Role of presentation time in Recall of Game and Random Chess Positions

Transcription

1 December 16, 1994 Presentation time in chess recall Role of presentation time in Recall of Game and Random Chess Positions Fernand Gobet and Herbert A. Simon Department of Psychology Carnegie Mellon University Complex Information Processing Working Paper #524 Correspondence to: Prof. Herbert A. Simon Department of Psychology Carnegie Mellon University Pittsburgh, PA Running head: Presentation time in chess recall

2 December 16, 1994 Presentation time in chess recall Abstract It is a widely cited result that experts' superiority over novices in recalling meaningful material from their domain of expertise vanishes when random material is used. A review of recent chess experiments where random positions were used as control material (presentation time between 5 and 10 seconds) shows, however, that strong players generally maintain some superiority over weak players even with random positions, although the relative difference between skill levels is smaller than with game positions. This paper investigates the role of presentation time (systematically varied from one second to sixty seconds) on recall of both game and random positions. We find that strong players are better than weak players with both types of positions. Their superiority with random positions is especially clear with long presentation times, but is also present after brief presentation times, although smaller in absolute value. It is proposed that strong players' superiority with random positions is due both to the large number of chunks they hold in LTM, strategies and to their better knowledge of the topology of the chessboard. The question of the recall of random material in other domains is raised.

3 December 16, 1994 Presentation time in chess recall Role of presentation time in i Recall of Game and Random Chess Positions A classical result in the study of expertise is that memorizing meaningful material from their domaii when the material is randomized. This result wa memory (Chase and Simon, 1973a; Jongman and ), and has since been widely cited in cognitive experts are better than non-experts at of expertise, but lose their superiority first obtained in the study of chess 5mmens, cited in Vicente & de Groot, psychology textbooks (e.g. Anderson, 1990; Lesgold, 1988), and hailed as one of the c ornerstones of the study of expertise (Saariluoma, 1989). The basic relation between skill and meaningfulness has been replicated in various domains, although wide variations in the presentation time of the stimuli make quantitative comparisons difficult: jo (Reitman, 1976); bridge (Engle & Bukstel, 1978; Charness, 1979); Othello (Wolff, Mi & Schwarz, 1979); computer programs (McKeith chell & Frey, 1984); electronics (Egan n, Reitman, Rueter & Hirtle, 1981); basketball (Allard, Graham & Paarsalu, 1980). Some studies, however, have found that experts keep their superiority over novices when tt sequence of pitch symbols (Sloboda, 1976) and f< 1991). A complete lack of difference in memory fo non-experts is somewhat counter-intuitive. Simon 10,000 hours, about ten years, of intense practice material is randomized: memory for r dance sequences (Allard & Starkes, random material between experts and and Chase (1973) have proposed that nd study are necessary to reach a high level of expertise. During their practice and study time experts have undoubtedly met with many situations that are close to "random", that is t at contain features not often observed. In the frame of Chase and Simon's (1973b) chunl ing theory, one could expect that the numerous chunks they have stored in LTM allows t em to recognize, more often than weak

4 December 16,1994 Presentation time in chess recall 4 ; / players, chunks that occur adventitiously in random positions, thereby obtaining an advantage in recall. It is also possible that strong players have developed strategies to cope with uncommon situations, which do occur sometimes in their practice. In addition, their familiarity with the materials (for example, in board games, better knowledge of the topology of the board and its attributes) should give them some advantage in comparison with non-experts. In this paper, we re-examine the recall of random material as a function of level of expertise, choosing to emphasize the chess domain mainly because many empirical data are available there. We shall see that there has been some overgeneralization of the empirical findings on recall of random chess positions. It is the goal of this paper to clarify the situation and to study to what extent presentation time affects the relation between skill level and recall. While random positions have been used mainly as a control of subjects' "general" memory capacity, some researchers have studied them for their own stake. Holding and Reynolds (1982) used semi-random positions to study problem solving in chess. In another study, Reynolds (1982) has shown that different degrees of "randomness" may be obtained by manipulating the quantity of control that the pieces have on the center. In the domain of memory, some research has examined the role of presentation time in recall of random positions. Djakov and al. (1927) presented for one minute a "random" position to Masters and to subjects in a non-chessplaying control group, and found that Masters' recall was better than control group subjects'. Two difficulties hamper the interpretation of this study. First, the subjects of the control group did not play chess at all, hence may have been wholly unfamiliar with the material. Second, the position was a chess problem. Chess problems are specially constructed situations where the first goal is to construct esthetic positions and combinations. Although this species of chess is quite different from

