The Kelly Criterion Formula

Developed by John L. Kelly Jr. at Bell Labs in 1956, the Kelly Criterion determines the optimal fraction of bankroll to wager on any bet with a positive expected value. Bet more than Kelly and you risk ruin; bet less and you underperform the optimal growth rate.

Kelly % = (b × p − q) / b Where: b = Decimal Odds − 1 (net profit per unit staked) p = Your win probability q = 1 − p (your lose probability) Bet Size = Kelly % × Bankroll

Example

You find a +150 line you believe has a 45% win probability.
b = 2.50 − 1 = 1.50 | p = 0.45 | q = 0.55
Full Kelly = (1.50 × 0.45 − 0.55) / 1.50 = (0.675 − 0.55) / 1.50 = 0.0833 = 8.33%
On a $1,000 bankroll: Full Kelly = $83.30 | Half Kelly = $41.65 | Quarter Kelly = $20.83

Full Kelly vs Half Kelly

Full Kelly maximizes long-term growth rate mathematically, but it assumes your probability estimate is perfect. In practice, most bettors use Half Kelly (50% of the full Kelly bet) because it protects against model overconfidence and produces a smoother bankroll curve with only marginally lower long-run growth.

Quarter Kelly is the most conservative approach and is appropriate when you have lower confidence in your probability estimate or are dealing with high-variance markets.

When Kelly Says Don't Bet

If Kelly returns a negative number, your estimated win probability is below the break-even rate implied by the odds. This is a -EV bet — Kelly is telling you to skip it. Never bet a negative Kelly fraction.

Kelly Assumes Independent Bets

The formula is designed for single bets in isolation. When betting multiple games simultaneously, fractional Kelly (Half or Quarter) provides additional protection against correlated bad runs.

Sibyl Sizes Every Pick with Kelly

Every pick in the Sibyl dashboard includes a Kelly % recommendation based on our model's edge estimate — so you always know exactly how much to bet.

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