The value of a game position, where mex is the smallest nonnegative integer missing from the values of its legal successors. Terminal positions have value zero. The Sprague-Grundy theorem explains why these values combine by exclusive or.
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The Grundy number, also known as the nimber, is a concept from combinatorial game theory used to analyze games, particularly impartial games. It is a measure of a position's winning potential in these games. In an impartial game, the players have the same options available to them regardless of who is about to move. A position in such a game can have a Grundy number that helps determine whether it is a winning position (for the player about to move) or a losing position.