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

The more improbable the message, the less "compressible" it is, and the more bandwidth it requires. This is Shannon's point: the essence is its improbability.

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

A bit is worth 10,000 basis points.

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

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

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.