Author: Gareth McCaughan
Date: 15:15:07 10/11/01
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Robert Hyatt wrote: > I believe Lewis published some of them quite some while back. But the > thing he published was mainly "deepest mate" and the like. I didn't follow > this very closely, and only remember Wendroff asking for "my contact" up at > Cray in trying to set the time up... The book "Games of No Chance" (edited by Richard Nowakowski, published by Cambridge University Press in the UK and maybe by MSRI Publications in the US) contains an article by Lewis Stiller entitled "Multilinear algebra and chess endgames". It contains a table giving, for each of 41 pawnless 6-piece endgames, the number and percentage of positions won for White, the maximum distance-to-win of any position with those pieces (among those that are wins for White), and the number of mutual zugzwang positions (i.e., positions where WTM draws and BTM loses). The class with the longest DTM is KRN v KNN. 78% of these positions are won for White; the longest DTM is 243 moves; there are 18176 mutual zugswangs. One position (perhaps the only one, up to symmetry; it's not clear) that takes the maximal number of moves is: [D]6N1/5KR1/2n5/8/8/8/2n5/1k6 w - - There is a position in KQR v KQR which is won for White but requires 92 moves to win. KRB v KNN, unlike KRN v KNN, is almost always won (96% of positions, the others presumably being ones where White has a piece en prise or something of the sort), but its longest DTM is 223 moves. (I use "won" to mean "won if the 50-move rule is temporarily repealed".) The book also contains some interesting mathematical analysis of a few chess endings. It's of more interest for mathematicians than for chess players, though. :-) As an example, they explain why this position [D]8/1p5p/p7/4k3/4Pp2/5K1P/PP5/8 w is a win for whichever player moves first. -- g
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