The problem is to find a legal chess position with the maximal number of possible plays for White. The problem arose in trying to determine whether a two-computer chess program could be played where the computers transmitted one 8-bit byte per move. The best encoding for moves seems to be to order all possible moves canonically (say lexically on start and destination square) and send the index of the move. If some position admits more than 256 possible moves, this scheme, and presumably the whole idea, fails. Regarding the reachability of the position, optimally we would like the position to be reachable from the start position. However, I realize that determining this is somewhat painful, so I will settle for reasonable approximations, e.g: - The set of pieces on each side should be consistent with a legal game, (e.g, at most 9 queens per side). - Pawns should not occupy the first or eighth rank. - At most one king should be in check (though White's king being in check seems improbable anyway). - The colors of bishops should be consistent with a legal game. Regarding pending pawn promotions, each promotion counts as a distinct move, so yes, an unblocked seventh-rank pawn with two possible captures yields 12 possible moves.