The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. in 1956 that determines the optimal stake size for a bet based on your estimated probability of winning and the odds offered. It aims to maximise the long-run growth of a bankroll while avoiding the risk of ruin.
The formula: Kelly % = (bp - q) / b
Where:
- b = net decimal odds (decimal odds - 1)
- p = your estimated probability of winning
- q = 1 - p (probability of losing)
If you estimate a 55% chance of winning at odds of 2.10 (b = 1.10): Kelly = (1.10 × 0.55 - 0.45) / 1.10 = (0.605 - 0.45) / 1.10 = 0.155 / 1.10 ≈ 14.1% of your bankroll.
Full Kelly stakes 14.1% of the bankroll on this single bet. This is mathematically optimal if your probability estimate is exactly right. In practice, probability estimates are uncertain, so most bettors use fractional Kelly — half Kelly (7%) or quarter Kelly (3.5%) — to reduce variance and protect against model errors.
When Kelly is negative: if your probability estimate is lower than the bookmaker's implied probability, Kelly returns a negative number. This means no edge exists and no bet should be placed. Kelly is both a staking plan and a decision tool — it tells you when NOT to bet as much as when to bet.
Example
You estimate a team has a 50% chance of winning. Odds are 2.40 (b = 1.40). Kelly = (1.40 × 0.50 - 0.50) / 1.40 = (0.70 - 0.50) / 1.40 = 0.20 / 1.40 ≈ 14.3%. On a £1,000 bankroll, full Kelly suggests staking £143. At half Kelly, you stake £71.50.