Using Math To Crush Your Opponents In Monopoly, And More

Everybody knows the board game Monopoly, a real estate board game where you try to add utterly destroy your friends. As a kid, and even to this day, it is my favorite board game because it allows me to practice business without actual money and usually, I dominate at it.

If you’ve ever read the rulebook (not many have), Monopoly and officially when everybody goes bankrupt the but one player. But because the game takes such a long time, it usually ends when your sister or father storms off, refusing to play, after the game stretches over 24 hours.

But, before this happens wouldn’t it be great to absolutely destroy your opponents?

Previously you may have thought and you just require a business-oriented mind, and some luck to win in this game. However, there is strategy and math that you can put into play, resulting in a big win. I thought that in this blog post it would be interesting to review how to actually play this game, discuss the math behind it and show how you can use your Monopoly skills in the real world.

The big rule you break, unintentionally

Face it, you have probably never read the rulebook to Monopoly, even if you are a seasoned player, and because of this, you are missing a critical element of the game.

In November, Twitter blew up when a user noticed something in the monopoly rulebook that nobody followed.

“According to Monopoly’s official rules, when you land on a property space and you choose not to buy it, the property must be auctioned off by the banker, and the other players can bid on it. The auction speeds up the game, makes it more strategic, and allows players to buy properties for less than they usually would,” states an Insider article.

This short, unknown rule brings the game up a level. By allowing everybody to bid on the property, it speeds up the game and brings the strategy/risk taking a level up. Writer, Jonny Nexus, created a campaign “For Real Monopoly”, with the intention of bringing this unknown fact to the publics eyes. He stated, “[It] makes the game much more skillful, since it is now more dependent on your ability to trick, bluff, and manage the other players.”

You can choose to accept or deny this rule, just know that it’s actually in the rulebook, and can speed up the game by hours.

Now that we’re over the rules, let’s get into the real juicy part of this blog post – how to use math to crush your friends. There are five major things to know:

  1. Understand the vehicle of the game – dice
  2. Know the best properties to own
  3. Know what properties you should develop
  4. Realize how chance and community chest cards impact the game
  5. How Jail can be used to your advantage.

All movement and randomness in Monopoly is dictated by the dice roll, so you should understand how and what the dice do to be great in this game.

Image result for dice probability chart

Notice how the most probable dice roll is seven in monopoly, meaning that space 7 on the board will receive a lot of traffic right off the bat. However, we also need to factor in rolling doubles, with a chance of that being 1 in 6. In Monopoly, if you roll doubles you get another roll. This throws a tiny wrench in our simple “7 is the most visited spot,” so we need to factor in that probability.

With that factored in, here are the most visited spots on the first roll.


So just teaches us a very basic, but needed principle of the game – you and your opponents will most likely roll at 7, but are also very likely to roll a 5, 6, 9 and 10. So, if possible try to build homes 5 through 10 spots ahead of your opponents.


Inexperienced players might think that Park Place and Boardwalk are the best properties to own, due to their high rent.

This, however, is not the case because the probability of landing on them is much lower than some other properties. This brings us to point two:

2. Know What To Own

We could do some very complicated math, and figure out which property is the best to own, but Monopoly champ Bjørn Halvard Knappskog already did that. He shared the following heat map of the squares that get the most and least traffic.

monopoly board heatmap property likelihood
You Want To Own The Red Squares.

You want to own properties in the orange and red neighborhood because probability dictates that players will land their most often. It makes sense, Jail is the most visited, and the properties 6-8 spots away from Jail are most visited.

Now that you know what properties are the best to own, let’s figure out which are the best to develop.

3. Know What To Develop

If you want to get the biggest return on your investment, you should build three houses at a time on your properties. This is the quickest way to make back more than what you’ve spent.

Houses increase rent on properties, and the biggest jump is between two and three houses, which raises the rent from $200 to $550 (on an orange property). While a fourth house and hotel will increase the rent to a maximum of $950, the increase per house is lower than that of the third house.

So, develop the heat spots with three houses each, as well as buying and developing properties that are about 7 spaces away from opponents.

Break Even Chart From Tim Darling

4. How Chance and Community Chest Cards Impact The Game

If you look at the first probability chart, you will notice that chance is the number one most landed on spot in the first move of the game, because it’s placed seven spots away from go.

These things mess with the simple mathematical probabilities of the game, because they can throw you to various parts of the board, but can be accounted for in calculations.

For Chance, there are 16 cards with five different outcomes:

  • You can get out of Jail free (1/16)
  • You collect money (3/16)
  • You advance somewhere on the board. (8/16)
  • You pay money (3/16)
  • You go to jail, directly. (1/16)

In 9/16 instances, you move to a different part of the board with a chance card. From a Business Insider presentation, here’s where you go:

Now let’s look at Community Chest. These cards also have five different outcomes:

  • You can get out of Jail free (1/164)
  • You collect money (9/16)
  • You advance somewhere on the board. (1/16)
  • You pay money (4/16)
  • You go to jail, Directly. (1/16)

So now, you can use math to figure out what is most likely to happen when you pick a card (chart from the same presentation):

So, because you have the greatest combine chance of moving to another space when you get a card, you should buy the properties that Chance sends you to —the Railroads, New York Ave, St. Charles Place, Illinois Ave and Boardwalk You should also buy properties neighboring these areas.

5. How Jail Can Be Used to Your Advantage.

If you look back to the heatmap, Jail is the most visited spot on the board, due to its placement, and the Chance/Community Chest cards.

So, use this to your advantage, and save the “get out of jail free” cards to sell to others. Also, invest in property that is a probable roll away from jail, as seen on the heat map.

Also, if you are one of the unfortunate players to get sent to jail (its common, the board is designed to do this to you), know that you have a 42% chance of getting out by a third turn. Based on the situation, you can use this to buy time, and get within 6-8 spaces ahead of your opponent and invest accordingly.

Here are the probabilities of being in a space in monopoly when you are well into the game. Note that orange and red neighborhoods are the most visited, as are Rail Roads. Rail Roads are great investments, and you should try to get them ASAP, as well as the properties on the most visited neighborhood.

Here Are The Things You Should Learn From This Game, And Apply In Real Life

  • Set Aside Money For Dark Days

You need to have money aside if you have bad luck in the game. Same should be for life. Start an emergency savings fund.

  • Know ROI

Know how long it will take to break even on investments (mainly real estate) determine their worth from it.

  • Use Math To Make Life Simpler

You can use math, especially in business to make stuff simpler.

  • Negotiation

There’s a big negotiation aspect in the game, as well as in life.

  • Risk Managment

Learn when to take risks, and when you shouldn’t.

P.S.: Whatever way you look at it, utilities are completely pointless.


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