Introduction

Ever since I was a kid, I’ve objected to the phrase, “winning isn’t everything”. If you’re not here to win, then what are you playing for? With that in mind I’d like to ask all of the losers of the world to click out of the window. This article is for the winners.

Hello Winners.

The game we’re going to discuss has actually been banned from family game night for “excess ruthlessness” and “downright inhumanity” as my mother puts it. It’s a game that takes no pity on the constructs of “family” and “friendship”. It’s a game that so perfectly epitomizes American styled capitalism that J.P. Morgan is the iconic mascot. Today we’re going to tackle the cut-throat game of skill, tactics, and cruelty known as Monopoly, by the Parker Brothers.

Monopoly is often summarized as “that game that lasts for four hours” or “that game where the guy with Boardwalk always wins”. As you will soon see, these hasty generalizations, as well as a number other of your own assumptions about the game, are wholly false.

Monopoly is a fundamentally short game.

Monopoly is more than just the dark blue.

Monopoly is ruled by statistics, as is all.

How The Die Work

The first and most critical aspect of the game to understand is the device that propels the game: the dice. If you’ve taken any high school level statistics class you probably already know the possible combinations presented by two die (as well as the infinitely useful deck of cards), but for those less fortunate, I’ll elaborate.

Each die rolled in the game has six possible outcomes: 1,2,3,4,5, or 6. If monopoly was ruled by one dice instead of two die, this would be simple. Each of the six possible outcomes would have an equal chance of occurring: 1/6, or approximately 17%. However, this is not how the game is played. The game uses two die, so we must account for the other possible combinations–another list of 1,2,3,4,5, or 6. Consequentially, introducing this second series of numbers actually increases the list of probabilities to thirty-six. This occurs because of the possible two number combinations, such as 1,1; 1,2; 1,3; and so on. The importance in noting this is that these numbers do not share the same equivalency that the single-list model did. There were six outcomes and six combinations; there are now only eleven possible outcomes, but thirty-six possible combinations.

This phenomenon occurs because of how the numbers combine. To get a roll of “2”, there is only one way the dice may be arranged: a one and a one. Since there are thirty-six combinations, this gives an approximate chance of 3% for any given roll to output a “2”. The rest of the outcomes are formulated the same way, so let me save you the math.

2: 3%

3: 6%

4: 8%

5: 11%

6: 14%

7: 17%

8: 14%

9: 11%

10: 8%

11: 6%

12: 3%

These probabilities prove incredibly useful in planning on how to attack the board, and it also yields a fundamental law of board games: the rule of seven.

The Rule of Seven

All that the rule of seven says is that the most likely outcome for any roll is the number seven. While it is not incredibly likely, with just around a 1/6 chance of occurring, it is rolled nearly twice as much as the numbers four and ten, and six times as much as the numbers two and twelve.

This rule is something to keep in mind when building houses on your monopolies. If a six, seven, or nine will land someone on one of your properties, then you have a 42% chance of collecting that sweet sweet payday; it is advisable to build on your properties in this scenario.

The Most Visited Space

How can we possibly find the most popular square on the board? Well, it’s actually quite simple; in fact, it’s staring right at us.

Between the two cards, there are six Chance and Community Chest spaces scattered around the board. These two stacks of cards yield quite a few “go directly to jail” commands, which, along with being a popular destination according to the rule of sevens, makes Jail the most visited space on the board, with a net 4% average of all rolls. Sound like an allegory for Americanism yet?

The fact that Jail is so frequently visited is also owed to the fact that when in Jail, many players consciously decide to finish their sentence of three turns. Why you may ask?

To avoid the dangerous monopolies on the board.

As the game progresses, the game becomes less about acquiring new properties, and more about avoiding the predatory monopolies that have already sprung up. A viable strategy to counter this is to try to get into the Jail. If you are in the Jail, you are not on the rest of the board. It is as simple as that.

The Most Valuable Properties

The rule of seven leads us to another incredibly useful discovery in Monopoly: the Orange monopoly is the most fruitful. The Orange monopoly is the most visited in the game, with roughly 8.8% collectively of all rolls. Most of these rolls come from Jail, as the Orange properties are 6, 8, and 9 spaces away from Jail respectively, giving the Orange a 39% chance to reap the benefits of the felons. The monopoly is helped by the fact that it only costs $100 to build a house on the Oranges, and that one card demands immediate travel to the Orange Block.

Railroads and Utilities

I felt a little dirty writing the previous section without mentioning my beloved railroads. The railroads are one of the most cost efficient sets of properties out there, with just a thirteen landing turnaround time if you own all four. Conversely, the utilities, to put it nicely, are complete and absolute filth. Their inefficiency comes mostly from a general inability to improve the monopoly, with just one possible improvement. Don’t be fooled by the multiplier, it’s not John Maynard Kenyes.

Stop Buying At Three

It may be tempting, over the course of a game, to lavishly pour obscene amounts of money into a single monopoly. I assure you, this is not the road forward. In fact, hotels are often never paid back. Instead, they lie their above your property, a testament to your bombast and stupidity.

The proper way to build on your monopoly is to stop at three. As seen in the graphic below, the third house is paid back with the least amount of rolls, hence it reduces your reliance on luck, and instead returns your fate into your hands.

The schedule below shows the number of residents you need to have pay rent before the your investment in the property is returned in full.

Conclusion

Well winners, that’s it. Monopoly is a game of skill, and shrewd business deals. Work hard to get your first monopoly, then remember your training. You’ve done all you can.

Oh, and remember: if by any chance you lose, it’s just a game of luck.

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