In
game theory, a ''futile game'' is a
game 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 (Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid with ''X'' or ''O''. ...
, though not all
variants
Variant may refer to:
In 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 e ...
are futile games. The term also does not apply to
intransitive games, such as
iterated prisoner's dilemma
The Prisoner's Dilemma is an example of a game analyzed in game theory. It is also a thought experiment that challenges two completely rational agents to a dilemma: cooperate with their partner for mutual reward, or betray their partner ("def ...
or
rock–paper–scissors
Rock paper scissors (also known by other orderings of the three items, with "rock" sometimes being called "stone," or as Rochambeau, roshambo, or ro-sham-bo) is a hand game originating in China, usually played between two people, in which each p ...
, 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.
Most games are partisan. For example, in chess, only one player can move the white ...
*
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 bet ...
*
Solved game
A solved game is a game whose outcome (win, lose or 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 full inform ...
References
Combinatorial game theory
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