Kelly Criterion

The Kelly Criterion is a stake-sizing formula introduced by John L. Kelly Jr. in 1956 that returns the mathematically optimal share of a bankroll to commit to a positive-expected-value bet. It reconciles two opposing aims: maximizing long-run growth while holding the risk of ruin in check. By scaling each wager to the perceived edge and the offered odds, Kelly compounds a bankroll faster than any rival staking method over time, yet never stakes so much on one bet that a single loss is fatal.

The core formula is Kelly % = (bp - q) / b, where b is decimal odds minus 1, p is the win probability, and q is the loss probability (1 - p). The output is the bankroll fraction to stake. In practice most bettors apply fractional Kelly — commonly one-quarter or one-half of the full figure — to dampen the volatility of aggressive sizing. Full Kelly is theoretically optimal but generates large bankroll swings that most find uncomfortable.

Example

Suppose a team has a 60% win chance and the book prices it at +120 (decimal 2.20). Plugging in: 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 bankroll. On a $1,000 bankroll, full Kelly is $267. Many would instead deploy half Kelly ($133.50) or quarter Kelly ($66.75) to smooth variance and hedge against a 60% estimate that is slightly off.

Key Points

• Maximizes long-term growth: Of all fixed-fraction staking methods, Kelly delivers the fastest bankroll growth rate when probability estimates are accurate.
• Sensitive to probability errors: A small error in your true win probability can cause Kelly to oversize stakes, raising the risk of severe drawdowns.
• Fractional Kelly is standard practice: Most seasoned bettors stake a fraction (typically 25% to 50%) of full Kelly to cut volatility and cushion estimation error.
• Never bets on negative EV: For edgeless bets the formula returns zero or a negative figure, confirming that no stake belongs there.
• Dynamic sizing: Kelly staking rescales bet size automatically as the bankroll moves, wagering more after wins and less after losses.