Math and Monopoly

Monopoly involves a bit of math, e.g., probability and Markov chains. You can really dig into it and get things involved and abstract.

Writing in “Probabilities in the Game of Monopoly,” Truman Collins says:

I recently saw an article in Scientific American (the April 1996 issue with additional information in the August 1996 and April 1997 issues) that discussed the probabilities of landing on the various squares in the game of Monopoly®. They used a simplified model of the game without considering the effects of the Chance and Community Chest cards or of the various ways of being sent to jail.

I was intrigued enough with this problem that I started working on trying to find the probabilities for landing on the different squares with all of the rules taken into account. I ran into some interesting problems but finally came up with the right answers, which you will find here along with some other useful derived data. Incidentally, I’m not much of a Monopoly® player myself, but I’ve always enjoyed interesting problems involving probability and statistics, of which this was one.

He shares some tables, such as “Long Term Probabilities for Ending Up on Each of the Squares in Monopoly” and “Expected Income Per Opponent Roll on all Properties Assuming Preferred Short Jail Stay.” Interesting, fun stuff.

You might also want to check out “Using Board Games and Mathematica® to Teach the Fundamentals of Finite Stationary Markov Chains” by Roger Bilisoly (Department of Mathematical Sciences, Central Connecticut State University); “Markov Chains in the Game of Monopoly” by Ben Li; “Markov and Mr. Monopoly Make Millions; Dartmouth’s “Markov Chains;” and Wikipedia’s “Markov Chain.”