Analysis of the Penney-Ante Game Using Difference Equations: Development of an Optimal and a Mixed-Strategies Protocol

Penney-Ante is a well known two-player (Player I and Player II) game based on an information paradox. We present a new approach, using \emph{difference-equations}, to analyzing the outcome for each player. One strategy yields a winning outcome of 75\% for Player II, the player playing second. The approach also permits investigation of non-optimal strategies, and demonstrates how mixing of such strategies can be used to tune the winning edge of either player. We generalize the analysis to accommodate the possibility of a biased coin.