Taking Chances: The Analysis of Simplified Parcheesi

Parcheesi is a compelling example of a two-player, strictly competitive game of perfect information with chance moves. In this game, there are only two possible outcomes: W (a win for Player I and a loss for Player II) or L (a loss for Player I and a win for Player II). The primary motivation for a rational player is to maximize the probability of winning. Parcheesi is played between Player I (White) and Player II (Black) on a (2 m + 1) × n board. The central cell in the first column of the board is shaded, marking the winning square. The objective is to be the first to reach this shaded square by following specific routes and rules. In this paper, we will focus on three board configurations: the 3 × 2, 3 × 3, and 5 × 2 boards. For the first two configurations, we will provide brief solutions. A comprehensive analysis will be dedicated to the 5 × 2 board. Finally, we will conclude with a conjecture regarding the general (2 n + 1) × 2 board configuration.