0 0 0 .
B e lo w , c la s s e s (A , B , e tc .) d iv i d e p la y e r s b y s l ic e s o f 2 0 0 E L O p o in t s .
P A T T E R N -R E C O G N IT IO N A N D S E A R C H
F IG . 3 .
307
U p p e r p a n e l : m e a n d e p t h o f s e a rc h (i n p lie s ) a s a f u n c tio n o f th e n u m b e r o f c h u n k s i n th e
d i s c ri m i n a tio n n e t. M id d l e p a n e l : r a t e o f s e a r c h (i n m o v e s p e r m i n u t e ) a s a f u n c tio n o f th e n u m b e r o f
c h u n k s i n t h e d is c ri m in a t i o n n e t . L o w e r p a n e l: le v e l o f f u z z in e s s (i n a rb i tr a ry u n its ) w ith w h i c h
e p i s o d e s a re e n d e d a s a fu n c t io n o f th e n u m b e r o f c h u n k s i n t h e d i s c r im in a t io n n e t .
307
308
GOBET
F IG . 4 .
U p p e r P a n e l : a r e a g ra p h o f th e p ro p o r tio n o f m o v e s g e n e ra t e d b y h e u r is tic s , c h u n k s o r
t e m p la te s , a s a fu n c t i o n o f th e n u m b e r o f c h u n k s in t h e d is c r im in a t io n n e t . L o w e r P a n e l : a r e a g ra p h o f
t h e p r o p o rt io n o f e p is o d e s s to p p e d b e c a u s e t h e le v e l o f fu z z i n e s s w a s t o o h ig h , b e c a u s e th e p o s i tio n
w a s e v a lu a t e d , o r b e c a u s e n o m o v e w a s p r o p o s e d , a s a f u n c tio n o f th e n u m b e r o f c h u n k s in t h e
d i s c ri m i n a tio n n e t.
308
P A T T E R N -R E C O G N IT IO N A N D S E A R C H
S to p p in g a n E p iso d e .
309
A g a in , S E A R C H m a k e s c le a r p re d ic tio n s a b o u t th e
w a y e p iso d e s a r e s to p p e d ( se e F ig . 4 b ). A t firs t, a b o u t 6 5 % o f e p is o d e s a re
sto p p e d b e c a u se n o m o v e is p ro p o se d a n d a little le ss th a n 2 5 % a r e s to p p e d
b e c a u s e th e in fo rm a tio n in th e m in d ’s e y e a n d in w o rk in g m e m o r y is to o fu z z y .
A s th e n u m b e r o f c h u n k s in c re a se s, th e p ro p o rtio n o f e p is o d e s e n d e d b y
e v a lu a tio n (th ro u g h c h u n k o r te m p la te re c o g n itio n , a s w e ll a s th ro u g h h e u r is tic s )
in c re a s e s to a b o u t 7 5 % w ith la rg e n e ts.
V a r ia b ilit y o f D e p t h o f S e a rc h
In S a a rilu o m a ’s (1 9 9 0 ) e x p e rim e n t, In te rn a tio n a l M a ste rs a n d G ra n d m a s te rs
te n d e d to s e a rc h le s s th a n re la tiv e ly w e a k M a s te rs (a r o u n d 2 2 0 0 E L O ). W h e n
p lo tte d a g a in st s k ill, b o th th e to ta l n u m b e r o f n o d e s se a rc h e d a n d th e m e a n d e p th
o f se a rc h sh o w e d a n in v e rte d U -c u rv e , w ith M a ste rs s e a rc h in g th e la rg e s t n u m b e r
o f n o d e s (5 2 ) a n d a t th e la r g e s t a v e ra g e d e p th (5 .1 m o v e s) . B y c o m p a ris o n ,
S a a rilu o m a ’s to p -le v e l p la y e rs s e a rc h e d th ro u g h a s p a c e o f 2 3 n o d e s w ith a n
a v e ra g e d e p th o f 3 .6 m o v e s.
N o te th a t, a s is u n fo rtu n a te ly th e ru le in c h e ss re se a r c h , S a a rilu o m a u se d fe w
p la y e r s a n d fe w te s t p o sitio n s. T h u s , o n e c a n e x p e c t la rg e flu c tu a tio n s ju s t b y
c h a n c e . T h is is a c tu a lly h o w S E A R C H b e h a v e s w h e n th e n u m b e r o f tria ls is lo w .
F ig u r e 5 illu stra te s th e r e s u lts o f sim u la tio n s w ith th e n u m b e r o f e p is o d e s f o r
e a c h n e t siz e lim ite d to 5 0 , w h ic h ro u g h ly c o rre s p o n d s to th e to ta l p ro d u c e d b y
fiv e p la y e r s s e a rc h in g a n a v e ra g e o f 1 0 e p iso d e s (S a a rilu o m a im p o se d a 1 0 -
m in u te lim it to h is p la y e rs). T h e o th e r p a ra m e te rs a re th e sa m e a s in th e c a n o n ic a l
m o d e l.
