Futile game

In game theory, a futile game is a game that permits a draw or a tie when optimal moves are made by both players.^[1]^[2] An example of this type of game is the classical form of Tic-tac-toe,^[3] though not all variants are futile games. The term does not apply to intransitive games, such as iterated prisoner's dilemma or rock–paper–scissors, in which there is no path to a draw or every strategy in the game can be beaten by another strategy.^[4]

References

^ Steinhaus, H. (1999). Mathematical Snapshots (3rd ed.). New York: Dover. p. 16.
^ Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics (2nd ed.). CRC Press. p. 1129.
^ Wang, Hao (2014-09-22). Popular Lectures on Mathematical Logic. Courier Corporation. ISBN 9780486171043.
^ Ashlock, Daniel (2006-04-04). Evolutionary Computation for Modeling and Optimization. Springer Science & Business Media. ISBN 9780387319094.

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[1] Steinhaus, H. (1999). Mathematical Snapshots (3rd ed.). New York: Dover. p. 16.

[2] Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics (2nd ed.). CRC Press. p. 1129.

[3] Wang, Hao (2014-09-22). Popular Lectures on Mathematical Logic. Courier Corporation. ISBN 9780486171043.

[4] Ashlock, Daniel (2006-04-04). Evolutionary Computation for Modeling and Optimization. Springer Science & Business Media. ISBN 9780387319094.

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v t e Tic-tac-toe
Variants	3D tic-tac-toe Gomoku Notakto Treblecross Number Scrabble Order and Chaos Pente Quantum tic-tac-toe Renju SOS Ultimate tic-tac-toe Wild tic-tac-toe
Related concepts	m,n,k-game n^d game Kaplansky's game Harary's generalized tic-tac-toe Hales–Jewett theorem Strategy-stealing argument Futile game Paper-and-pencil game
Similar games	Nine men's morris Score Four Tic-Stac-Toe Gobblet Quarto Three men's morris Nine Holes Achi Connect Four Connect6 OXO Toss Across Pentago

See also

References