5 December 16, 1994 Presentation time in chess recall 5 normal chess games, it produces positions that are far from random. Lories (1987) found an effect of skill with one-minute presentation of the semi-random positions 1 generated by Holding and Reynolds (1982). Finally, Saariluoma (1989) used a procedure similar to Chase and Ericsson's (1982) for the memory of digits, dictating positions at the pace of 2 or 4 seconds per piece. He found that strong players are better in the recall of both game and random positions. While it is agreed that Masters do better with random positions in some extreme situations, like the ones studied by Saariluoma (1989), the general view among students of expert memory has been that there is no difference in recall with the standard presentation time of five seconds (see for example Ericsson & Charness, 1994; Holding, 1985). However, an analysis of data from various experiments in the literature that used recall of random positions as a control condition makes it clear that strong players show rather reliably a superiority over weaker players (see Table 1). Insert Table 1 about here We see that for each experiment, with the exception of Chase and Simon's results (1973a) where the Master performed worse than the novice, the more skilled players do remember more pieces than the less skilled. That these differences were in most cases not Tories' study is difficult to interpret because the positions he used, taken from Holding and Reynolds (1992), are not really random. Some (semantic) constraints were applied in generating the positions, such as no pawn on the first or eighth rank or no piece attacked without being defended. As a matter of fact, a statistical analysis shows that equiprobalitity of White and Black pieces' distribution on the board may be rejected at p<.001 (Gobet, 1993).

6 December 16, 1994 Presentation time in chess recall 6 statistically significant may be explained both by the small size of the effect and the small number of subjects in these experiments. Thus, while randomization does severely reduce the recall of strong players, it does not destroy their superiority over weaker players. Note that this skill difference in recall with random positions is small (roughly one piece per additional 400 ELO points), much less than for the recall of game positions, where an increase of 400 ELO points yields typically an increase of about six pieces. Note also that this skill difference with random positions is predicted by Chase and Simon's (1973b) chunking theory, because Masters, having a larger repertoire of chunks in LTM, are more likely to find rare patterns in LTM than weaker players. What are the processes that allow strong players to perform better than weak players with random positions? In the introduction, we have hinted at three possibilities: (1) a large database of chunks in LTM, occasionally allowing the recognition of rare patterns; (2) the possession of strategies for coping with uncommon positions; (3) better knowledge of the topology of the chessboard. The hypothesis of better knowledge of the topology of the board is supported by Saariluoma's (1991) data, which show that Masters are better than novices at deciding whether a square, denoted by its algebraic notation (e.g. "e4") is White or Black. Following this hypothesis, Masters possess chunks of squares (with or without pieces on them), that may be used in random positions to organize patterns of pieces. For example, Masters may know that the squares "al" and "c2" are at a Knight's distance, and may use this schema of squares to encode the pattern "White Pawn al, Black Pawn c2", even though, because the rules of the game prohibit Pawns on the first rank, they are not likely to have learned this precise chunk through past experience. To study one of these three factors, pattern recognition enabled by a large database of chunks, we can vary the presentation time of the positions. Recognition of chunks

7 December 16, 1994 Presentation time in chess recall 7 should insure strong players' superiority even with short presentation times (say one second), while applying inferential processes strategies and better knowledge of the board should give them an edge over a longer time. Manipulation of the presentation time should reveal the role of pattern recognition in random positions. A similar manipulation with game positions may shed light on the chunking processes, and may offer important data for understanding skilled memory in chess. We have seen that little is known about the effect of presentation time with random positions. In studies of the effects with game positions (Saariluoma, 1984; Lories, 1987), increase in presentation time, not surprisingly, facilitates recall. However, it is difficult to estimate precise functional relations between presentation time and recall, because the studies have provided only a few data points (two in Lories, 1987; at most four in Saariluoma, 1984). Methods Subjects. 21 subjects participated in this experiment, with ELO ratings ranging from 2595 to One subject, rated at 2345, quit the experiment after about 15 minutes, complaining about inability to concentrate. The 20 remaining subjects were assigned to three skill levels: Masters (n=5, mean=2498, sd= 86.6 ), Experts (n=8, mean=2121, sd=100.8) and Class A players (n=7, mean=1879, sd= 69.8). The mean age was 32.9 years (sd = 11.6), the range from 20 years to 70 years. 2When possible, the International rating was used. For Swiss players without international rating (n=10), the Swiss rating was used. Finally, four American subjects were given a corrected rating: American rating - 50.

