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MatPlus.Net Forum General Percentage of legal positions with legal material

### 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

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.

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.

Oh.... my memory was not right :). That was a different estimate.

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

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