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Analysis of 'The Settlers of Catan' Using Markov Chains
Nagel, Lauren
Nagel, Lauren
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Date
2021
Additional date(s)
2021-05-19
Abstract
Markov chains are stochastic models characterized by the probability of future states depending solely on one's current state. Google's page ranking system, financial phenomena such as stock market crashes, and algorithms to predict a company's projected sales are a glimpse into the array of applications for Markov models. Board games such as Monopoly and Risk have also been studied under the lens of Markov decision processes. In this research, we analyzed the board game "The Settlers of Catan" using transition matrices. Transition matrices are composed of the current states which represent each row i and the proceeding states across the columns j with the entry (i,j) containing the probability the current state i will transition to the state j. Using these transition matrices, we delved into addressing the question of which starting positions are optimal. Furthermore, we worked on determining optimality in conjunction with a player's gameplay strategy. After building a simulation of the game in python, we tested the results of our theoretical research against the mock run throughs to observe how well our model prevailed under the limitations of time (number of turns before winner is reached).
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Subject
Markov Chains
Catan
Catan
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Department
Mathematics