8 December 16, 1994 Presentation time in chess recall 8 Subjects were recruited at the Fribourg (Switzerland) chess club, during the Biel Festival and in the CMU community. The subjects were paid the equivalent of $10 ($20 for players having a FIDE tide) for their participation. Materials. Nineteen game positions were selected from Bronstein (1979), Euwe (1978), Lisitsin (1958). Moran (1989), Reshevsky (1976), Smyslov (1972) and Wilson (1976) with the following criteria: (1) the position was reached after about 20 moves; (2) White is to move; (3) the position is "quiet" (i. e. is not in the middle of a sequence of exchanges); (4) the game was played by (Grand)masters, but is obscure. The mean number of pieces was 25. Ten random positions were created by assigning the pieces from a game position to squares on the chessboard according to random numbers provided by a computer. Positions were presented on the screen of a Macintosh SE/30, and subjects had to reconstruct them using the mouse. (For a detailed description of the experimental software, see appendix in Gobet & Simon, 1994b.) The screen was black during 2 seconds preceding display of the blank chessboard on which the subject was to reconstruct the position. No indication was given of whether White or Black was playing the next move, and no feedback was given on the correctness of placements. Design. Subjects were first familiarized with the computer display and shown how to select and place pieces on the board. They then received 2 warm-up positions (1 game and 1 random position) presented for 5 sec each. For each duration (1, 2, 3, 4, 5, 10, 20, 30, 60 sec), two game positions and one random position were presented, except that Masters did not receive game positions with presentation times over 10 seconds, for they were expected to reach nearly perfect

9 December 16, 1994 Presentation time in chess recall 9 performance by that time. The presentation times were incremented from 1 second to 60 seconds for about half of the subjects in each group, and decreased from 60 seconds to 1 second for the others. Results Percentage of correct pieces. 1) Game positions3. The upper panel of Figure 1 shows the performance expressed as percentage of pieces replaced correctly. The Masters' superiority is obvious. In 1 sec, they are at about the same level of performance as Experts after 10 sec and perform only slightly worse than Class A players after 30 sec. Note also that, while Class A players and Experts improve their scores monotonically, Masters approach a ceiling rapidly, after about 2 sec. The three skill levels differ statistically significantly at presentation times of 10 sec or less: F(2,16)=27.63, jk.001; so do Experts and Class A players with presentation times above 10 sec: E(U3)=10.92, <.01. Insert Figure 1 about here How do Masters achieve their superiority? Do they have only a perceptual advantage, already evidenced at short presentation times and produced by the availability of more and bigger chunks in STM, or are they also able to profit from the supplementary presentation time to encode information into LTM (a "learning" advantage)? We have fitted some simple functions to the data whose parameters can shed light on these questions. A 3 One Class A player refused to recall positions (game or random) below 5 seconds. One Grandmaster refused to recall any random position. Their (partial) results are included in our analysis.

10 December 16, 1994 Presentation time in chess recall 10 power law (average r2 for Experts and Class A players4 =.67) and a logarithmic function (average r2 =.65) fit the data reasonably well, better than a simple linear regression line (average r2 =.58). However, the best fit was provided by the logistic growth function, P = Be-c(M) (1) where P is the percentage of correct answers, (100-B) is the percentage memorized in 1 second, c a constant, and t the presentation time, in seconds. The average r2 for Experts and Class A players is.69. This function supposes that the rate at which additional pieces are stored after one second is proportional to the number of pieces not already retained. Table 2 gives the parameters fitting the data best, for the three skill levels, and Table 3 indicates the goodness of fit. One sees that both (100-B), the percentage learned in 1 sec, and the subsequent learning rate, c, increase with skill. The parameter c increases by a factor of 2 from class A to Experts, and by a factor of 15 from class A to Masters. The parameter (100-B) increases by a factor of 1.3 from class A to Experts, and a factor of nearly 3 from class A to Masters. The function does not account as well for the Masters' results as for the others', for the Masters have a relatively wide spread of scores at 10 sec, where they get an average of 92.4 %. At 10 sec, two Masters performed at about 85%, while the three others were above 96%. Using only the data for the latter three players, we get a better fit (r2 =.54), with B = and c = 0.72 (the latter, more than 20 times the rate achieved by Class A players). Insert Table 2 about here 4Because of the ceiling effect shown by the Masters, these functions do poorly with this skill group.

