  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.
