The Markov Chains Game

1750 WordsJan 28, 20187 Pages
Markov Chains Game Introduction Probabilistic reasoning goes a long way in many popular board games. Abbott and Richey [1] and Ash and Bishop [2] identify the most portable properties in Monopoly and Tan [3] derives battle strategies for RISK. In RISK, the stochastic progress of a battle between two players over any of the 42 countries can be described using a Markov Chain. Theory for Markov Chains can be applied to address questions about the probabilities of victory and expected losses in battle. Tan addresses two interesting questions: If you attack a territory with your armies, what is the probability that you will capture this territory? If you engage in a war, how many armies should you expect to lose depending on the number of armies your opponent has on that territory? A mistaken assumption of independence leads to the slight misspecication of the transition probability matrix for the system, which leads to incorrect answers to these questions. Correct speciation is accomplished here using enumerative techniques. The answers to the questions are updated and recommended strategies are revised and expanded. Results and endings are presented along with those from Tan's article for comparison. The Markov Chain The object for a player in RISK is to conquer the world by occupying all 42 countries, thereby destroying all armies of the opponents. The rules to RISK are straight forward and many readers may need no review. Newcomers are referred to Tan's article
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