Part III: Business & Regulation · Gambling Mathematics & Probability

61. Kelly Criterion

Risk Management

The Kelly Criterion is a mathematical formula that determines the optimal fraction of a bankroll to wager on a positive expected value bet to maximize the long-term geometric growth rate of the bankroll while eliminating risk of ruin. The formula is: f* = (bp - q) / b, where f* is the optimal fraction of bankroll to bet, b is the net odds received on the wager, p is the probability of winning, and q is the probability of losing. In practice, most professional gamblers use “fractional Kelly” (betting 1/4 to 1/2 of the full Kelly amount) to reduce volatility and account for estimation errors in their edge calculation. Casino operators encounter the Kelly Criterion concept when setting maximum bet limits relative to house bankroll and when evaluating advantage play threats.

In practice

Full Kelly betting produces extreme volatility — bankroll swings of 50% or more are common. Half-Kelly reduces volatility by 50% while retaining 75% of the growth rate. Quarter-Kelly is popular among professional bettors as a conservative approach. Overbetting Kelly (betting more than the optimal fraction) actually reduces growth rate and increases risk of ruin.

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