A game in which the number of points are fixed: for example, chess and checkers.

Since the number of points are fixed, any time one player gains points, another player directly loses those points --- or the potential of gaining those points. The total change in points for each move is zero, and the sum of all changes at the end of the game is therefore zero.

In any zero sum game, it is impossible for all players to win and equally impossible for all players to lose --- ties are the result of stalemates or other cyclical game loops.

See also NonZeroSumGame.