Author: Graham Laight
Date: 07:49:06 05/09/01
Go up one level in this thread
>> It's very possible that to solve chess you'd need more material than >>>exists in the universe just to store the information, so again it's a pointless >>>argument. >> >>You need less than it but it is not practical for the near future. >>For Storing all the legal positions you need less than 10^50 bytes. >> >>Uri > > >10^50 is not _close_. Each position is much more than just the squares the >pieces are on. It must include the game history to reach that position to >account for repetitions and 50-move counting. > >You are confusing the difference between "how many unique ways can I arrange >the chess pieces on the board?" with "how many unique positions are there in >the game when you factor in all the rules?" The latter is so much bigger than >the former that the former is worthless except as an exercise to determine the >perfect size for a hash signature. One factor that massively reduces the number of games is increasing the skill level of the players. If one were to maximise the number of possible games, one would select moves randomly, giving a lower weighting to a move where a pawn is pushed or a piece taken (unless this would trip the 50 move rule. Draws by repetition would also have to be avoided (if draws by repetition are allowed to happen without being claimed, then obviously the number of possible games is infinite)). Then you would have a massive number of games - most of which would be excrutiatingly boring. However - once you introduce skill into the players, the number of possible games deteriorates sharply. The more skill you introduce into the game, the more rapidly the number of possible games falls. To get the true number of games one can play at the maximum skill level, one only has to follow 2 rules: 1. You must never make a move that would put yourself in a losing position. If forced to do so, you must resign immediately. 2. On a given move, either black or white must make a move which represents progress. This means advancing a pawn, taking a pawn or a piece, winning, or making a move that will lead to one of these events (positional moves must be shown to lead to a progressive event). If neither side makes progress, a draw is declared. Now all we need is a way to discover whether a position is losing. However - to know that, we probably have to calculate out all the possible games from this position. Which puts us back where we started. Oh well - worth a try. -g
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