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

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

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

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

People tend to be clueless about prices. Contrary to economic theory, we don't really decide between A and B by consulting our invisible price tags and purchasing the one that yields the higher utility, he says. We make do with guesstimates and a vague recollection of what things are “supposed to cost.”

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.

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.