## MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

## May 21, 2007

### Monopoly Cheat Sheet

Have you ever been stuck in one of those never-ending Monopoly games,* the sort your mom makes you move to the basement because she doesn't want tiny hotels in the mashed potatoes? If you have, you probably think Monopoly is pretty much a game of endurance (who can stand it the longest) rather than of strategy. After all, you have no control of where you land when you throw the dice and every player follows the same strategy: Buy everything in sight.

But mathematicians who have built computer models of the game would tell you otherwise. You don't have an equal chance of landing on every square. Instead, you are more likely to hit some than others. The square players spend the most time on is Jail, which shouldn't be too surprising because there are so many different ways of being sent there. The next-most-popular squares include ones players tend to hit when they leave Jail (Illinois Avenue, Go, B&O Railroad, Free Parking, and Tennessee Avenue). Mediterranean, Baltic, and Park Place, in contrast, get little traffic, something you might want to consider before buying them.

Although it is tempting to race around the board buying up every available property, you can gain an advantage by being choosy. Which properties are best depends on the stage of the game. At first, railroads and utilities are good investments because a lot of players land on them. But as players gain monopolies and build houses and hotels, railroads and utilities become less important because they pay back much more slowly than other properties.

So what is the best real-estate investment? The orange properties get a lot of traffic from players leaving Jail, they don't cost much, and they have relatively high rents. Together this means they are the fastest to pay back the money you put into buying them. It takes a lot longer for green or purple properties to break even.

On the other hand, if you're certain your fellow players are going to stick it out to the bloody end, you might want to go for green. The green properties are relatively expensive but they pay the most per visitor. So once you've paid them off, you can sit back and rake it in. (Avoid purple at all costs. Those properties take forever to break even, and they pay the least per visitor.)

Of course there's a lot more to the game than rolling dice and buying property. You have to know when to make deals and what to bid in property auctions. In those situations you might want to rely on skills computers can't mimic: schmoozing and sneakiness.

* Just so you know: according to Hasbro, the maker of Monopoly, the longest game ever played lasted 70 straight days. (Is that with or without sleep breaks? we'd like to know.)

Muse, January 2003, p. 18-19.