Use "entropy" and you can never lose a debate, von Neumann told Shannon - because no one really knows what "entropy" is.

Kelly was aware that there is one type of favorable bet available to everyone; the stock market.

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

Bernoulli's real contribution was to coin a word. The word has been translated into English as "utility". It describes this subjective value people place on money.

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.

The best strategy is one that offers the highest compound return consistent with no risk of going broke.

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