Monopoly as a Markov Process

Robert B. Ash, Richard L. Bishop
1972 Mathematics Magazine  
The limit frequencies of the positions in the game of Monopoly are calculated on the basis of Markov chains. In order to make the process Markovian some minor modifications in the rules are necessary. A parameter is introduced so that by varying this parameter we can determine how distorted our mode is compared with the actual game. The convergence properties of Markov chains are so nice that it was feasible to use hand computation. A neat trick with power series played an important role in
more » ... rmining how the limit frequencies depend on the parameter. A method for determining higher eigenvalues is illustrated. These eigenvalues yield a good estimate on the rapidity of convergence to the limit frequencies: to within one percent after 20 turns. Finally, expected income from the bank and expected rents on properties are calculated from the limit frequencies. This allows us to give a quantitative estimate of the relative value of the various properties.
doi:10.2307/2688377 fatcat:sph7yzaugzcwxnwbinyakihnuy