Futile game

In combinatorial game theory, a futile game is a game in which a draw, or tie, is a possible outcome when both players make optimal moves, as opposed to a game that always produces a winner under perfect play from both sides. Tic-tac-toe is the standard example: when both players follow a correct strategy, neither can force a win, and the game always ends in a draw. The category is specifically defined to exclude intransitive games such as rock-paper-scissors or the iterated prisoner's dilemma, in which a draw is either impossible by the rules of the game or every fixed strategy can in principle be beaten by some other strategy, since those games do not fit the same notion of a single jointly optimal line of play leading to a tie. The term is used mainly within the mathematical study of games rather than in everyday descriptions of gameplay, giving theorists a precise way to classify a game's set of possible optimal outcomes.