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Markov chains are an important example for a course on stochastic processesbecause simple board games can be used to illustrate the fundamental concepts.For example, a looping board game (like Monopoly) consists of all recurrentstates, and a game where players win by reaching a final square (like Chutesand Ladders) consists of all transient states except for the last one. With theavailability of computer algebra packages, these games can be analyzed. Forexample, the mean times in transient states and the stationary probabilitiesfor recurrent states are easily computed. This article analyzes some simpleboard games with Mathematica, and indicates how this can be extended to morecomplex situations.

Using Board Games and Mathematica to Teach the Fundamentals of Finite Stationary Markov Chains