Samuelson spotted a mistake in Bacheliers work. Bachelier's model had failed to consider that stock prices cannot fall below zero.

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.

Your second ducat, like your second million, is never quite as sweet.

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

Carl Friedrich Gauss, often rated the greatest mathematician of all time, played the market. On a salary of 1,000 thalers a year, Euler left an estate of 170,587 thalers in cash and securities. Nothing is known of Gauss's investment methods.

Expectation is a statistical fiction, like having 2.5 children.

A bit is worth 10,000 basis points.