Probabilities in the Game of Monopoly

My old site has a link to this great article, but it apparently moved a while back. Fortunately, I was able to find it again. I’ll be the first to admit that I’m not much into math, but if you have even a mildly mathematical mind, this is required reading. It’s also very interesting.

The best part is that it might also help your Monopoly® strategy quite a bit. From the page by Truman Collins:

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.

After reading the article, it actually confirmed a suspicion Jay and I had about which properties really had more value. I’m not going to reveal all of that here. It wouldn’t be any fun that way, plus I don’t want the entire world able to beat me. (Although if enough people ask, I’ll probably write a few things on Monopoly strategy.)

Read the article and find out for yourself.

One Comment to “Probabilities in the Game of Monopoly”

Ken says

In the game of Monopoly, because we usually do not have the chance to pick which properties we want to buy, I have a feeling that the long-term percentages are somewhat secondary. At any time, our choices may be one or several of these:
– New Property: Buy or Auction
– Old Property: Mortgage/Payoff
– House/Hotel: Buy/Sell
– Jail: Try for Double, Pay Bail, Use Card
– Negotiate
Of course, which choice is best depends on the Expected Values of each of these choices and that’s where the probabilities and values kick in. However, note that you are not just trying to get the highest expected value for yourself, you may also want the lowest expected value for the other players.

A really useful model seems to be non-trivial.

December 27, 2008 at 1:04 am

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