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

TL;DR

This paper demonstrates how simple board games can be used to teach finite stationary Markov chains, utilizing Mathematica for analysis of state properties and extending to more complex scenarios.

Contribution

It introduces a practical approach to teaching Markov chains through board games combined with computer algebra tools like Mathematica, highlighting educational benefits.

Findings

Board games illustrate key Markov chain concepts.

Mathematica enables analysis of mean times and stationary probabilities.

Method can be extended to complex Markov chain models.

Abstract

Markov chains are an important example for a course on stochastic processes because 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 last one. 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 analyzes some simple board games with Mathematica, and indicates how this can be extended to more complex situations.