11 December 16, 1994 Presentation time in chess recall 11 2) Random positions. The three skill levels differ significantly for short presentation times (ten seconds or less): F(2,15)=7.74, jk.005, as well as for long presentation times (more than ten seconds): F(2,16)=14.36, <.001. We have fitted the data from the random positions with the same growth function (Figure 1, lower panel). The best fitting parameters are shown in Table 2, lower panel, and the goodness of fit in Table 3. Again, skill levels differ both in the amount of information acquired quickly (100-B) and in the continuing rate of acquisition (c). The parameter c doubles from class A to Experts, and triples from class A to Masters. The parameter (100-B) increases by a factor of 1.5 from class A to Experts, and doubles from class A to Masters. Notice that the relative superiority after 1 second of Masters' over Experts and Class A players is almost the same for game positions and random positions; but the superiority of Masters in learning rate (percentage of remaining pieces learned) for longer intervals is much greater for game positions than for random positions. These results indicate that strong players achieve higher percentages of recall both because (1) they perceive and encode a more information in the first 1 second of exposure and (2) they improve thereafter at a faster rate, recognizing more and bigger chunks. Both B and c are larger for game than for random positions. For Experts and Class A players, c is about six times as large for game as for random positions, while (100-B) is a little more than 2 times as large. For Masters the ratio for c is nearly 25, and for (100-B) about 3.5, confirming the view that chess Masters use their experience of the domain for recalling meaningful board positions. Chunks. We have also analyzed the distributions of chunk sizes. As in Chase and Simon (1973a), chunks are defined as sequences of pieces having corrected latencies of less than 2

12 December 16, 1994 Presentation time in chess recall 12 seconds between successive pieces. Pieces placed individually are not classified as chunks. Chase and Simon (1973a), as well as Gobet and Simon (1994b) have shown that the 2- second boundary is the result of converging evidence both from the distribution of latency times in a copy task and from the contrast of the many within-chunk chess relations with the relatively few between-chunk chess relations (see also Gobet and Simon, 1994c, for an in-depth discussion of the operational definition of chunk). 1) Game positions. Our first variable is the size of the largest chunk per position. Figure 2 shows that Masters reconstruct large chunks, even after a one-second view of the board, and that the size of the largest chunk does not increase much with additional presentation time. Experts' largest chunks start with about 9-10 pieces, and increase logarithmically up to about 17 pieces at 60 seconds. A comparable increase may also been seen with class A players, who start, however, with smaller maximal chunks (about 4-5 pieces). Statistical tests indicate that the three groups differ for the presentation times equal to or below 10 second: F(2,16) = 6.30, =.01. Experts and Class A players also differ with longer presentation times: F(l,13) = 6.11, p. <.05. Insert Figure 2 about here The second variable, the number of chunks, shows two different patterns, the first displayed by Masters and Experts, the second, by Class A players. Masters' number of chunks increases from 2.9, at one second to 4.2 at four seconds, and then decreases to 3.3 at 10 seconds. Experts start with 2.2 chunks at a presentation time of 1 second, show a maximum with 4.5 chunks at 10 seconds, and then decrease to 2.9 at 60 seconds. Class A players increase the number of chunks from 2.2 at 1 sec to 5.4 at 60 seconds. The three skill levels do not differ reliably with presentation times equal to or below 10 seconds

13 December 16, 1994 Presentation time in chess recall 13 [F(2,16) = 0.40, ns.]. By contrast, Experts and Class A differ with presentation times longer than 10 seconds [F(l,13) = 8.34, p <.05]. 2) Random positions. For the largest chunks, we see (1) that all groups increase in a logarithmic fashion with additional time and (2) that the stronger players have larger maximal chunks than weaker players (see Figure 2, lower panel). The difference between the three skill levels is not statistically significant with PT equal to or below 10 seconds [F(2,15) = 2.05, ns], and is marginally significant with PT longer than 10 seconds [F(2,16)=3.41, =.058]. The standard deviation is high within each skill level (average sd = 2.0, 2.3 and 2.9 pieces for Masters, Experts and class A players, respectively). For all skill groups, the number of chunks increases as a function of presentation time. The number of chunks with a presentation time of 1 sec and 60 sec is 1.7 and 3.3, respectively, for Masters, 1.4 and 4.5 for Experts, and 1.2 and 4.3 for Class A players. The Skill levels do not differ significantly over the 9 presentation times [ (2,15) = 0.32, ns]. In summary, data on chunks in random positions show that stronger players tend to place larger chunks and that the size of the largest chunk tends to increase with additional time. The number of chunks increases also with additional time, but there is no difference in number due to chess skill. Errors. 1) Game positions. The number of errors of omission correlates (negatively) with the presentation time (r, = -0.43, JK.001). With 1 sec, Masters miss 6.1 pieces by omission; with longer presentation times, they place the same number of pieces as in the stimulus position. For Experts, the number of errors of omission is 12.6 with 1 sec, then decreases logarithmically to end up close to zero with 60 sec. Finally, Class A players commit 16.5 errors of omission with 1 sec and close to zero with 60 sec. The three skill levels differ

