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.
Samuelson, however, hedged his personal bets - by putting some of his own money in Berkshire Hathaway.
For reasons mathematical, psychological, and sociological, it is a good idea to use a money management system that is relatively forgiving of estimation errors.
Are there any mythical beasts which aren't simple pastiches of nature? Centaurs, minotaurs, unicorns, griffons, chimeras, sphinxes, manticores, and the like don't speak well for the human imagination. None is as novel as a kangaroo or starfish.
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.
Paradox is thus a much deeper and universal concept than the ancients would have dreamed. Rather than an oddity, it is a mainstay of the philosophy of science.
The story of the Kelly system is a story of secrets - or if you prefer, a story of entropy.
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.
Samuelson spotted a mistake in Bacheliers work. Bachelier's model had failed to consider that stock prices cannot fall below zero.
A bit is worth 10,000 basis points.
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.
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.
In American culture the coin toss is the paradigm of the random event. A coin toss decides who kicks off the Super Bowl. Looked at another way, a coin toss is not random at all. It is physics.
The problem with winning at blackjack and sports betting is that sooner or later a big guy in a suit tells you to leave.
The best strategy is one that offers the highest compound return consistent with no risk of going broke.