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.

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

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

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

Samuelson, however, hedged his personal bets - by putting some of his own money in Berkshire Hathaway.

The engine driving the Kelly system is the "law of large numbers." In a 1713 treatise on probability, Swiss mathematician Jakob Bernoulli propounded a law that has been misunderstood by gamblers (and investors) ever since.