Fortune's Formula

Let's consider a game with a positive expected value. Say I offer you even money on a biased coin with a 55% chance of landing on heads. You start with a bankroll of $100. How much should you bet? If I offer you just a single toss, your expected value is maximized when you bet your entire bankroll on heads. But if we play the game repeatedly, this is not a good strategy; on any flip there is a 45% chance of losing your entire bankroll. Turns out that your long-term expected value is maximized when you bet exactly 10% of your bankroll on every flip. This is known as the Kelly criterion. Surprisingly, it is equivalent to maximizing the expected mean of the logarithm of your bankroll--i.e., utility--or the geometric mean of outcomes.

William Poundstone's book Fortune's Formula gives a history of the Kelly criterion in the context of gambling, organized crime, and investing. With such juicy topics, you can't help but enjoy the book. At the same time, the book is big deal about nothing. The author knows that the Kelly Criteria isn't an investing panacea--it results in great volatility, and you need to fight the efficiency of the market--so he just makes endless hints and casual suggestions. It's like listening to the president talk about Iraq.