OR 389 Student Seminar

"Monopoly as a Markov Process"

Robert B. Ash and Richard L. Bishop

Math. Mag. 45 (1972): 26-29

"Take a Walk on the Boardwalk"

Stephen D. Abbott and Matt Richey

College Math. J. 28:3 (1997): 162-171



Game Board

Assumptions

Two Models

State Space

Observations

Matrices

Limiting Distributions (Long-Term Probabilities)

Visual Demonstration of Convergence to Limiting Distribution (RIJ)

Expected Revenue Per Opponent Roll, for Fully Improved Monopolies

Expected Revenue Per Opponent Roll Per Dollar Invested, for Fully Improved Monopolies

Cost-Reward Analysis

Expected Number of Rolls Until Player Lands in Jail

Expected Number of Rolls Until All Rental Properties Have Been Landed On (Hence Purchased)

Limiting Distributions with no Chance or Community Chest Cards

Conclusions

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