The Number Mysteries: A Mathematical Odyssey through Everyday Life (MacSci) by du Sautoy Marcus

Author:du Sautoy, Marcus
Language: eng
Format: epub
Publisher: Palgrave Macmillan
Published: 2011-05-24T00:00:00+00:00

HOW CAN MATH HELP YOU WIN AT MONOPOLY?

Monopoly appears to be a pretty random game. You throw two dice and speed around the board in your car or strut along in your top hat, buying property here, building hotels there. Every now and again you might come second in a beauty contest thanks to a Community Chest card or have to cough up $20 for drunk driving. Each time you pass GO, you collect another $200. How on earth can math give you an edge in this game?

Over the course of the game, which is the most visited square on any Monopoly board? Is it the GO square where you start, the Free Parking diagonally opposite, or perhaps Virginia Avenue or the Boardwalk? The answer is in fact the Jail square. Why? Well, you could just throw the dice and find yourself just visiting, or you might find that the dice takes you to the square diagonally opposite, where a policeman tells you to go to jail. You might even be unlucky and pick up one of the Chance or Community Chest cards that send you straight to jail. And if that wasn’t enough ways to send you down, if you throw a double, you get to go again, but if you throw three doubles in a row, then rather than being rewarded for your impressive feat of dice rolling, that too is punished with a three-turn sentence.

As a result, on average, players find themselves visiting the Jail square about three times more often than most other squares on the board. That isn’t much help to us at the moment, because you can’t buy the jail. But here is where the math comes to the fore: where are players most likely to land after being in jail? The answer depends on the most likely throw of the dice when they leave that square.

Each die can land equally on one of the six faces. With two dice, that gives 6 x 6 = 36 different possible throws, each equally likely. But when you analyze those possibilities, you find that a score of 2 or 12 is very unlikely, because there’s only one way to make either of these combinations, whereas there are six ways to make a total score of 7.

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