14 December 16, 1994 Presentation time in chess recall 14 reliably with PT less to or equal to 10 seconds [ (2,16)=7.62, =.005]. The difference between Experts and Class A players reaches significance with PT longer than 10 seconds [E(U3)=4.49, =.054]. The three skill levels present different patterns for errors of commission. Masters make fewer than 3 errors from 1 sec to 4 sec, and then reduce this number to an average of 1.25 with 5 and 10 sec. For Experts the numbers of errors of commission decrease more or less logarithmically from 5.5 with 1 sec to 0.5 with 60 sec. Finally, the number of errors of commission is constant for Class A players from 1 second to 30 seconds (an average of 4.5). Even with 60 seconds, Class A players commit on average 2.8 commission errors. The skill differences are not statistically significant with PT less or equal to 10 seconds [F(2,16)=1.98, ns]; Experts and Class A players differ with PT longer than 10 seconds [F(l,13)=8.35, <.05]. 2) Random positions. For all skill levels, the number of errors of omission is high with short presentation times (21.4 pieces, on average, with 1 sec), and decreases logarithmically with longer presentation time. Masters tend to produce fewer errors of omission than Experts, and Experts fewer than Class A players. These differences are larger with longer presentation times. For example, the numbers of errors of omission at 10 sec are 14.7, 15.1 and 16.5 for Master, Experts and Class A players, respectively, while the corresponding numbers at 60 sec are 4.5, 6.6 and 9.0. The three groups do not differ with PT equal to or less than 10 seconds [F(2,15) = 1.12, ns], they differ with PT longer than 10 seconds [F(2,16) = 4.17, p. <.05]. Finally, the negative correlation of errors of omission with percent correct is strong (r = -0.74, jk.ool). All skill levels make more errors of commission with longer presentation times. With 1 sec, the average number of errors of commission is 2 pieces; with 60 sec, it is 5.5

15 December 16, 1994 Presentation time in chess recall 15 pieces. In general, Masters tend to make fewer errors of commission than Experts and Class A players, though the difference is not statistically significant [F(2,16 = 1.14, ns]. Discussion Saariluoma (1989), using auditory presentation at a rate of 1 piece per 2 seconds (a total of about 50 seconds per position), found that stronger players achieve a better recall of random positions. Lories (1987) found the same effect of skill with semi-random positions and visual presentation for 1 minute. Both results indicate that skilled players have better memory for random positions than weaker players when presentation time is sufficiently long. Our results confirm these findings and show also that, surprisingly, there is a difference in recall for random positions with rapid presentation. We note first that this difference is small (about 20% between Masters and Class A players at a presentation time of five seconds) in comparison with the difference for game positions (60% percent in the data of this experiment). But still, there is a difference. The growth curve, of a type that has been shown to fit a wide variety of learning and memory data (Lewis, 1960), fits our data quite well. The difference of intercept between players at different Skill levels (the 1- B parameter) is predicted by the Chase- Simon theory: strong players recognize larger chunks more rapidly, and is confirmed by our data on the size of the largest chunk. Chase and Simon (1973,a) found that, for game positions, stronger players place both larger chunks and more chunks (remaining within the 7±2 chunk size of the STM). Our data replicate this finding, with the qualifications that the difference in number of chunks tends to disappear with longer presentation times and that the chunk size of our subjects was larger than theirs'. With random positions, we found that strong players placed both larger chunks and more chunks.

16 December 16,1994 Presentation time in chess recall 16 The difference in the c parameter in the game positions means that strong players not only perceive (and retain) more information during the first seconds of exposition, but that they also recognize and/or learn more or larger patterns afterwards. As the total numbers of chunks held and recalled, at all level of skills and for all presentation times, appear to be generally within the short-term memory limit of 7±2, it may not appear that many (if any) new chunks must be acquired in LTM during the experiment. We must be cautious about this point, however, for G. A. Miller's (1956) traditional "magical number" for STM capacity is based on data for auditory, not visual, stimuli, and such estimates as we have for visual memory suggest a smaller capacity, perhaps not more than 3 chunks (Zhang & Simon, 1984). The rapid increase in recall during the first seconds (perhaps 2 or 3 seconds for Masters and 5 or 10 for Experts) most likely reflects the time required to notice successive patterns on the board. As we know that a single act of recognition of a complex pattern requires 0.5 sec or more (Woodworth & Schlossberg, 1961, p. 32 to 35), it is likely that subjects, after the initial recognition of a pattern, spend some time scanning the board searching for additional familiar patterns that are present, the less practiced subjects taking longer to discern patterns than the more expert. The initial differences among the various skill levels, reflected in the values of (1-B), would then largely reflect the sizes of their initial chunks, while the differences in c would largely reflect the rates at which new chunks were noticed, or additional pieces added to chunks. Beyond the first 5 or 10 sec, there is some opportunity to fixate new chunks or to augment chunks that are already familiar. Estimates of fixation times in verbal learning experiments suggest that it may take about 8 sec to add an element to an existing chunk or to form a new chunk (Simon, 1976). However, to account for the differences in the magnitude of c at different skill levels, we have to assume that experts and Masters do not usually add single pieces to chunks, but combine smaller chunks into larger. This would

