Author: Robert Hyatt
Date: 12:42:56 10/01/01
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On October 01, 2001 at 15:14:07, Slater Wold wrote: >I am not a math expert, and I know a lot of you (Uri) out there are. So I ask >all you experts to solve this problem: > > *How many legal positions are their in chess?* > >Also, please take into account that the king will always be present on the >board. > >I understand that there will more than likely be more positions than actually >possible. Such as the position of PPPPPPPPK vs ppppppppk. But I am willing to >deal with these. > >What would be the formula, and more importantly, the solution to this? > >Thanks! > > > >Slate The best bet is around 2^168. Someone has worked out an arithmetic encoding scheme that can represent the entire 64 square board + castling rights and ep status into 168 bits. It might be possible to improve on this slightly. But so what? That number is way big enough. If you want to talk about chess as a game, however, then this number is _way_ small. Because chess positions have a history that is important to the game outcome (ie repetitions, 50 move counter, etc.) You could have the same position with zillions of different "history values"
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