Kelly Criterion
A formula that pinpoints the ideal stake by weighing your edge against your bankroll for the fastest sustainable growth.
The Kelly Criterion is a staking formula that John L. Kelly Jr. introduced in 1956 to pinpoint the mathematically ideal share of a bankroll to put on a positive-expected-value bet. It tunes two opposing goals against each other: pushing long-term growth as high as possible while keeping the odds of going broke in check. By scaling each stake to your perceived edge and the price on offer, Kelly is designed to compound a bankroll faster than any rival staking method over time, all while keeping any single wager small enough that a loss never becomes fatal.
The core 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 output is the slice of your bankroll to bet. In the real world, plenty of bettors run a fractional Kelly setup, usually staking a quarter or a half of the full figure to tame the swings that come with aggressive sizing. Full Kelly is optimal on paper, yet it tends to generate sharp bankroll lurches that most people find hard to stomach.
Example
Say you peg a team at a 60% chance to win, and the book is offering +120 (decimal 2.20). Run the numbers: 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. With a $1,000 bankroll, full Kelly puts $267 in play. Many bettors would instead drop to half Kelly ($133.50) or quarter Kelly ($66.75) to smooth the ride and hedge against the chance that the 60% read is a touch off.
Key Points
- Maximizes long-term growth: Out of every fixed-fraction staking approach, Kelly delivers the fastest bankroll growth rate when your probability reads are accurate.
- Sensitive to probability errors: If your true-win-probability estimate is even slightly off, Kelly can call for stakes that run too big, ramping up the risk of heavy drawdowns.
- Fractional Kelly is standard practice: Most seasoned bettors run a fraction (commonly 25% to 50%) of full Kelly to dial down volatility and build in a cushion against estimation slip-ups.
- Never bets on negative EV: For any edgeless bet, the formula naturally returns zero or a negative number, signaling that no stake belongs there.
- Dynamic sizing: Kelly staking recalibrates stakes automatically as the bankroll moves, betting more after wins and pulling back after losses.