Author: Louis Fagliano
Date: 23:13:16 01/20/05
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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. Yes there is. If there are no pawns on the board then you can take advantage of the fact that all the pieces can move backwards as well as forwards and left as well as right by rotating the board by 90° as well as 180° and 270° and have the "same" position. But unfortunately thr ratio of the total number of legal postions to the number of legal positions without pawns on the board is very small. 99.9999+ percent of all legal positions have pawns on the board.
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