Kelly Criterion

The Kelly Criterion is a staking formula developed by John L. Kelly Jr. in 1956 that calculates the mathematically optimal percentage of a bankroll to wager on a bet with a positive expected value. The formula balances the competing goals of maximizing long-term growth and minimizing the risk of ruin. By sizing bets in proportion to the perceived edge and the odds offered, the Kelly Criterion aims to grow a bankroll faster than any other staking method over the long run, while never risking so much on a single wager that a loss becomes catastrophic.

The basic formula is: Kelly % = (bp - q) / b, where b is the decimal odds minus 1, p is the probability of winning, and q is the probability of losing (1 - p). The result is the fraction of the bankroll that should be wagered. In practice, many bettors use a fractional Kelly approach, typically betting one-quarter or one-half of the full Kelly amount, to reduce the volatility that comes with aggressive bet sizing. Full Kelly staking, while optimal in theory, can produce dramatic bankroll swings that most bettors find uncomfortable.

Example

You believe a team has a 60% chance of winning, and the bookmaker offers odds of +120 (decimal 2.20). Applying the Kelly formula: b = 1.20, p = 0.60, q = 0.40. Kelly % = (1.20 x 0.60 - 0.40) / 1.20 = (0.72 - 0.40) / 1.20 = 0.267, or 26.7% of your bankroll. If your bankroll is $1,000, the full Kelly stake would be $267. Many bettors would instead use half Kelly ($133.50) or quarter Kelly ($66.75) to smooth out the ride and account for the possibility that their 60% probability estimate is slightly off.

Key Points

• Maximizes long-term growth: Among all fixed-fraction staking strategies, the Kelly Criterion produces the fastest bankroll growth rate when probability estimates are accurate.
• Sensitive to probability errors: If your estimate of the true win probability is even slightly wrong, Kelly can recommend bet sizes that are too large, increasing the risk of significant drawdowns.
• Fractional Kelly is standard practice: Most experienced bettors use a fraction (commonly 25% to 50%) of the full Kelly amount to reduce volatility and provide a buffer against estimation errors.
• Never bets on negative EV: The formula naturally returns zero or a negative number for bets without an edge, confirming that no stake should be placed.
• Dynamic sizing: Kelly-based staking automatically adjusts bet sizes as the bankroll grows or shrinks, betting more after wins and less after losses.