Author: Jesper Antonsson
Date: 02:46:24 05/10/01
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On May 09, 2001 at 18:28:13, Robert Hyatt wrote: It seems I cannot restrain myself, I just have to answer one more time. :-) >I am not sure what you mean. There is no "linear" list of chess positions >in any way I can think of using "linear". The complexity issue simply asks >"how hard will it be to compute this function if I increase the number of >inputs by 1?" In the case of chess, an "input" is a "ply"... Yes, agreed. >How do you define "deep enough?" If we could prove that white wins within 80 >plies, then that would do it. but so far, we have not proven that. And since >the game isn't over until mate or stalemate occurs, unless the two players >decide to call it a draw for various reasons, I'm not ready to say it is >"finite" until someone offers reasonable proof that it is... 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.
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