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

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

The best strategy is one that offers the highest compound return consistent with no risk of going broke.

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.

Expectation is a statistical fiction, like having 2.5 children.

"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.