Simulating Monopoly

Last summer I spent a good deal of time playing Monopoly. It was my final summer of marching drum corps and we were taking Amtrak out to the midwest for the last leg of our summer tour. There isn’t really much to do on a train for 3 days except eat, sleep, and sit in the observation car playing Monopoly.

One of the other corps members was absolutely destroying us. He clearly knew what he was doing when it came to fictional property management. He let me in on a little secret, though. Not all properties are created equal.

What he meant was that certain properties are statisically more likely to be landed on than others. It made sense when he explained it, but I wasn’t sure just how much of an actual difference it made. When I got home from the summer tour, I sat down and wrote some code to find out.

Thankfully in the game of Monopoly, a player’s movement around the board is very much decoupled from their financial transactions. What I mean by that is that they continue to move around the board in the same way, regardless of which properties they chose to buy, how much they have to pay to other players, or which properties they trade. The only exception is when a player goes bankrupt, and ceases to circle the board.

What this allowed me to do is write a very simple simulation in a few hours without having to worry about realistic AI. The players didn’t have to make financial transactions at all. They merely had to roll the dice and move according to the rules of Monopoly. I did need to account for the actions of the Chance and Community chest cards, but only when it impacted their position on the board or their future turns.

Certain spaces on the board can also affect the player’s position and future, so that had to be accounted for as well. For example, landing on Go to Jail will send a player directly to the jail square, and a player in jail has to go through a series of dice rolls or use a Get of Jail Free card to move again.

The game board used in a game of monopoly.

As I was finishing up writing the simulation, I began to suspect that the advice I had received on the train was correct. The claim was that the orange properties (St. James Place, Tennessee Avenue, and New York Avenue) were the most lucrative on the board because players were more likely to land on them. This indeed makes sense, because several Chance cards send you directly to jail and so does the Go to Jail square. Thus, the most common starting point for a dice roll is Jail. Since the most common dice roll for 2 six-sided dice will be in the 6-8 range, it only makes sense that those are the most commonly landed-on properties.

Indeed, this is exactly how it plays out. My simulation played 2000 games with 6 players and 1000 turns per game, and dumps the “landed-on” percentages out for each space along with a heat map overlayed onto the above Monopoly board. Let’s take a look at the results.

Raw results from the Monopoly simulation.

Squares landed on more often are "hotter" (tinted red) and squares landed on less often are "cooler" (tinted blue).

The orange property tract is certainly the most lucrative. But when you look at the raw percentages, it’s a little disappointing. The most landed-on property on the board (Community Chest #2, exactly 7 spaces away from Jail) is less than 1% more trafficked than the least landed-on property (Mediterranean Avenue).

Keep in mind though, that’s when it’s averaged out over 1000 turns, which is a massively long game of Monopoly. On top of that, those results are averaged over 2000 games. This smooths out the heat map quite a bit.

In a single game of Monopoly, the percentage swings will be much higher. The Orange properties could be red hot. They could also be colder than Mediterranean. However, given that in the long run they are hotter than the other spaces, it doesn’t hurt to try to score the orange properties. More often than not, they will see more action than any other tract on the board.