# Monopoly Math

So it was family game night tonight, and we decided to play Monopoly. Because the game can take a while, we generally set a time limit, something between 1.5 to 3 hours depending on how late we start the game. My strategy for playing is pretty straight forward: collect as many railways and utilities as possible, and go for orange, yellow, and dark blue property groups. It tends to work pretty well for me, so I decided to do some data recording this game. I tallied up every squared landed on in Excel, including Chance/Chest cards like “Go directly to jail”, “Advance to boardwalk”, “Go to go”, and so on. We don’t play with any custom rules that affect moving, so the data reflects standard Monopoly procedures.

Unfortunately the game only lasted around 1 hour 20 minutes (I had a lucky start & early win), so the dataset isn’t very big. I wasn’t about to ask for a rematch though and we probably won’t play Monopoly again for a week or two, so I decided to work with what I had. Here’s the full organized data and analysis; click for full-size of course:

Haha, go Orange and Railways! I knew I was backing the right horse. 🙂 I think the reasoning behind the high frequency of orange landings has to do with the fact that it’s outside of the jail. Some of the most probable rolls on two dice (6,8,9) will land you on orange. There are also Chance/Chest cards that take the player to the pink squares right before orange, and the railway right before orange. Railways/corners are obviously going to be popular because of the aforementioned cards, and because they’re well spread around the board. Same goes for Chance/Chest, which combined make up 6/40 or 15% of the game board. Also, I find it funny that Tax squares received the least hits.

There’s a lot more I could do with this as far as comparison to theory goes, but the problem is calculating theoretical probabilities for each square. Since there are a lot of different routes to get to squares, with the possibility of going to jail, getting a Chance/Chest card that moves the player, etc things get complicated. I do intend to sit down and work through the math later tonight/tomorrow, so I’ll post again with an update at that point. And, as always, if anyone wants the data to play with: Monopoly.xlsx. The first Sheet is the raw data, and the second is the analysis page shown above.

T