17 December 16,1994 Presentation time in chess recall 17 account for the gradual decrease in the number of chunks recalled by Masters after 4 sec and by Experts after 10, while the average chunk sizes continued to increase. But research on expert memory in recent years has revealed another mechanism that is available to Masters and Experts. They can, by practice and training, acquire retrieval structures in LTM containing not only the usual kinds of information that constitute chunks, but also containing "slots" or variables with which new information can be associated at a rate of about one item per second (Chase & Ericsson, 1982; Gobet & Simon, 1994a). In the case of chess, the retrieval structures would mainly be templates representing familiar opening positions after 10 or 15 moves. When a game position is recognized (say, as a Tarrasch defense with White attack on the King's side), the corresponding stored representation of the chess board provides specific information about the location of a number of pieces (perhaps a dozen) together with slots that may possess default values ("usual" placements in that opening) that may be quickly revised. This accessibility to more powerful retrieval structures would explain the large initial chunks recalled by Masters in game positions and, to a lesser extent, Experts. For templates, cued by salient characteristics of the position, would be likely to be recognized early and quickly enlarged by filling slots and altering incorrect default values. The template mechanism also explains why the advantage of Masters over weaker players is much more pronounced in game positions, which typically evoke large templates, than in random positions, which do not correspond to any familiar templates and contain only small chunks at best (see Gobet and Simon, 1994,a, for a more detailed discussion of chess templates). Notice, in Table 2, that the values of 1-B and c (and especially the latter) for Masters in random positions are substantially lower than the values for class A players in game positions.

18 December 16, 1994 Presentation time in chess recall 18 Summary We can now summarize our explanation of the experimental findings. The duration of the presentation will determine: (1) accessibility of the template (core + unconnected default values); this occurs in the same latency range as recognition processes (hundreds of msec); (2) ability to correct default values and instantiate other slots (a few seconds); (3) ability to elaborate the template (at least several minutes, possibly hours). On the basis of the assumed parameter values, we expect the following results in game positions for Masters, who are the most likely to possess many templates and chunks: the size of the largest chunks (corresponding to the templates) will increase during the first seconds and then will stay more or less constant. This prediction is supported by our data; the size of Masters' largest chunks increases slightly between presentation times of 1 second (13 pieces) and 4 seconds (16.5 pieces), and then seems to stay constant (16.1 pieces with 10 sec). Combining this with the nearly constant mean number of chunks, for Masters, for times less than 10 seconds (2.9 with 1 sec, 4.2 with 4 sec and 3.3 with 10 sec), we speculate that 1 sec does not allow additional chunks to be inserted in the template, but that a few additional seconds do. We began this paper by reviewing several studies using random positions as a control task, with a presentation time ranging from five to ten seconds. We found that, contrary to the general opinion, the recall of random position varies somewhat as a function of chess skill. This skill difference was also found in our experiment, where the presentation time was systematically varied from one second to 60 seconds. Although it was larger with long presentation times, the difference was still present with short presentation times. The absolute differences in percentage correct between skill levels is smaller than for game positions, but still statistically significant. We showed then that recall performance as function of duration of presentation may be fitted well with an exponential growth function, both for game and random positions.

19 December 16,1994 Presentation time in chess recall 19 Strong players differ from weaker players both in the percentage of correct pieces they recall in one second and the rate at which asymptote is approached. We discussed the application of the template theory, an extension of the chunking theory (Chase and Simon, 1973b) to these data. As in the chunking theory, it is proposed that chunks are accessed in LTM through an discrimination net. In addition, some chunks that are met frequently in Masters' practice evolve into more complex structures, which we call templates and which have slots that may be filled in rapidly. We propose that templates play an important role in Masters' recall of chess positions taken from games. The superiority of strong players with random positions is very largely explained by their larger repertoire of (small) chunks. The remaining variance may be accounted for by their better knowledge of the topology of the chess board, and by general heuristics. As with chess, most studies on experts memory have used a minimal number of subjects (Charness, 1988; Gobet, 1993). It is a question for future research whether the lack of difference between experts and non-experts found in various domains of expertise when random material is genuine or is due to the low power of the experimental design used in these studies. Taken together with results on the memory for sequence of pitch symbols (Sloboda, 1976) and for dance sequences (Allard & Starkes, 1991), this paper indicates that the relation between expertise and "meaningless" material taken from the domain of expertise may be more complex than has been described previously, but that the notion of chunking is able to account for most of the phenomena, quantitatively as well as qualitatively.

