During a rather frustrating monopoly game, I was wondering if there is any good strategy to play the game, because there are not so many actions for a player to begin with.

In particular, players have no choice over their movement. They stumble from turn to turn through the game, which is a pretty good abstraction of life. However, players may choose one of these actions

• Buy property
• Build houses/hotels
• Choose to prematurely buy themselves free from the jail
• Table flip.

Thus, the first question which popped to my mind was What’s the best property to buy? and Wouldn’t the player’s probability density make a nice graph?. The first question could have been answered by having a look at wikipedia, where it states that “[…]the Orange property group is the best to own because players land on them more often[…]” but that wouldn’t have yielded a nice graph. So I wrote a small python script which simulates the player movement, ignoring the financial aspects for now. And this was the result:

Probabilty distribution of a player visiting a given field. Estimated by 10000 games of 400 moves each game, neglecting capital and only considering the movement rules. Also, the player immediately buys himself/herself free from the jail.

Moreover, the strategy section on the english wikipedia doesn’t say that players visit the first and second station more often than the second and the fourth nor that you spend a disproportional amount of time in jail (although every monopoly player probably can tell without this graph as well).

So only based on how often a player ends up at a given field, it really appears to be a good strategy to acquire the orange, violet and red streets… or to own the prison.

My follow up question was Is this still the result if money is taken into account as well? and What is the expected income depending on the number of houses?.

Expected income per throw of each field with zero houses or hotels or collections of streets. Estimated by 10000 games of 400 moves each game.

This result, in turn supports the intuition, that streets closer to the end are more desirable in the beginning without property or double income. Buying a station, however, still seems to be a good choice prefering the first and the third over the other two.

I’d guess that the expected income of the streets equipped with property will exhibit a similar distribution.

To be continued…