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Audit the size. Calculate the optimal fraction of your bankroll to wager to maximize long-term growth and avoid ruin.
Step-by-step breakdown of the underlying equations.
The **Kelly Criterion** ensures you bet just enough to grow your wealth exponentially without the risk of "Gambler's Ruin." For a 55% win probability at 1.0:1 odds, the math suggests risking exactly 10.0% of your total capital.
The Kelly Criterion Calculator determines the optimal percentage of your bankroll to wager on a bet with positive expected value. It balances the tradeoff between betting too little (leaving money on the table) and betting too much (risking ruin from variance).
When used correctly over many bets, Kelly betting maximizes the geometric growth rate of your wealth while providing a natural protection against going broke—even if you experience bad luck.
Scenario: You have a coin flip bet where you win $2 for every $1 wagered (2:1 odds), but the coin is biased—you win 55% of the time.
Practical tip: Consider betting 25-50% of the Kelly amount (fractional Kelly) to reduce volatility while still capturing most of the expected growth. This is especially important when probabilities are estimated rather than known.
The Kelly Criterion is a formula developed by John Kelly Jr. at Bell Labs in 1956 for maximizing the long-term growth rate of a bankroll. It determines the optimal fraction of your capital to risk on a bet with positive expected value. It's used by professional gamblers, traders, and investors to size positions mathematically.
A negative Kelly fraction means the bet has negative expected value—you should not bet at all. This happens when the odds don't adequately compensate for the probability of losing. In this case, the Kelly recommendation is to wager 0% of your bankroll.
Full Kelly betting can be volatile and psychologically difficult to stick with. Half Kelly (betting 50% of the recommended amount) reduces volatility significantly while still capturing about 75% of the long-term growth rate. Many professionals use fractional Kelly (1/4 to 1/2) to smooth out the equity curve and reduce risk of large drawdowns.
Yes, but with caution. For stocks, you need to estimate win probability and payoff ratio—both difficult to know precisely. Small errors in these estimates can lead to significant over-betting. Most quant investors use fractional Kelly and diversify across multiple uncorrelated positions. Kelly works best for binary outcomes with known probabilities.
Kelly assumes: (1) You know the exact win probability, (2) Outcomes are independent, (3) You can bet fractional amounts, (4) You want to maximize long-term growth (not short-term utility), (5) You'll play many rounds. In reality, probabilities are estimated, not known—so Kelly provides a ceiling, not an exact recommendation.