A lth o u g h th e c u rv e s c a n b e w e ll fitte d b y a p o w e r fu n c tio n , o n e c a n o b se rv e
im p o rta n t v a ria tio n s fro m o n e c u rv e to a n o th e r. A ll c u rv e s sh o w a n in c re a s e , w ith
d ip s a n d p e a k s, a n d a ll p re d ic t th a t s o m e c a te g o ry o f stro n g e r p la y e rs w ill se a rc h
le ss d e e p ly th a n s o m e c a te g o ry o f w e a k e r p la y e r s. T h e b e s t e x a m p le w ith re sp e c t
to S a a rilu o m a ’s d a ta is th e b o tto m c u rv e . H is ( w e a k ) M a s te r s m a y b e c o m p a re d
to th e 4 0 ,0 0 0 -c h u n k n e t, w h ic h s h o w s d e e p e r s e a rc h th a n th e la r g e r n e ts,
in c lu d in g th e n e ts c o rre sp o n d in g to G ra n d m a s te rs.
T h u s, S a a rilu o m a ’s d a ta a re c o n s is te n t w ith S E A R C H a n d its p re d ic tio n th a t
d e p th o f se a rc h is a p o w e r fu n c tio n o f s k ill. T h a t M a s te rs se a rc h d e e p e r th a n to p le v e l p la y e rs m a y b e a c c o u n te d f o r b y ra n d o m f lu c tu a tio n s, a s sh o w n in th e
sim u la tio n s.
S E A R C H : S U M M A R Y A N D C O N C L U S IO N S
A c o m p u te r m o d e l o f s e a r c h in c h e s s h a s b e e n p re se n te d , b a se d o n th e te m p la te
th e o ry . T h e m o d e l e m p lo y s h e u ris tic s a n d p a tte rn re c o g n itio n (b o th o f c h u n k s
a n d te m p la te s) to g e n e ra te in d e p e n d e n t e p iso d e s . W h ile it is a ss u m e d th a t th e
p a ra m e te rs re la te d to h e u ris tic s a re c o n sta n t a c ro ss s k ill le v e ls, it is p ro p o se d th a t
th e p a r a m e te rs re la te d to p a tte rn re c o g n itio n v a ry a s a lo g a rith m fu n c tio n o f th e
310
GOBET
F IG . 5 .
M e a n d e p th o f s e a rc h ( in p l ie s ) a s a f u n c tio n o f t h e n u m b e r o f c h u n k s in t h e d is c ri m i n a tio n
n e t , in fi v e s im u la t io n s w h e re th e n u m b e r o f e p i s o d e s is s m a ll ( n = 5 0 ).
310
P A T T E R N -R E C O G N IT IO N A N D S E A R C H
311
n u m b e r o f c h u n k s. O th e r p a ra m e te rs re la te d to tim e n e e d e d to c a rry o u t a n
o p e ra tio n a n d to le v e l o f f u z z in e ss in th e s y ste m a re a ls o u s e d . T h e m o d e l
a c c o u n ts r e a so n a b ly w e ll f o r s e v e ra l e m p iric a l d a ta , b o th q u a lita tiv e ly a n d
q u a n tita tiv e ly (e .g . m e a n d e p th o f se a r c h a n d ra te o f se a rc h ). It a lso s h e d s lig h t o n
S a a rilu o m a ’s (1 9 9 0 ) e m p iric a l re su lts , w h ic h p re v io u s ly se e m e d a n o m a lo u s.
P e rh a p s m o re im p o rta n tly , th e m o d e l p ro v id e s s o m e n e w th e o re tic a l in s ig h t
w ith re s p e c t to th e ro le o f c h u n k s in p ro b le m so lv in g . C h a se a n d S im o n ’s
c h u n k in g th e o ry , a lth o u g h sim p le in a p p e a ra n c e , h a s u n e x p e c te d c o n se q u e n c e s
d u e to th e n o n -lin e a r d y n a m ic s in v o lv e d in th e a c q u isitio n o f c h u n k s. F o r
e x a m p le , it h a d b e e n o v e rlo o k e d fo r 2 5 y e a rs th a t C T (c o rre c tly ) p re d ic ts a sk ill
e ffe c t in th e re c a ll o f ra n d o m p o sitio n s (G o b e t & S im o n , 1 9 9 6 b ). T h e c u rre n t
p a p e r sh o w s th a t, c o n tra ry to a c o m m o n in te rp re ta tio n o f C T , a c q u is itio n o f m o re
c h u n k s le a d s to d e e p e r se a rc h .
