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]
See also
- Partisan game
- Impartial game
- Solved game
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.
- v
- t
- e
Tic-tac-toe
- 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
- m,n,k-game
- nd game
- Kaplansky's game
- Harary's generalized tic-tac-toe
- Hales–Jewett theorem
- Strategy-stealing argument
- Futile game
- Paper-and-pencil game
- 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
This game-related article is a stub. You can help Wikipedia by expanding it. |
- v
- t
- e