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arXiv · 1406.2212

A Markov Chain Analysis of a Pattern Matching Coin Game

James Brofos
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Abstract

In late May of 2014 I received an email from a colleague introducing to me a non-transitive game developed by Walter Penney. This paper explores this probability game from the perspective of a coin tossing game, and further discusses some similarly interesting properties arising out of a Markov Chain analysis. In particular, we calculate the number of "rounds" that are expected to be played in each variation of the game by leveraging the fundamental matrix. Additionally, I derive a novel method for calculating the probabilistic advantage obtained by the player following Penney's strategy. I also produce an exhaustive proof that Penney's strategy is optimal for his namesake game.

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James Brofos. 2014-06-09. A Markov Chain Analysis of a Pattern Matching Coin Game. https://arxiv.org/abs/1406.2212

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