# Nontransitive game

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A **non-transitive game** is a game for which the various strategies produce one or more "loops" of preferences. In a non-transitive game in which strategy A is preferred over strategy B, and strategy B is preferred over strategy C, strategy A is *not* necessarily preferred over strategy C.

A prototypical example non-transitive game is the game rock, paper, scissors which is explicitly constructed as a non-transitive game. In probabilistic games like Penney's game, the violation of transitivity results in a more subtle way, and is often presented as a probability paradox.

## Examples[edit]

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## References[edit]

- Gardner, Martin (2001).
*The Colossal Book of Mathematics*. New York: W.W. Norton. ISBN 0-393-02023-1. Retrieved 15 March 2013.

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