Monopoly is Rigged

You’re not paranoid.

Monopoly is out to get you.

Even with a data-driven, YouTuber certified, “can’t lose” strategy, you can still go bankrupt.

Improbably, a hotel-enhanced Connecticut Avenue led to my recent downfall .

“Six hundred bucks, dad,” my son called out.

THREE. FREAKING. TIMES.

Penniless, I cursed the dice and mumbled about my rotten luck.

He just laughed.

There is a reason why Monopoly is the most banned board game.

Perhaps, you have experienced similar financial ills from Illinois Avenue or been bankrupted by Boardwalk. With this post, we will find the “hot” properties and why we land on them so much, why playing the odds doesn’t always work, and finish with some tips to stay financially solvent.

Need a rules refresher? Start here.

Mechanics of Monopoly

To start, there are 40 positions on the game board (numbered in red):

Figure 1: Monopoly game board. Positions numbers from 1 (GO) to 40 (Boardwalk)

During gameplay, we take turns rolling two, 6-sided dice, sum the total, and move that many spaces. Roll doubles and we roll again but roll three consecutive doubles and we go to jail for “speeding”.

If we land on any of the 22 properties (e.g. Boardwalk), four railroads (e.g. Reading Railroad), two utilities (Electric Company and Water Works), Income Tax, Luxury Tax, Free Parking, Jail, or GO, we remain there at the end of our turn.

Conversely, the other seven positions can cause additional movement . GO TO JAIL is self-explanatory. The others, three Community Chest and three Chance, lead to card draws for some unknown fate. While both 16-card decks contain “Advance to GO” and “Go directly to Jail”, Chance has eight more movement-inducing cards sending us to St. Charles Place, Illinois Avenue, Boardwalk, Reading Railroad, the next railroad, the nearest railroad, the next utility, or back three spaces.

There’s a lot going on, but already we see a couple of things:

1. We are going to jail. A lot!

One position is Jail. Another sends us to Jail. Cards send us to jail. “Speeding”? Jail. We will end our turn on jail more than any other position. This also has a secondary effect: Properties one or two rolls away from jail will see a bump up in their end of turn probabilities.

2. We probably won’t stay on Chance if we land there

Ten of the 16 cards send us elsewhere on the board. Chance should be the least frequent end of turn position. We should also end on positions called out by the cards, e.g. GO and Reading Railroad, more frequently than other places on the board.

With the mechanics in mind, let’s find those hot spots!

Methodology

We have two ways to find the probability of ending a turn on each property: analytical and empirical.

For an analytical solution, we need to identify every combination of 40 board positions, 216 dice roll combinations (to account for speeding), and 20,922,789,888,000 possible Chance and Community Chest decks. The numbers get astronomical in a hurry.

Option two is an empirical approach: play the game and count as we go. Looking at a 50-move game, the end of turn distribution might look like this:

Figure 2: End of turn distribution for a simulated 50-move game (left) and Monopoly game board (right).

In this game, we ended on some positions 8% of the time and several others not at all! There’s no way to tell where the true hot spots are based on this alone. We need more data. In fact, it takes about 20,000 games to reach a steady state where the probabilities change a negligible amount regardless of how many additional games we play. In other words, the probabilities after 20,000 games and 1,000,000 games look almost identical.

With normal play taking 60 minutes per game, it would take us over 800 days to hit steady state. Thankfully, computers are much more effective at this type of work! Business Insider, for example, put together this analysis:

Figure 3: End of Turn Steady State Probabilities for game play. Simulated players “posted bail” immediately after being sent to jail. https://www.youtube.com/watch?v=7_SXFtdf65s

All things equal, we land on each position 2.5% of the time. But they’re not equal. Jail, as expected, is tops at 6.3%. The top five properties are Illinois Ave (3.2%), B&O Railroad (3.2%), GO (3.1%), New York Avenue (3.1%), and Reading Railroad (3.0%). Note that all five are associated with Chance cards.

The bottom 3? All Chance. We knew it!

This is all very nice, but it still doesn’t explain Connecticut Avenue. How did a property with a 2.3% end of turn probability put me in the poor house?!?

It’s due to the chaotic nature of dice rolls and card draws that led to an unexpected (and unprofitable!) result. While the steady state analysis provides a good strategy, a single Monopoly game will never get to steady state. We expect to land on Connecticut Avenue once per 50-turn game (2.3% x 50 turns = 1.15) but it’s possible to land there over 12 times! I lost, in part, because my son snagged the property early on, built a hotel, and cashed in on my unlikely string of landings.

Rigging Monopoly in our favor

Steady state or no, we want to win! This succinct guide will improve our odds.

Some highlights:

1. Buy orange and red properties

These are on the hottest part of the board. Scoop ’em up, finish the monopoly, build houses, and collect that rent!

2. Build three houses on your monopolies ASAP

This provides the optimal balance of the cost to build houses and the benefit of higher rent. Properties with three houses make money back sooner than any other situation.

3. Stock up on railroads; avoid the utilities

Railroads rake in the rent, especially when we get all four. The utilities? Not so much.

With these tips and an understanding of the game’s statistics, we will be ready for our next Monopoly matchup. And while it might not make strategic sense, if my son even thinks about buying Connecticut Avenue, he’s grounded!


Gratitude

Thanks for reading! Comment below about what you liked (or didn’t!).

Also, a big thank you to the Foster crew – Chris, Stew, Joel, David, and Christine – for edits and suggestions!

Further reading

Here are a few more resources to check out:

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