search heuristics of chess players of different calibers

7/28/2019 Search Heuristics of Chess Players of Different Calibers

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Search Heuristics of Chess Players of Different CalibersAuthor(s): Robert I. ReynoldsReviewed work(s):Source: The American Journal of Psychology, Vol. 95, No. 3 (Autumn, 1982), pp. 383-392Published by: University of Illinois PressStable URL: http://www.jstor.org/stable/1422131 .

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AMERICAN JOURNAL OF PSYCHOLOGYFall 1982, Vol. 95, No. 3, pp. 383-392

Searchheuristicsof chessplayersof differentcalibersROBERT I. REYNOLDSNasson CollegeInformation-processingmodels of chess-playing ability have distinguishedbetween playersof different calibers solely in terms of perceptualencodingand recognition of chess configurations. A reanalysis of deGroot'sverbalprotocolsof 1965 indicates that playersof different calibersdirect their at-tention towarddifferent areas of the board. Grandmastersand masterscon-sider squares that are affectedby many pieces, while lesser players directtheirattention towardsquareson which the piecesare located. In a recallex-periment, chesspositionswerepresentedthat had been randomlygeneratedso as to differ only in the degree to which the pieces converge on the samesquares. Masters showedsuperiorrecallforbrieflypresented positionsonlywhen the materialaffects a highly centralized area of the board.The game of chess has been repeatedly selected as an ideal task for theinvestigation of problem-solving behavior. Chess has the complexityand variety of everyday problem solving, while the restricted domainof the chess board provides valuable experimental and descriptivecontrols, i.e. only one move can be made at a time, to only 1 of a pos-sible 64 squares. In no other nonlaboratory activity is there such aprecise measure of performance as that of the chess rating system.The progression from beginner to tournament chess player (0-1999points), through expert (2,000-2,199), master (2,200-2,399), seniormaster (2,400 and above), and grandmaster (approximately 2,500-2,700) levels, requires a minimum of 10 years of intensive study andpractice. Chess is therefore a highly desirable task for investigatingproblem-solving strategies of problem solvers with different degreesof expertise.During the past 15 years there have been a number of studies in-vestigating chess players' information-processing ability. Thesestudies have been based on the pioneering research of the Dutch psy-O 1982 Board of Trustees of the University of Illinois0002-9556/82/0300-0383 $1.00/0

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384 REYNOLDSchologist Adrian deGroot (1965), who posed the question, What dis-tinguishes the accomplished grandmaster from the average chessplayer? He presented novel middle-game positions to chess players ofdifferent calibers and elicited verbal protocols during their search forthe best move. DeGroot concluded that he could find no quantitativedifference between the thought process of the world's best players andthe average chess player. The only difference deGroot discovered be-tween strong and weak chess players was that the former have aquicker grasp of the position. "Within the very first five to ten sec-onds, the master subject is apt to have more relevant informationabout the position available to him than the lesser player can accumu-late in, say, a quarter of an hour of analysis" (deGroot 1965, p. 324).In Chase and Simon's (1973a) theory, "the most important processesunderlying chess mastery are those immediate visual-perceptual pro-cesses rather than the subsequent logical-deductive thinking pro-cesses" (p. 215).The speed with which a novel configuration is grasped is reflectedin the stronger player's superior recall ability when chess positions arepresented for brief durations (deGroot 1965, 1966; Jongman 1968).Chase and Simon (1973b) found that master chess players have supe-rior recall for real chess positions, but not for positions with randomlygenerated configurations of pieces. They suggest that masters havesuperior recall and chess-playing ability because they can recognize agreater number of patterns of related pieces. They characterize thesepatterns as "local clusters of pieces of the same color that usually de-fend each other. These structures are built around visual features,such as color and spatial proximity" (p. 236). Simon and Gilmartin(1973) estimate that a master chess player would require storage ofsome 50,000 chess configurations. According to Chase and Simon(1973a), the chess master's superior playing ability arises as this vastnumber of patterns becomes associated with plausible moves, andstored in long-term memory.

