Jake Mckeegan

Have you ever played Monopoly? Chances are, you have. It’s a great game, and I love it. But, when I play with family members, I play to win. So, I ran a monte carlo simulation to see which properties you are most likely to land on. And yes, I included chance cards and go to jail, and everything. Monte Carlo simulations are simulations in which you run something, even something driven by randomness, over and over and over again, until it is accurate. In this Monte Carlo simulation (more info at this link: https://www.investopedia.com/terms/m/montecarlosimulation.asp), I also assumed that a player would stay in jail for three turns unless they rolled doubles. The results are as follows:

Landing Probabilities:
Jail / Just Visiting 10.38%
Illinois Avenue 3.01%
GO 3.00%
New York Avenue 2.84%
Tennessee Avenue 2.83%
Free Parking 2.80%
B&O Railroad 2.75%
Water Works 2.72%
St. James Place 2.69%
Kentucky Avenue 2.62%
Atlantic Avenue 2.58%
Pacific Avenue 2.58%
Ventnor Avenue 2.58%
Electric Company 2.57%
Indiana Avenue 2.56%
Pennsylvania Railroad 2.55%
St. Charles Place 2.55%
Marvin Gardens 2.52%
North Carolina Avenue 2.52%
Virginia Avenue 2.43%
Pennsylvania Avenue 2.39%
Short Line Railroad 2.32%
Community Chest 2: 2.32%
Community Chest 3: 2.28%
Reading Railroad 2.26%
Income Tax 2.25%
States Avenue 2.20%
Vermont Avenue 2.18%
Connecticut Avenue 2.16%
Oriental Avenue 2.15%
Luxury Tax 2.11%
Baltic Avenue 2.11%
Boardwalk 2.10%
Park Place 2.10%
Mediterranean Avenue 2.08%
Community Chest 1: 1.86%
Chance 2: 1.56%
Chance 3: 1.24%
Chance 1: 1.23%

Wow! Maybe buying Boardwalk and Park Place isn’t the best idea, statistically speaking. But, while this monte carlo simulation is great and all, it doesn’t give us the full picture. Boardwalk and Park Place pay a lot more if someone lands on them, and Mediterranean Avenue and Baltic Avenue don’t cost that much. So, doing some math, I found the Return per roll, based on costs, landing probabilities, etc (although with three houses, because that is usually the sweet spot). Here are the numbers:

Corrected results (Return Ratio = Expected income per roll ÷ Total cost, shown as % per roll)

So, now we know that Orange is the best set to buy and develop, followed by Red and Yellow. We also find that, surprisingly, Green has a higher expected income per roll, in fact the highest, at $69.8 per roll. This is likely due to a combination of higher landing probabilities and more properties (though Dark Blue does beat Green in Return Ratio (% per roll)). Coming in last in my Return Ratio (% per roll) Table, we find that Utilities are the worst investment in monopoly at 1.23% Return Ratio (% per roll). Following Utilities, we have Brown (1.35%) and Light Blue (2.36%), though Brown and Light Blue are fairly far apart percentage wise.

All in all, we now know the best and worst properties in Monopoly using math, and we know the exact Return Ratio (% per roll) of each Monopoly set, as well as the expected income per roll, the cost to develop each color set, and the probabilities of landing on each property. So, we know to invest in Orange, Yellow, and Red, and we know that we should stay away from Utilities. At the end, we finally ask ourselves:

How did we bring complex math and monte carlo simulations into a simple board game?

See you next time.

Citations:

Kenton, Will. “Monte Carlo Simulation: What It Is, How It Works, History, 4 Key Steps.” Investopedia, 2 June 2025, http://www.investopedia.com/terms/m/montecarlosimulation.asp.