As children growing up in Sri Lanka, we were addicted to the game Monopoly. When a bunch of us cousins got together during school vacations, we would play games over and over again late into the night, with a lot of shouting and laughter.
I now positively detest the game. There is something about having the goal of forcing other players into poverty where they cannot pay the rent and are forced to declare bankruptcy that strikes me as morally repugnant.
But the game does have some interesting statistical features. On the surface, one would think that the chance of landing on any particular square is the same as for any other. But there are obvious variations. For example, since everyone starts at GO, the chances of landing on the first twelve squares will follow the probability of getting that total from the throw of two dice. But in a long game that variation would be small effect. But there are other special cases, such as landing in jail or drawing a Chance or Community Chest cards that sends one to particular squares, that also introduce some non-random elements. Also rolling doubles gives you another turn, further skewing the randomness.
Now Walter Hickey has gone to the trouble of looking into the research that takes all these things into account and calculates the overall probability of landing on each of the squares. Some of the suggestions for increasing your odds of winning are those that many regular players would have intuitively realized on their own without a statistical analysis. (More on the math can be seen here and one set of tables of probabilities based on that math can be found here.)
Here are the steady state probabilities.
What conclusions can be drawn from this? Hickey gives some tips.
- The red and orange properties are exceptional investments.
- Particularly earlier in the game, you’ve got to get the railroads.
- Properties between Jail and Go To Jail get landed on more frequently than properties between Go To Jail and Jail.
Hickey also looks into the question of when one should build properties.
- While Park Place and Boardwalk are excellent for crushing opponents, early in the game their ROI [Return On Investment] is not ideal.
- Owning all the railroads is an exceptional position to be in.
- The best investment in Monopoly is building the third house on the orange block of St James, Tennessee and New York.
- Three houses is the way to go.
There’s a lot more specific advice for aficionados.
I pass this valuable information along to anyone who plays the game so that you can use it as part of your strategy.