Thursday, June 23, 2011

Math and Chess -- and Euwe Mystery

Occasionally, I used this blog for something that is not, strictly speaking, related to Jewish chess history. This time we make a foray into mathematics and chess, in the person of Dr. Euwe, who was, as is well known, not Jewish -- but a mathematician as well as the world champion 1935-1937. He was also a good friend of Israel and of Jews, as this blog (among many other places) shows.

In Martin Gardner's The Magical Numbers of Dr. Matrix (New York: Dorset, 1985), a collection of essays on recreational mathematical subjects, the following appears (p. 242-3, bracketed comments mine):
Max Euwe, a former world chess champion, was among the first to recognize that the Thue sequence [a sequence of 0s and 1s discovered by the mathematician Thue in 1912] provides a method of playing an infinitely long game of chess. The so-called German rule for preventing such games declares a game drawn if a player plays any finite sequence of moves three times in succession in the same position. Two players need only create a position in which each can move either of two pieces back and forth, regardless of how the other player moves his two pieces. If each now plays his two pieces in a Thue sequence, neither will ever repeat a pattern of moves three times consecutively.
On the internet I found the following:

In 1929 [Euwe] published a mathematics paper in which he constructed [sic] an infinite sequence of 0's and 1's with no three identical consecutive sub-sequences of any length. He then used this to show that, under the rules of chess that then were in force, an infinite game of chess was possible. It had always been the intention of the rules that this should not be possible, but the rule that a game is a draw if the same sequence of moves occurs three times in succession was not, as Euwe showed, sufficient. (
This implies that the so-called 'three-fold repetition' rule was in 1929 written in the 'same sequence of moves occurs three times in succession' language, and that the 50-move rule is ignored. The reason is that if the threefold repetition (as today) no longer has to be in succession, but  merely having to occur, or else the 50-move rule applies, both trivially make chess a finite game, the first because there is a limited number of captures and/or pawn moves, the second because there is a limited number of legal (or for that matter illegal) chess positions that can be repeated.

But don't the 50-move rule and the "modern" (i.e., not in succession) threefold repetition rule go back, at least, to the beginning of the 20th century? Surely Euwe of all people would not make a mistake about the rules of the game in a published work! Can any reader resolve the inconsistency? Perhaps the original paper would clarify matters. 


Sorry about the crazy character breaks. 

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