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A disconcerting 28 percent of participants went broke despite having an advantage, and a shocking two thirds bet on tails at some point in the game, which is never rational. On average, the participants walked away with $91 (winnings were capped at $250). This might seem like an ample take for someone starting with $25, but the researchers calculated that over the 300 coin tosses time allowed for, the average winnings of players using the optimal strategy (described below) would be more than $3 million!
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Consider betting on red or black at the roulette table. The payout is even. (That means if you bet $1 and win, you win $1. But if you lose, you lose your $1.) And, for simplicity, assume that you really have a 50–50 shot of calling the correct color. (Real roulette tables have some additional green pockets on which you lose, giving the house a slight edge.) We’ll also suppose that the table has no maximum bet.
Economists warn that although the Kelly criterion works for generating wealth, it’s still a gamble with pitfalls of its own. For one, it assumes that you know your probability of winning a bet, which can be true in many casino games but less so in fuzzy domains such as the stock market. Also, Kelly asserts that in the coin-toss experiment, you’re most likely to grow your wealth if you keep betting 20 percent of it. But if you have $1 million to your name, it’s perfectly reasonable not to want to gamble $200,000 on a coin flip. At some point, you will need to price in your personal level of risk aversion and adjust your fiscal decisions to respect your own preferences.
You might object that this strategy makes money only if you eventually call the right color in roulette, whereas I promised guaranteed profit. The chance that your color will hit at some point in the long run, however, is, well, 100 percent. That is to say, the probability that you’ll lose every bet goes to zero as the number of rounds increases. This holds even in the more realistic setting where the house enjoys a consistent edge. If there is at least some chance that you’ll win, then you will win eventually because the ball can’t land in the wrong color forever.
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