20 December 16, 1994 Presentation time in chess recall 20 References Allard, F., & Starkes, J. L. (1991). Motor-skill experts in sports, dance and other domains. In K. A. Ericsson (Eds.), &, J. Smith, Toward a general theory of expertise. Prospects and limits. Cambridge: Cambridge University Press. Allard, F., Graham, S. & Paarsalu, M. E. (1980). Perception in sport: Basketball. Journal of Sport Psychology, 2, Anderson, J. R. (1990). Cognitive Psychology and Its Implications. New York: Freeman. Bronstein, D. (1979). Zurich International Chess Tournament Translated from the second Russian edition by Jim Marfia. New York: Dover Publications. Charness, N. (1979). Components of skill in bridge. Canadian Journal of Psychology, 33, Charness, N. (1988). Expertise in chess, music and physics : A cognitive perspective. In Obler, L. K. & Fein D. A. (Eds.) The exceptional brain : The neuropsychology of talent and special abilities. New-York, Guilford Press. Chase, W. G., & Ericsson, K. A. (1982). Skill and working memory. In G. H. Bower (Ed.), The psychology of learning and motivation (Vol. 16). New York: Academic Press. Chase, W. G., & Simon, H. A. (1973a). Perception in Chess. Cognitive Psychology, 4, Chase, W. G., & Simon, H. A. (1973b). The mind's eye in chess. In W. G. Chase (Ed.), Visual information processing. New York: Academic Press. de Groot, A. D. (1946). Het denken van den schaker. Amsterdam, Noord Hollandsche. de Groot, A. D. (1978). Thought and Choice in Chess. The Hague: Mouton Publishers.

21 December 16, 1994 Presentation time in chess recall 21 Djakow, I. N., Petrowski, N. W., & Rudik, P. A. (1927). Psychologic des Schachspiels. Berlin: de Gruyter. Egan, D. E., & Schwartz, E. J. (1979). Chunking in recall of symbolic drawings. Memory & Cognition, 7, Engle, R. W., & Bukstel, L. (1978). Memory processes among bridge players of differing expertise. American Journal of Psychology, 91, Ericsson, K. A., & Charness, N. (1994). Expert Performance. Its Structure and Acquisition. American Psychologist, 49, Gobet, F. (1993). Les memoires d'un joueur d'echecs. Ph. D. Thesis. Fribourg (Switzerland): Editions Universitaires. Gobet, F. & Simon, H. A. (1994a). Templates in Chess Memory: A Mechanism for Recalling Several Boards. Complex Information Processing Paper #513, Carnegie Mellon University, Pittsburgh, PA Gobet, F. & Simon, H. A. (1994b). Expert Chess Memory: Revisiting the Chunking Hypothesis. Complex Information Processing Paper #515, Carnegie Mellon University, Pittsburgh, PA Gobet, F. & Simon, H. A. (1994c). Recall of Random and Distorted Chess Positions: Implications for the Theory of Expertise. Submitted for publication. Holding, D., & Reynolds, R. (1982). Recall or evaluation of chess positions as determinants of chess skill. Memory and Cognition, 10, Lesgold, A. (1988). Problem Solving. In R. J. Sternberg, &, E. E. Smith, The psychology of human thought. Cambridge: Cambridge University Press. Lewis, D. (1960). Quantitative Methods in Psychology. New York: McGraw-Hill. Lisitsin, G. M. (1958). Strategia i taktika shahmat. Moskva: Fisikultura i sport.

22 December 16,1994 Presentation time in chess recall 22 Lories, G. (1987). Recall of random and non random chess positions in strong and weak chess players. Psychologica Belgica, 27, Me Keithen, K. B., Reitman, J. S., Rueter, H. H., & Hirtle, S.C. (1981). Knowledge organization and skill differences in computer programmer. Cognitive Psychology, 13, Miller, G. A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63, Moran P. (1989). A. Alekhine: agony of a chess genius. Jefferson, N.C.: McFarland & Co. Reitman, J. S. (1976). Skilled perception in go: deducing memory structures from inter- response times. Cognitive Psychology, 8, Reshevsky, S. (1976). The Art of Positional Play. New York: McKay. Reynolds, R. I. (1982). Search heuristics of chess players of different calibers. American Journal of Psychology, 95, Saariluoma, P. (1984). Coding problem spaces in chess: A psychological study. Commentationes scientiarum socialium 23. Turku: Societas Scientiarum Fennica. Saariluoma, P. (1989). Chess players' recall of auditorily presented chess positions. European Journal of Cognitive Psychology, 1, Saariluoma, P. (1991). Aspects of skilled imagery in blindfold chess. Acta Psychologica, 77, Simon, H. A. (1976). The Information Storage System Called "Human Memory". In M. R. Rosenzweig and E. L. Bennett (Eds.), Neural Mechanisms of Learning and Memory. Cambridge: MA: MIT Press. Simon, H. A., & Chase, W.G. (1973). Skill in Chess, American Scientist, 61,

