The Probability of Landing on Different Properties in Monopoly

One of my favorite board games is Monopoly. I have noticed when I’ve played Monopoly that it seems like you always land on certain squares more than others. For instance, it seems like no one ever lands on Boardwalk, and players land on the pink and orange properties more often than they land on the others. The aim of this exploration is to find out if, over the course of a Monopoly game, a player will land on some squares more often than others and to use this information to figure out which properties are most profitable. This knowledge could help a player decide which properties to buy.

The rules of Monopoly are fairly simple. In each turn, the player rolls two dice and moves the number of squares that is the total dice roll. The player then may buy the property he or she lands on if it is available, or if another player already owns it, the first player pays rent according to the instructions on the card associated with the property. If a player owns all the properties in a color group, he or she can increase the rent that other players pay when they land on a square by buying houses or hotels. There are some more complications in the game, but they are not important to this exploration.

I decided that the most practical way to find out if a player will land on some squares more than others was to run a simulation. In order to do so, I needed to figure out how many times a player would roll the dice in a game of Monopoly, as that was the number of repetitions I would need to have in my simulation. To find that number, I played a game of Monopoly which I timed and counted the number of rolls in. It was 93 minutes long and the dice were rolled 201 times. I divided the time by the rolls to find the time per roll . The average game of Monopoly is 60 to 240 minutes long (Wikipedia) so I decided to use the middle value, 150. I divided the average length of a Monopoly game by the average time per roll to find the number of rolls in an average length Monopoly game . I decided to assume a four person game, so I divided 324 by 4 and got 81 rolls per person.