2014/06/09 by Brofos, James
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1406.2212
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.