23 December 16, 1994 Presentation time in chess recall 23 Sloboda, J. A. (1976). Visual perception of musical notation: Registering pitch symbols in memory. Quarterly Journal of Experimental Psychology, 28, Smyslov, V. V. (1972). My best games of chess. New York: Dover. Vicente, K. J. & de Groot, A. D. (1990). The Memory Recall Paradigm: Straightening Out the Historical Record, American Psychologist, February, Wilson, F. (1976). Lesser-known chess masterpieces: New York: Dover. Wolff, A. S., Mitchell, D. H. & Frey, P. W. (1984). Perceptual skill in the game of Othello. Journal of Psychology, 118, Woodworth, R. S., and Schlossberg, H. (1961). Experimental psychology (revised edition). New York: Holt, Rinehart and Winston. Zhang, G., & Simon, H. A. (1985). STM capacity for Chinese words and idioms: Chunking and acoustical loop hypothesis. Memory and Cognition, 13,

24 December 16, 1994 Presentation time in chess recall 24 Authors note Preparation of this article was supported by grant no from the Swiss National Funds of Scientific Research to the first author and grant no DBS from the National Science Foundation to the second author. Correspondence concerning this article should be addressed to Herbert A. Simon, Department of Psychology, Carnegie Mellon University, Pittsburgh, Pennsylvania, The authors extend their thanks to Howard Richman, Jim Staszewski and Shmuel Ur for valuable comments on parts of this research.

25 December 16, 1994 Presentation time in chess recall 25 Table 1. Number of pieces correctly replaced for random positions as a function of skill, in various studies. Except Prey andadesman (1976), who used a presentation time of 8 sec., and Gold and Opwis (1992), who used a presentation time of 10 sec., all studies use a presentation time of 5 sec. Source N of subjects Rating (in Elo points)3 < >2400 b Chase & Simon (1973a) b Frey & Adesman (1976), 8 sec c Saariluoma (1984), exp. 3 c Saariluoma (1984), exp. 4 d Saariluoma (1985), exp. 3 c Saariluoma (1990), exp. 1 ce Saariluoma (1990), exp. 2 ce Gold & Opwis (1992), 10 sec c Gobet & Simon (1994a), exp. 1 c Gobet & Simon (1994c), exp. 1 c Gobet & Simon (1994c), exp a The group mean rating is used for classification b USCF rating is used c International rating, or equivalent, is used d Finnish rating is used e The difference between skill levels is significant at the.05 level.

26 December 16, 1994 Presentation time in chess recall 26 Table 2. Recall percentage as a function of time presentation. Parameter estimation of the function P = Be~ c(t ~ 1) Game positions Parameter Estimate ASE J 95% Confidence Interval Lower Upper Class A Experts Masters B c B c B c Parameter Estimate Random positions 95% Confidence ASE 1 Lower Interval Upper Class A Experts Masters B c B c B c Asymptotic Standard Error

27 December 16, 1994 Presentation time in chess recall 27 Table 3. Recall percentage as a function of time presentation. Goodness of fit obtained with the function P = Be~ c(t ~ 1) and the parameters estimated In Table 2. Goodness of fit r2 using all data points r2 using group means Games Random Games Random Class A Experts Masters

28 Figure captions Figure 1. Percentage of correct pieces as function of presentation time and chess skill for game positions (upper panel) and random positions (lower panel). The best fitting exponential growth function is also shown for each skill level. Figure 2. Largest chunk (in pieces) per position as function of presentation time and chess skill for game positions (upper panel) and random positions (lower panel).

29 Game positions ' it I I I- > i i * MASTERS o EXPERTS postions 100 * MASTERS o EXPERTS. CLASS.JL Ecesa±atioi tine (in sec.) T ~

30 Game positions CD O CD Q. -t i- 15 j*: c 13 O -4 ' CO CD 0) Presentation time sir Masters A Experts j Class A Random positions CD O 'CL 02,._ 15 XL 5 -t > CO CD P CO 10 0 * 6- -ft- HA S v W Masters Experts Class A Presentation time