Using Board Games and Mathematica to Teach the Fundamentals of Finite Stationary Markov Chains (original) (raw)

Markov chains are an important example for a course on stochastic processes. Simple board games can be used to illustrate the fundamental concepts. 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 computer algebra packages, these games can be analyzed. For example, the mean times in transient states and the stationary probabilities for recurrent states are easily computed. This article shows several simple board games analyzed with Mathematica®, and indicates how more complex games can be approached.