Warning, this chapter contains a little math. It's nothing intimidating, mostly multiplication and some simple algebra, but I know a lot of people don't like it. If that describes you, I urge you to read the chapter anyway. It's one of the most important in the book. You can skip the math and get the ideas anyway.
Two of the most important discoveries about risk were made in the 1950s by Harry Markowitz and John Kelly. Markowitz's result became the basis of modern finance. Kelly's result received much less academic attention, and was rejected by many mainstream economists. From a practical standpoint, however, the situation was reversed. Markowitz's theory was crucially important, but the computer power available at the time was insufficient to translate it into practical results. When advances in computers solved that problem, the pure Markowitz portfolios proved to be unusable.
In contrast, Kelly's result proved invaluable for practical risk takers. It did not require computer power. It was not a useful abstraction for understanding the true nature of things; it was a practical formula for direct application. However, it could not achieve its full power until it was linked with Markowitz's work, something that did not happen until the late 1980s.
This chapter explains the two ideas and their interaction in a historical counterfactual. What if Kelly had been in the University of Chicago library one fateful afternoon when Harry was musing over some ...