I am struggling a bit with the definition of symmetries and symmetric states in a game. If I understand it correctly, a symmetry S is such a permutation of the game board that each possible state A produces the same "winning output" as S(A). By "winning output" I mean either a win for white player or a win for black player or neither of those. Since this should hold true for all states, I think there doesn't need to be any additional conditions (like that the possible moves in A produce a set of states symmetric to the states produced by the possible moves in S(A)). What do you think? [Edited by - crypto_rsa on October 30, 2009 4:04:55 AM]