About: Subtraction game

In combinatorial game theory, a subtraction game is an abstract strategy game whose state can be represented by a natural number or vector of numbers (for instance, the numbers of game tokens in piles of tokens, or the positions of pieces on board) and in which the allowed moves reduce these numbers. Often, the moves of the game allow any number to be reduced by subtracting a value from a specified subtraction set, and different subtraction games vary in their subtraction sets. These games also vary in whether the last player to move wins (the normal play convention) or loses (misère). Another winning convention that has also been used is that a player who moves to a position with all numbers zero wins, but that any other position with no moves possible is a draw.