From Unequal Chance to a Coin Game Dance: Variants of Penney’s Game

Abstract We start by exploring and analyzing the various aspects of Penney’s game, examining its possible outcomes as well as its fairness (or lack thereof). In search of a fairer game, we create many variations of the original Penney’s game by altering its rules. Specifically, we introduce the Head-Start Penney’s game, the Post-a-Bobalyptic Penney’s game, the Second-Occurrence Penney’s game, the Two-Coin game, the No-Flippancy game, and the Blended game. We then analyze each of these games and the odds of winning for both players.