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Abstract:
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In a stochastic processes class, Markov chains are an important example and simple board games can be used to illustrate their fundamental properties. For example, a looping board game (like Monopoly) consists of all recurrent states, and a game where players win by reaching a final square (like Chutes and Ladders) consists of all transient states except for the recurrent ending state. With the availability of symbolic mathematics packages, complex games can be analyzed, for example, the mean number of visits to the transient states and the stationary probabilities for recurrent states are both easily computed. This talk shows how to analyze simple board games with Mathematica and includes analyses of Chutes and Ladders, the Gambler's Ruin and Monopoly. For example, we demonstrate that the most likely square (besides Jail) in Monopoly is Illinois Avenue.
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