T h e m o d e l a ls o d ra w s a tte n tio n to s e a rc h fe a tu re s n o t h e e d e d in c u rre n t
re se a rc h a n d p o se s n e w e m p iric a l q u e stio n s . F o r e x a m p le , w h a t is th e ro le o f th e
fu z z in e s s p a ra m e te r, a n d w h a t is its re la tio n to w o rk in g m e m o ry ? A re v a ria b le s
su c h a s d e p th a n d ra te o f se a rc h b e st a p p ro x im a te d b y a p o w e r fu n c tio n o f s k ill,
u b iq u ito u s in c o g n itiv e p sy c h o lo g y , o r b y a lin e a r fu n c tio n , a s p ro p o se d , a m o n g
o th e rs, b y C h a rn e ss (1 9 8 1 ) a n d H o ld in g (1 9 8 5 )? F in a lly , th e m o d e l is a f irs t
a tte m p t to rig o ro u s ly lin k a m o d e l o f c h e ss p ro b le m so lv in g to a th e o ry o f
m e m o ry a n d p e r c e p tio n (th e te m p la te th e o ry a n d its C H R E S T im p le m e n ta tio n ),
th u s p ro v id in g a first ste p in to a u n ifie d , c o m p u ta tio n a l th e o ry o f c h e ss p la y e rs ’
c o g n itio n .
T h e S E A R C H m o d e l a d m itte d ly ta c k le s o n ly a s u b se t o f p ro b le m so lv in g — it
m a y b e c o m p le m e n te d b y N e w e ll a n d S im o n ’s ( 1 9 6 5 ) o r W a g n e r a n d S c u rra h ’s
(1 9 7 1 ) m o d e ls— b u t it m a k e s p re c ise a n d c le a r p re d ic tio n s . T h is is a d istin c t
a d v a n ta g e in c o m p a riso n w ith o th e r c u rre n t th e o rie s o f c h e ss p ro b le m so lv in g ,
su c h a s S E E K (H o ld in g , 1 9 8 5 ) , w h ic h a re ty p ic a lly v a g u e .
T o w h a t e x te n t d o th e th e o re tic a l id e a s p u t fo rw a rd in th is p a p e r g e n e r a lise to
o th e r d o m a in s o f e x p e rtis e ? O n e o f th e m a in te a c h in g s o f re c e n t re se a rc h is th a t
d iffe re n t ta sk e n v ir o n m e n ts ta x c o g n itiv e fu n c tio n s d if fe r e n tly . In p a rtic u la r,
e n v iro n m e n ts d iffe r m a ss iv e ly in th e a m o u n t o f s e a rc h n e e d e d to c a rry o u t th e
ta sk su c c e s sfu lly . H e n c e , it is u n lik e ly th a t fin d in g s fro m c h e s s re se a r c h w ill
a p p ly w ith o u t q u a lific a tio n to o th e r d o m a in s. H o w e v e r, th e in te ra c tio n s b e tw e e n
lo w -le v e l a n d h ig h -le v e l re p re se n ta tio n , o n th e o n e h a n d , a n d b e tw e e n
k n o w le d g e a n d se a rc h , o n th e o th e r h a n d , a re a lso a p p a r e n t in se v e ra l d o m a in s,
su c h a s m e d ic a l d ia g n o s is , p h y sic s, a n d te x t c o m p re h e n sio n . T h e te m p la te
th e o ry , w h ic h a c c o u n ts fo r th e s e in te ra c tio n s, th u s o ffe rs th e p e rsp e c tiv e to
in te g ra te th e se v a rio u s d o m a in s o f e x p e rtise in to a sin g le fra m e w o rk .
T h e c h u n k in g th e o ry h a s so m e tim e s b e e n m is in te rp re te d a s a c la im th a t
re c o g n itio n o f fa m ilia r p a tte rn s a n d re trie v a l o f m o v e s a s so c ia te d w ith th e m is
a lm o s t th e so le b a sis o f e x p e rtis e in c h e ss ( e .g . H o ld in g , 1 9 8 5 ) . T h e c o rre c t
c la im , a n d th e o n e a c tu a lly m a d e b y C h a s e a n d S im o n , is th a t sk ill in p la y in g
312
GOBET
c h e ss d e p e n d s b o th o n (a ) re c o g n isin g fa m ilia r c h u n k s in c h e ss p o sitio n s w h e n
p la y in g
g a m e s, a n d
(b )
e x p lo rin g
p o s sib le
m oves
and
e v a lu a tin g
th e ir
c o n se q u e n c e s . H e n c e , e x p e rtis e d e p e n d s b o th o n th e a v a ila b ility in m e m o ry o f
in fo rm a tio n a b o u t a la rg e n u m b e r o f fre q u e n tly re c u rrin g p a tte rn s o f p ie c e s, a n d
o n th e a v a ila b ility o f stra te g ie s f o r h ig h ly s e le c tiv e s e a rc h in th e m o v e tr e e .
E x p e rt m e m o ry in tu rn in c lu d e s slo w ly a c q u ire d stru c tu re s in lo n g -te rm m e m o ry
(te m p la te s) th a t a u g m e n t sh o rt- te rm m e m o ry w ith s lo ts (v a ria b le p la c e s) th a t c a n
b e fille d r a p id ly w ith in fo rm a tio n a b o u t th e c u rr e n t p o s itio n .
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