Despite Chase and Simon's success in inspiring research, theirtheory has not been strongly supported by other memory and recon-struction studies, nor does it account for data that directly analyzeschess players' search for the best move. If, as Simon and his collabora-tors suggest, masters are superior because of their experience withand storage of a large number of chess configurations, then we shouldexpect them to be better able to reconstruct the configurations ofhighly typical positions. DeGroot (1966) has generated a positionbased on the highest frequency of piece distribution found in pub-lished games. He calls it "the stereotypic position par excellence."



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SEARCH HEURISTICS 385

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Figure 1. DeGroot'sstereotypic positionThis position (see Figure 1) was used in the memory experiment ofHolding and Reynolds (1982) and yielded approximately the samerecall scores for players ranging from class C to expert. Goldin (1978)found that positions taken from real games and judged to be "highlytypical" were better recalled and recognized than "atypical" positions.However, chess players ranked "high"(between class A and master)were not significantly different (p < .06) in recall performance fromthose ranked "low" classes B, C, and D). Finally, deGroot (1966) hadsubjects make blind guesses as to the distribution of material in highlytypical positions selected from published games. He found no dif-ference between masters and "weak" players in guessing the place-ment of chess positions in such highly typical positions.Tikhomirov and Poznyanskaya (1966) monitored eye movementsin order to determine the area of the chess board actually consideredduring search. "One of the basic characteristics in the selection of amove is that the subject considers only a part of formally possible con-tinuations. Out of all the elements a zone of orienting emerges, ex-pressed by the total number of elements of the situation on which theeye concentrates. These elements, in turn, do not have equal value inthe frequency and duration of fixation" (Tikhomirov & Poznyan-skaya, 1966, p. 7). They observed that the "zone of orienting" did notnecessarily involve squares connected with important pieces or objec-tively powerful moves. The protocol of eye fixations from an expertsubject indicates that of the squares attended to most frequently, sixconsisted of his own pieces, four of his opponent's, and nine emptysquares. During the 106 sec used to make a move, the square e5 wasfixated 23 times. Though this square is unoccupied and unaffected byany piece, it was fixated more often than 40 other squares fixated dur-ing the session. Simon and Barenfeld (1969) developed a computer



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386 REYNOLDSsimulation of eye movements during chess perception. The basicassumption of PERCEIVER,onsistent with the subsequent theory ofChase and Simon (1973a), was that "the information being gatheredduring the perceptual phase is information about pieces" (p. 475).Consequently, all of PERCEIVER's fixations" of the Tikhomirov andPoznyanskaya position fell on squares occupied by pieces, when, infact, the human subject was concerned with spares and primarily asquare not even immediately affected by a piece.I believe that deGroot's analysis and Simon's extrapolations haveboth failed to notice that chess players of different calibers concen-trate their attention on different areas or "zones of orienting." Suchdifferences may, in fact, be found in deGroot's protocols and will beanalyzed in the following section. What we will find is that thestronger players do not attend so much to piece configurations as tocritical distributions of affected squares.REANALYSIS OF DEGROOT'S PROTOCOLS

The following analysis has been performed on one of deGroot's(1965) positions (Figure 2), which was taken from an actual game.This position provides the largest sample of protocols: 5 grandmas-ters, 4 masters, 5 experts, 2 chess players.We may plot two objective distributions on any chess board: oneconsists of the squares on which the pieces are situated (P distribu-tion), the other consists of the squares affected by the pieces (Adistribution). The geometric midpoint of the P distribution is thepoint midway between all of the pieces. The midpoint of the Adistribution is derived by assigning to each square the value equiva-lent to the number of times that the square is affected and then calcu-lating the (weighted) center of affected squares. A similar analysis canbe performed on the protocols in order to determine the subjects' cen-ter of attention or "zone of orienting." This is done by calculating themidpoint of squares mentioned in response to deGroot's position(Figure 2).Table 1 presents the midpoints in terms of x-y coordinates forgrandmasters (G), masters (M), experts (E), and class players (C), aswell as the center of pieces (P), and affected squares (A) in Figure 2.Table 2 presents the distance between the midpoints of the objectivedistributions and the players' area of attention. On the average, boththe grandmasters' and masters' center of attention is closer to the cen-ter of affected squares than it is to the piece center. The experts' center



