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In game theory
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...
, a ''futile game'' is a game
A game is a structured type of play usually undertaken for entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or video games) or art ...
that permits a draw or a tie when optimal moves are made by both players. An example of this type of game is the classical form of Tic-tac-toe
Tic-tac-toe (American English), noughts and crosses (English in the Commonwealth of Nations, Commonwealth English), or Xs and Os (Canadian English, Canadian or Hiberno-English, Irish English) is a paper-and-pencil game for two players who ta ...
, though not all variants
Variant may refer to:
Arts and entertainment
* ''Variant'' (magazine), a former British cultural magazine
* Variant cover, an issue of comic books with varying cover art
* ''Variant'' (novel), a novel by Robison Wells
* " The Variant", 2021 epis ...
are futile games. The term does not apply to intransitive games, such as iterated prisoner's dilemma or rock–paper–scissors
Rock, Paper, Scissors (also known by several other names and word orders) is an intransitive hand game, usually played between two people, in which each player simultaneously forms one of three shapes with an outstretched hand. These shapes ar ...
, in which there is no path to a draw or every strategy in the game can be beaten by another strategy.
See also
*Partisan game In combinatorial game theory, a game is partisan (sometimes partizan) if it is not impartial. That is, some moves are available to one player and not to the other, or the payoffs are not symmetric.
Most games are partisan. For example, in chess, on ...
* Impartial game
In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric. In other words, the only difference be ...
* Solved game
A solved game is a game whose outcome (win, lose or tie (draw), draw) can be correctly predicted from any position, assuming that both players play perfectly. This concept is usually applied to abstract strategy games, and especially to games with ...
References
Combinatorial game theory {{Game-stub