Author: Uri Blass
Date: 07:40:02 01/21/05
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On January 21, 2005 at 09:56:50, Louis Fagliano wrote: >On January 21, 2005 at 03:33:21, Uri Blass wrote: > >>On January 20, 2005 at 20:45:23, Dann Corbit wrote: >> >>>On January 20, 2005 at 20:04:22, Louis Fagliano wrote: >>>[snip] >>>>Actually 10^43rd power does not shrink at all. You started out "shrinking" by >>>>throwing out idiotic moves when considering all possible chess games which is >>>>something like 10^120th power. That number can be "shrunk" by throwing out >>>>idiotic games. But 10^43rd power is the number is the number of legal positions >>>>in chess, not the number of different possible games since there are an >>>>inumberable ways of reaching any particular legal position by an inumberable >>>>number of different move orders. The number of legal positions can never be >>>>"shrunken" because every legal position must be considered in order to solve >>>>chess regardless of whether or not the moves that preceeded it in order to reach >>>>that position were idiotic or masterful. >>> >>>10^43rd power can be shrunken by a factor of 4 through simple reflections of the >>>board. Perhaps there are additional symmetry arguments that can reduce it >>>further. >> >> >>Where is the proof that 10^43 is correct? >> >>I read that Vincent claimed that it is correct but I saw no proof for it. >>I do not say that it is wrong but we need a link to some proof before claiming >>that it is at most 10^43 >> >>Uri > > >I believe the number of legal positions came from >http://mathworld.wolfram.com/Chess.html where it is given as: > > >64!/(32!*((8!)^2)*((2!)^6) ¡Ö 10^43 Thanks That estimate is wrong because it does not consider promotions and consider only positions with exactly 32 pieces. It is possible to improve the estimate for positions with 32 pieces. Uri Uri
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