Mathematical Recreations; October 1996; Scientific American Magazine; by Stewart; 3 Page(s)

In the April column I described a mathematical model of the board game Monopoly. At the start of the game, when everyone emerges from the GO position by throwing dice, the probability of the first few squares being occupied is high, and the distant squares are unoccupied. Using the concept of Markov chains, I showed that this initial bunching of probabilities ultimately evens out so that the game is fair: everyone has an equal chance to occupy any square and to buy that property. This outcome is true, however, only when certain simplifying assumptions are made. Monopoly enthusiasts were quick to point out that in the real game, the long-term distribution of probabilities is not even.

So what are the true probabilities? The Markov chain method can also be applied to the real game; I have to warn you, however, that the analysis is complex and requires substantial computer assistance. Let me first remind you how Markov chains are used for Monopoly. A player can be in any one of 40 squares on the board, which, for convenience, we number clockwise from zero to 39, starting with GO (which is zero).