Author: Graham Laight
Date: 09:34:52 05/11/01
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On May 11, 2001 at 09:47:34, Robert Hyatt wrote: >On May 10, 2001 at 09:43:18, Graham Laight wrote: > >>On May 10, 2001 at 09:27:58, Robert Hyatt wrote: >> >>>On May 10, 2001 at 00:35:50, Uri Blass wrote: >> >>>>10^50 is an upper bound of the number of the legal positions(2 positions are the >>>>same if the pieces are in the same places and both sides have the same right to >>>>castle and the same rights to capture by the en passant rule). >>>>After less than 10^50 moves the same position happens twice >>>> >>>>If you can mate in 10^50 moves the game contains a repetition of the same >>>>position twice. >>>>If you can win with repetition you have a shorter win without repetition. >>>> >>>>It means that the problem of finding if a position is a draw or a forced mate is >>>>solvable in a finite time even without the 50 move rule >>>> >>>>Uri >>> >>> >>>Actually 10^50 simply means chess will never be solved. That is getting very >>>close to the number of atoms in the universe. How are you going to store that >>>information? >> >>No need to. Franz Morsch's Saitek Kasparov Travel Champion 2100 plays a strong >>game with only 2 Kb of memory. Much of that space will be needed for storing >>settings + move history. Clearly, it's not storing much information about the >>game tree. >> >>>and I am not convinced 10^50 is the right number. There are positions and there >>>are positions... the history (or move path) to a position is just as important >>>to its identity as is the location of each of the pieces. Because without this, >>>repetitions and 50-move rule won't work at all. >> >>Uri's point was that if any given position is repeated, you can get to any >>subsequent position more quickly by removing the moves from the previous >>occasion the position occurred to the current one. >> >>-g > > >How will you know they are repeated if you don't store them? > >:) Depends what you're doing. If you're systematically generating all possible chess positions, there's no need to store them - just generate one, then the next, then the next etc. If you're systematically generating all possible chess games, then, in any given chess game, you only have to remember the moves in one game - which - with the 50 move rule - is a maximum of a few thousand. In either case, you don't need much memory. -g
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