The infinite expectation is a big problem for anyone who wants to use math to decide what to do in the real world. It implies that no amount of money is too much to pay for the privilege of playing this game. Were a casino to charge a million dollars to play this game, rational customers should jump at the chance, it would seem. Same if the casino

In the most direct human terms, LTCM’s problem was group-think. Under John Meriwether, there was an organizational culture in which questions of risk were pressed only so far. This appears to have led to systematically rosy projections. Too little of the fund’s brainpower went to skeptical probing of what could have gone wrong.

Within a few years as U.S. Attorney, Giuliani was probably the nation’s best-known crime-fighter since J. Edgar Hoover. That was due both to how many important convictions he secured and to his genius for promoting them. Though Giuliani expanded the U.S. Attorney’s office to 132 assistants, he presented himself as the iconic figurehead of that offi

Meriwether did not himself possess a first-rate mathematical mind. Instead, he recruited the top academic talent. No finance professor was more respected than Robert C. Merton. Merton had consulted for Salomon Brothers, so Meriwether already knew him. He agreed to come on board. Meriwether’s other great coup was recruiting Myron Scholes. As journal

The consumer of VaR reports is led to believe that the numbers are reliable because smart people have gone to a lot of trouble to work them out. The numbers are only as good as the assumptions underlying them.

The Kelly system manages money so that the bettor stays in the game long enough for the law of large numbers to work.

The best you can do right now is to choose a portfolio with the highest geometric mean of the probability distribution of outcomes, as computed from current means, variances, and other statistics. The returns and volatility of your investments will change with time. When they do, you should adjust your portfolio accordingly, again with the sole obj

The core of John Kelly’s philosophy of risk can be stated without math. It is that even unlikely events must come to pass eventually. Therefore, anyone who accepts small risks of losing everything will lose everything, sooner or later. The ultimate compound return rate is acutely sensitive to fat tails.

The Kelly formula says that you should wager this fraction of your bankroll on a favorable bet: edge/odds The edge is how much you expect to win, on the average, assuming you could make this wager over and over with the same probabilities. It is a fraction because the profit is always in proportion to how much you wager. Odds means the public or to