There is a deep connection between Bernoulli's dictum and John Kelly's 1956 publication. It turns out that Kelly's prescription can be restated as this simple rule: When faced with a choice of wagers or investments, choose the one with the highest geometric means of outcomes.

Expectation is a statistical fiction, like having 2.5 children.

The story of the Kelly system is a story of secrets - or if you prefer, a story of entropy.

There were many at Bell Labs and MIT who compared Shannon's insight to Einstein's. Others found that comparison unfair - unfair to Shannon.

At a bare minimum, understanding entails being able to detect an internal contradiction: a paradox.

The best paradoxes raise questions about what kinds of contradictions can occur-what species of impossibilities are possible.

The ultimate compound return rate is acutely sensitive to fat tails.