Expectation is a statistical fiction, like having 2.5 children.

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.

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

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

"Average" isn't so hot at the race track given those steep track takes. "Average" is pretty decent for stocks, something like 6 percent above the inflation rate. For a buy-and -hold investor, commissions and taxes are small.

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

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.