This is basically a user-friendlization of some of the rather unwieldy tables Probabilities in the Game of Monopoly®, which uses a Markov-chain-based approach. If you can compute the probability that a given space gets landed on, then you know how often you'll collect rent for that space if you have it; this in turn lets you know which properties are good to buy, put houses on, and so on. (Incidentally, the best return on investment in the game seems to come from buying the third house on any given property.)

However, the assumption that underlies all this is that when playing Monopoly, you're trying to

*maximize your expected winnings*. Unless you play for actual money (and maybe not even then), what you're actually trying to do is

*stay in the game longer than everybody else*, which is different. In an actual game you might want to take bets that are more likely to pay out rather than bets that are risky but pay extraordinarily well when they do. This doesn't really apply to Monopoly the way I've stated it (all the squares have roughly equal probabilities of being landed on), but it seems to imply that if you want to play conservatively (say, because you're winning and you'd like to preserve that), you can do so by building up two sets of cheap properties than one set of expensive properties. Conversely, if you're behind you probably want to build on expensive properties and hope desperately that someone lands on them. Diversification is

*usually*good, but not in those cases where the expected value is kind of crappy and only the best possible outcomes will keep you alive.

## 1 comment:

You should read this:

http://www.bjmath.com/bjmath/kelly/kelly.pdf

A player should try to maximize the expectation of the log of his fortune.

Post a Comment