Adriaan de Groot's 1944 test of chess memory, by the numbers

Four players and a few seconds

In 1944 Adriaan de Groot showed Max Euwe a chess position and took it away five seconds later. The position came from a game between Rohacek and Rabar, after White's 20th move, with 22 pieces on the board. Euwe, world champion from 1935 to 1937, then dictated where every piece stood. He got all 22 right.

De Groot, a master himself, took the same test, added one pawn that was not there, and scored 21 points. A. Fast, the 1942 champion of Utrecht, placed 17 pieces correctly but judged the material equal when it was not, and scored 16. G. P. Hauer, a weaker class player, scored 9.

Retellings disagree about the exposure time and the percentages, so the figures below come from de Groot's own book.

A master who studied masters

De Groot played for the Netherlands at the Chess Olympiads of 1937 and 1939. Between 1938 and 1943 he wrote down what players said as they thought aloud while choosing a move. His subjects included the grandmasters Keres, Alekhine, Flohr, Fine, Euwe, and Tartakower.

By his counts, grandmasters did not look further ahead than expert players, and they did not examine more moves. "The master does not necessarily calculate deeper," he wrote. De Groot suspected that the difference showed in the first seconds of looking at the board, and he designed the 1944 experiment to test that idea.

What the 1944 experiment measured

One player stood for each class. Euwe represented the grandmasters, de Groot the masters, Fast the experts, and Hauer the weaker class players.

Each position came from a master game and stayed in view for 2 to 10 seconds, with one exposure of 15 seconds. The two weaker subjects got 3 to 4 seconds on the shortest trials so that they would not score zero. Each subject was asked to take about half a minute to organize what he retained. Euwe and de Groot then dictated the position from memory, and Fast and Hauer set it up on a board.

The scoring gave one point for each correct piece and took points off for pieces added, dropped, or shifted. De Groot discarded two positions, the first in the series and one with a timing fault, and counted fourteen, which ranged from 7 to 26 pieces. Out of 234 possible points, the four subjects scored as follows.

Euwe scored 217 points, or 93%, with five positions perfect.

De Groot scored 217 points, or 93%, with four perfect.

Fast scored 158 points, or 68%, with none perfect.

Hauer scored 119 points, or 51%, with none perfect.

De Groot then set aside two trials with long exposures, 15 and 7 seconds, and two that a lapse in concentration had spoiled. In the remaining ten, with intended exposures of 2, 3, or 5 seconds, the mean scores were 93.0%, 92.6%, 72.3%, and 51.1%.

Both tables are his, which is probably why retellings give the expert either 68% or 72%. The exposure was never a fixed five seconds.

De Groot cared most about the gap in the middle, which he called "the gulf that separates the master from the non-master." His explanation was that a master does not store 22 separate pieces. He perceives a large group of pieces as one unit, because he knows how that group arises and what it is for.

A few such units cover the board, and on de Groot's account a weaker player has fewer of them. Later researchers called the units chunks.

From a Dutch thesis to random boards

De Groot presented the work in 1946 in his doctoral thesis at the University of Amsterdam, Het denken van den schaker. Mouton published the English edition, Thought and Choice in Chess, in The Hague in 1965.

In 1973 William Chase and Herbert Simon reran the test at Carnegie Mellon with a master, a Class A player, and a beginner. They fixed the exposure at 5 seconds. Their middle-game positions had 24 to 26 pieces, and the master recalled about twice as many pieces as the Class A player.

They videotaped each reconstruction and treated a pause longer than 2 seconds as the boundary between two chunks. The master's first chunk averaged 3.8 pieces against 2.6 for the Class A player, and he produced 7.7 chunks per position against 5.7. Of his 77 chunks across fourteen positions, 47 contained a pawn chain, and Simon and Chase counted 10 castled king positions.

Their addition was a control, the same pieces placed on random squares. Simon and Chase reported that every player then recalled about three or four pieces, fewer than the beginner managed on real positions. They noted that W. Lemmens and R. W. Jongman had found the same result in the Amsterdam laboratory and never published it.

Chase and Simon's own introduction presents the random-board result as de Groot's, and many later accounts repeat that. His book reports no random-board trial.

What later research changed

Textbooks took that result to mean a master has no advantage at all on meaningless boards. In 1996 Fernand Gobet and Herbert Simon checked that reading against thirteen experiments with exposures of 10 seconds or less. In twelve of the thirteen, the strongest group recalled more random pieces than the weakest. The exception was Chase and Simon's own study, where the master did worst.

The advantage is small. Gobet and Simon put it at about one extra piece per 400 Elo points on random boards, against about five extra pieces on game positions. In a 1998 review, Gobet gave the averages at 5 seconds as 5.5 random pieces for masters and 2.6 for players below class B.

The explanation leaves de Groot's idea standing. A player with a very large store of patterns sometimes finds one by accident in a jumble. Random boards shrink the expert's edge without removing it. Gobet and Simon added that small samples hide so small an effect, and the 1973 study had three subjects.

Try de Groot's test

Set Memory Chess to 22 pieces and 5 seconds. That matches the size of de Groot's Rohacek against Rabar position and the time Euwe had to look at it. Rebuild the board and work out what share of the pieces you placed correctly. About half is where Hauer finished, about 70% is where Fast finished, and 93% is what Euwe and de Groot averaged.

The comparison is rough, because de Groot also took points off for errors. Then check which pieces you kept. They probably came in groups, such as a pawn chain or a castled king.