Definition
The Kelly Criterion is a formula developed by John L. Kelly Jr. in 1956, originally for telecommunications and later adopted by bettors and investors. It calculates the optimal percentage of your bankroll to wager in order to maximize long-term growth while minimizing the risk of ruin.
How It Works
Formula: f* = (bp - q) / b
Where: f* = fraction of bankroll to wager, b = decimal odds - 1 (net profit per dollar staked), p = estimated probability of winning, q = probability of losing (1 - p). The result is the mathematically optimal stake as a percentage of your current bankroll.
Example
Bet: win at odds 2.50, estimated probability 45%
- b = 2.50 - 1 = 1.50
- p = 0.45, q = 0.55
- f* = (1.50 x 0.45 - 0.55) / 1.50 = (0.675 - 0.55) / 1.50 = 0.0833 or 8.33%
For a $1,000 bankroll, the Kelly stake is $83.30. Most professionals use fractional Kelly (1/4 or 1/2) to reduce variance:
- Full Kelly: 8.33% = $83.30
- Half Kelly: 4.17% = $41.65
- Quarter Kelly: 2.08% = $20.83
Half Kelly sacrifices about 25% of optimal growth but dramatically reduces drawdowns.
Why It Matters
The Kelly Criterion is the only staking method with a mathematical proof of long-term optimality. It automatically bets more when you have a bigger edge and less when your edge is slim. However, it assumes your probability estimate is correct -- overestimating your edge leads to dangerously large stakes. This is why fractional Kelly (1/4 or 1/2) is the standard in practice.
The Kelly Criterion assumes you accurately estimate the true probability. Overestimating your edge leads to overbetting. Always use fractional Kelly (1/4 or 1/2).