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388 REYNOLDSA RECALL EXPERIMENT

It is notable that in deGroot's (1965) study, the grandmasters, mas-ters, and experts most often mention first a square near to the centerof their particular zone of orienting. We might expect that when a po-sition is presented for only a few seconds, players will concentrate onthose squares most often attended to in free-viewing situations. Itfollows that stronger players will have superior recall for the locationof briefly presented chess positions when those pieces are associatedwith and concentrated upon a small area of affected squares. Therandom assignment of pieces to the chess board in the recall experientof Chase and Simon (1973b) diminished not only the number ofrecognizable configurations, but also the central clustering of affectedsquares. Similarly, deGroot's (1966) guessing experiment precludedsubjects from grasping the centralization of the hidden positions. Inthat experiment, masters still did not outperform lesser players, eventhough configurations familiar to them were used.

METHODStimuliIn the following experiment, playersof different calibers were presentedchess positions generated by randomly assigning pieces according to thedegree of affect grouping. The conditional randomization describedbelowwas designed to control the distributionof affectedsquares,while equatingand reducing familiarityof piece configurations.A first-ordergrouping isgeneratedby firstlisting all of those squareson which the pieces may affect(i.e., attack or defend) the three inner perimeters.The pieces are then ran-domly assigned to one of those 34 squares, with the condition that neitherking is in check. A second-ordergroupingis generatedby first listing all ofthe squareson which a piece may affectone of the 16 squaresin the two in-ner perimeters, followedby randomassignmentto one of those squares.Athird-ordergroupingis generated by randomlyassigningpieces so that eachpiece affectsone of the four centralsquares.Three positionsof each group-ing were so generated. An expert chess player (United States chess fi-nalist = 2100) selectedone position from each groupingso as to equate, asmuch as possible, the familiarityof configurationsof pieces. Figure3 repre-

sents these three positions.Subjects and procedureThe subjectsin this study were three masters, threeclass A players, andthree class C players (mean ratings:2,235, 1,861, 1,533, respectively).Eachsubjectfirst viewed and reconstructeda practiceposition- deGroot'sstereo-



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SEARCH HEURISTICS 389

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390 REYNOLDStypicchessposition(Figure 1). They then viewedeach of the three test posi-tions. The order of presentationof positions was randomizedfor each sub-ject. Subjectswere presenteda position for 8 sec (comparableto the exper-iments of deGrootand of Simon), after whichtime the pieceswere abruptlyremoved from the board. Their taskwas to reconstructthe position, trying"newpositions until you feel satisfiedwith the reconstruction,or until youcan no longer rememberthe position."Approximately2 min. separatedthepresentationof successivepositions.RESULTS

Table 3 presents the number of pieces placed correctly in relationto the degree of affect grouping and caliber of player. The mastersshow a graded increase of 82% in recall performance with the in-crease from the first-order to the third-order affect grouping. Theclass C and class A players, in contrast, actually show poorer recallfor the higher levels of affect grouping (though this is not statisticallysignificant). All classes of players, including the masters, have thesame recall performance when the affect grouping is low. The higherthe affect grouping, the better does the position serve as a discrimina-tor for different calibers of chess players. The third-order groupingyields a statistically significant difference between groups (Kruskal-Wallace: H = 6.44, p < .05).In relation to the earlier analysis of search heuristics, we may saythat master chess players show superior recall for positions with dis-tributions concentrated about the area they most often attend to infree-viewing situations, namely the center of affected space.GENERAL DISCUSSION

The game of chess is a task so complex that an algorithmic search ofall possible continuations would require a modern computer's contin-Table 3. Mean number of pieces correctlyrecalledfor positionsof increas-ing affectgrouping (see Figure 3)Mean class First-order Second-order Third-order

rating grouping (A) grouping(B) grouping (C)1533 (C) 5.00 3.67 3.671861 (B) 5.00 4.00 4.332235 (A) 5.67 6.33 10.33



