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| (1) Posted by Hauke Reddmann [Saturday, Aug 3, 2013 19:15] |
Percentage of legal positions with legal material
Foreign thread needs retro buffs!
http://mathoverflow.net/questions/138133/what-proportion-of-chess-positions-that-one-can-set-up-on-the-board-using-a-leg/138365#138365
Hauke
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| (2) Posted by seetharaman kalyan [Wednesday, Aug 7, 2013 08:37] |
The book 'A guide to Fairy chess' by ASM Dickens had an estimate of the legal positions possible in a game of chess, but I cant locate my copy.
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| (3) Posted by Eugene Rosner [Thursday, Aug 8, 2013 17:00] |
according to the Dickins book(p.28) all 32 men regardless of legality can stand~4.6x10^42. it does not give an estimate of legal positions, as mentioned before, far less.
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| (4) Posted by seetharaman kalyan [Friday, Aug 9, 2013 10:17] |
Oh.... my memory was not right :). That was a different estimate.
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| (5) Posted by Diyan Kostadinov [Saturday, Aug 10, 2013 07:28] |
Ram, I upload the book here, so you can download:
http://dox.bg/files/dw?a=b0dfd631e1
The link will be active till 24.08.2013
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| (6) Posted by Hauke Reddmann [Sunday, Aug 11, 2013 16:47] |
Unfortunately, the estimate helps nil for the asked question.
As you can see in the MathOverflow thread, the percentage of
legal positions with 32 pieces is only an almost vanishing part
of the possible ones. And the problem is that the ratio
(Positions with n pieces)/(Positions with n-1 pieces) is of
order 1, where (Legal percentage of Positions with n pieces)/
(Legal percentage of Positions with n-1 pieces) skyrockets
with falling n, and you have almost no idea where the one
effect outdoes the other.
Or does it? At how many pieces "almost any" pawn structures
become legal?
Hauke
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