In this master’s thesis we will examine the application of Markov chains in modelling of the board game Monopoly. The chosen game is well suited to this type of analysis, as it involves random player movement based on dice rolls as well as special rules associated with individual board spaces. This creates a dynamic system of transitions between different states. In addition to movement around the board, the purchase of properties and buildings, as well as the payment of rent, also play an important role.
Using several simplified models of the game, we analyse how dice rolls, cards, doubles and jail rule affect the transition probabilities between individual states and the long-run probabilities of visiting board spaces. The results show that the introduction of additional rules lead to uneven distribution of visits. Cards increase the probability of visiting the spaces to which they redirect the player, while the rule concerning doubles alters the transitions within a single turn. With the introduction of a model that includes jail, the state space is further expanded, and jail has an effect on the stationary distribution and on the frequency with which other spaces are visited. The resulting probabilities are also related to expected revenues, which are calculated using specific examples. The results confirm that Markov chains can be used to mathematically evaluate the influence of individual game rules on the long-term behaviour of the game.
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