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SEARCH HEURISTICS 391uous operation for well over 100 years. Only in positions of extremelyreduced material will a human chess player attempt an exhaustivesearch. In fact, the grandmaster relies on heuristic search even wherealgorithmic search through the tree of possible moves is psychologi-cally feasible. The reanalysis of deGroot's protocols indicates thatmaster and grandmaster chess players direct their attention to a dif-ferent area of the board from that of players of lesser expertise. Whilethe beginning tournament player is captivated by configurations ofblack and white pieces of wood, the masters and grandmasters centertheir attention on those squares affected by the pieces.

In the Tikhomirov and Poznyanskaya (1966) study, the expert pri-marily fixated upon a square unoccupied and unaffected by anypiece. By calculating the piece and affective centers for that position,we find that that square (e5) is the center of all the material on theboard (i.e., the P distribution). The midpoint of all his fixations islocated between the piece and affective centers, as in the deGroot pro-tocols from experts.Simon and Gilmartin (1973) developed a computer simulation ofmemory for chess positions which they call MAPP. t incorporates theirsimulation of eye movements during chess perception (PERCEIVER)and a simple theory of rote verbal learning (EPAM). MAPP's recall forreal chess positions was compared with a class A and a master chessplayer. The program's recall performance closely matched that of theclass player, but was 24% lower than that of the master. Classplayers, unlike masters, encode chess positions according to localclusters of pieces.In recent years, computer programs have become relatively suc-cessful in human competition. Their steady increase in performancehas been a function of increasing reliance on the computer's largestorage capacity. In fact, the most successful programs today use noheuristic search, but calculate all possible first moves to a depth muchfurther than that of the human chess player. The move generators ofexisting programs are based on the storage of configurations ofpieces, much as described by Simon and his collaborators. The aboveanalysis indicates that move generation based on configurations ofpieces may inadvertantly lead to the simulation of expert class chessplayers. The leading chess-playing programs are, in fact, performingat the level of expert. The analysis of search heuristics suggests thefeasibility of programming a simulation of different calibers of chessplayers. The progression to master and grandmaster levels will, I be-lieve, require an adoption of search heuristics directed toward the dis-tribution of affected space.



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392 REYNOLDSNotesRequests for offprints may be sent to Robert Reynolds, Department of Psy-chology, Nasson College, Springvale, ME 04083. Received for publicationJune 23, 1981; revision received December 21, 1981.

ReferencesChase,W. G., &Simon,H. A. The mind's ye in chess. In W. G. Chase(Ed.), Visual nformationrocessing. ew York: Academic Press,1973. (a)Chase, W. G., & Simon, H. A. Perception in chess. CognitivePsychology,1973, 4, 55-81. (b)Goldin, S. E. Memory for the ordinary: Typicality effects in chess memory.Journal of ExperimentalPsychology.-Human Learningand Memory, 1978, 4,605-616.deGroot, A. D. Thoughtand choice n chess. The Hague: Mouton, 1965.deGroot, A. D. Perception and memory versus thought: Some old ideas andrecent findings. In B. Kleinmuntz (Ed.), Problem olving.-Researchmethodand theory.New York: Wiley, 1966.Holding, D., & Reynolds, R. Memory does not determine chess skills.Memory& Cognition, 1982, 10, 237-242.Jongman, R. W. Het Oog van de Meester. (Doctoral dissertation, Univer-sity of Amsterdam). Assen: Van Gorcum & Company, 1968.Simon, H. A., & Barenfeld, M. Information-processing theory of percep-tual processes in problem solving. PsychologicalReview, 1969, 76,473-477.Simon, H. A., & Gilmartin, K. A simulation of memory for chess positions.CognitivePsychology,1973, 5, 29-46.Tikhomirov, O. K., & Poznyanskaya, E. D. An investigation of visualsearch as a means of analyzing heuristics. Soviet Psychology,1966, 5,3-15.

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