01 October 2007

Martingale road

I recieved in the mail at school today a brochure about being a "Chartered Enterprise Risk Analyst" from the Society of Actuaries.

The Society of Actuaries has a return address on Martingale Road, in Schaumburg, Illinois.

I suspect the name of this road is not a coincidence.

The martingale was originally an excessively silly betting system. Imagine you're betting on the flipping of a fair coin, and you will receive whatever you bet if the coin turns up heads but must pay the same amount if the coin comes up tails. Then you can guarantee that you win money by betting $1 on the first flip, $2 on the second flip, $4 on the third flip, and so on; once you win you quit the game. You are guaranteed to win exactly $1. Unfortunately this guarantee only holds if you begin with an infinite amount of capital. The probability-theoretic version of the martingale (see Wikipedia is inspired by this; of course, a lot of probability-theoretic notions are inspired by gambling.

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