Part III: Business & Regulation · Gambling Mathematics & Probability

Kelly Criterion

Risk ManagementREPORTED

(1) 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. (2) A formula determining optimal bet size based on edge and bankroll.

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. Used by professional gamblers and investors.

One entry from the Casino Industry Glossary, 1,090 terms written for surveillance, compliance and operations professionals rather than for players. Definitions describe industry usage; where a term carries a regulatory meaning, verify against the instrument that governs your jurisdiction.