Kelly Criterion

The Kelly Criterion is a staking formula, introduced by John L. Kelly Jr. in 1956, that identifies the mathematically optimal share of a bankroll to commit to a wager carrying a positive expected value. Its purpose is to reconcile two objectives that usually pull against each other: accelerating long-term capital growth while keeping the probability of ruin under control. By scaling each stake to both the perceived edge and the price on offer, Kelly is designed to compound a bankroll more efficiently than any rival method over a long horizon, yet it never commits so much to one bet that a single loss proves ruinous.

The formula is written as Kelly % = (bp - q) / b, in which b denotes the decimal odds minus 1, p is the probability of winning, and q is the probability of losing (1 - p). The output is the proportion of the bankroll to stake. In real-world use, many bettors adopt a fractional Kelly, committing a quarter or a half of the full figure, precisely to dampen the swings that aggressive sizing produces. Full Kelly is theoretically optimal, but it generates bankroll fluctuations severe enough to unsettle most practitioners.

Example

Suppose you judge a team’s chance of winning at 60%, and the bookmaker prices it at +120 (decimal 2.20). Feeding those values into the 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 the bankroll. On a $1,000 bankroll, full Kelly calls for a $267 stake. Many bettors would scale that back to half Kelly ($133.50) or quarter Kelly ($66.75), smoothing the variance and hedging against the chance that the 60% estimate is somewhat off.

Key Points

• Maximizes long-term growth: Of all fixed-fraction staking approaches, Kelly delivers the quickest bankroll compounding when the underlying probability estimates hold true.
• Sensitive to probability errors: Even a modest miscalibration of the true win probability can lead Kelly to recommend oversized stakes, raising the danger of severe drawdowns.
• Fractional Kelly is standard practice: Seasoned bettors commonly stake a fraction of full Kelly (typically 25% to 50%) to temper volatility and build in a cushion against estimation error.
• Never bets on negative EV: For any wager lacking an edge, the formula naturally yields zero or a negative figure, signalling that no stake belongs there.
• Dynamic sizing: Kelly staking recalibrates automatically as the bankroll expands or contracts, wagering more after gains and less after losses.