## Wednesday, December 19, 2012

### Win at Monopoly using Monte Carlo simulations

Now that we are experts at Risk, let's turn to Monopoly, the classic board game. In Monopoly, players determine whether to buy properties and build houses, so as to maximise rental yield. To some extent, one should gun for the most visited spaces, so that your opponents pay rent more often.

Which spaces are the most popular? Once again, drawing out the theoretical probabilities would be rather tedious, so we turn to Monopoly game simulations.

Using Excel, I simulated the 55 Monopoly games, each with 4 players and 100 rolls. This gave me 22,000 location readings, quite a substantive number! I managed to model double rolls and the go to jail square, but had to ignore chance and community chest cards, as well as the rule where you go to jail if you have rolled doubles thrice.

With the simulated data, I calculated the odds of landing on each space which are shown below. This is based on the Singapore board. The most popular space is St Andrews Road, the last property in the orange zone (right before free parking), followed by Collyer Quay, last property in the red zone.

One property that stands out is the expensive Queen Astrid Park, which gets visited a paltry 0.4% of all visits. This makes it quite an unattractive property - it's rent is at best 2 times that of the orange-green zones, yet it's visited at least 4 times less than these zones.

You might also like to know that:
• You row doubles 18% of the time
• You draw a card in 12% of all turns
• The likelihood of landing on GO, Free Parking, Income Tax, or Luxury Tax is 2.0%
Which property groups are the most commonly visited? As shown in the graph below, the orange group gets the most hits (aside from railroads), followed by the red and yellow groups. So gunning for properties in these areas seems like a sensible strategy!

#### 1 comment:

1. Actually, you roll doubles .166667 of the time. 18% is too high. (6/36 = .166667) And you certainly don't need a simulation to determine that. This is simple probability.