Author: Graham Laight
Date: 05:14:26 05/10/01
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On May 10, 2001 at 08:01:16, Graham Laight wrote: >On May 10, 2001 at 05:46:24, Jesper Antonsson wrote: >>Great, then, hopefully, this is *the* point where we disagree. Now, the 3-fold >>repetition rule and 50-move rule are not mandatory, but they are there. How do >>you handle these positions in the search in Crafty (your "algorithm")? I would >>assume that you label them a draw and search no deeper. Perhaps you do not >>always *claim* the draw when such a position is at the root, but, as I said, you >>probably treat them as draws in the search. This is because mini-max "assumes" >>best play from both sides, and either the position is a draw whether 3/50 rules >>are used or not, in which case it is safe to return draw-score, or the player >>that is losing, using "best play", should claim the draw, in which case minimax >>should also return a draw score. >> >>So, from a search perspective, or solving-chess-perspective, we should treat >>these positions as draws, and when we do, a "good" chess algorithm in theory >>stops it's exponential behaviour at a certain depth. > > >Given the application of the 50 move rule, one can easily estimate an absolute >limit to the number of possible chess games. > >Number of pieces which can be taken: 30 >Number of possible pawn pushes: 6 * 16 = 96 >Total number of 50 move rule avoidence events: 96 + 30 = 126 >Maximum possible number of moves: 126 * 49 = 6,174 >Maximum possible number of plies: 6,174 * 2 = 12,348 This also allows us to estimate when chess will be fully solved (all possible chess games generated). Max possible plies in a chess game: 12,348 Number of years per increase of 1 in search ply depth: 3 (just a guess, I admit) Number of years to wait: 3 * 12,348 = 37,044 Actual year: 37,044 - 2001 = 35,043 This is, of course, assuming that Moore's law continues to hold (which is not a safe assumption based on only 35 years of history). -g >Average number of possible moves per position: 37 (you could work with a maximum >possible if you prefer) >Maximum possible number of games: 37 ^ 12,248 >= 1.4 e+19,364 > >-g
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