Author: Dann Corbit
Date: 12:27:30 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? Nobody knows. Estimates vary from about 1.3e30 to 4e50 (2^100 to 2^168). But that does not take everything into account. In particular, the half-move clock changes the meaning of the position. For sure the number of distinct board positions (discounting 50 move rule and non-reversible moves) is not larger than 2^168 because chess positions have been encoded perfectly in 168 bits. Therefore, we can number them all in 4e50 distinct encodings. And that does not subtract all the illegal moves. I belive that Uri has done some interesting work on counting legal board positions. I even built a binary for him once, but I don't remember what the result was. The figure of 2^100 comes from an entropy study where GM's asked yes/no questions about the board position and were able to deduce the actual arrangment in less than 100 guesses.
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