Kelly Criterion Calculator
Enter your bankroll, the bookmaker odds, and your estimated true probability. The Kelly criterion returns the mathematically optimal stake size to maximise long-term bankroll growth.
Full Kelly maximises long-term geometric bankroll growth but is volatile. Most pros use half-Kelly or quarter-Kelly to reduce variance.
What is the Kelly Criterion?
The Kelly criterion is a formula for determining the optimal stake size on a bet given your bankroll, the bookmaker odds, and your estimated true probability. It maximises long-term geometric bankroll growth - but it\'s volatile, which is why most pros use a fraction (half-Kelly, quarter-Kelly).
How to use the Kelly Criterion
- Enter your total bankroll.
- Enter the decimal odds offered by your bookmaker.
- Enter your estimated true probability for the outcome (as a percentage).
- Choose a Kelly fraction (1 = full Kelly, 0.5 = half-Kelly is conservative).
- The recommended stake appears on the right.
The formula
Kelly fraction = (b × p − q) / b
where:
b = decimal odds − 1 (net profit per unit staked)
p = your estimated true probability
q = 1 − p
Stake = Bankroll × Kelly fraction × Your chosen fraction (1, 0.5, 0.25, etc.)
If Kelly fraction is negative, the bet has no edge - stake $0.Worked example
Bankroll: $1,000. Odds: 2.10. Your estimated probability: 52%.
- b = 2.10 − 1 = 1.10
- p = 0.52, q = 0.48
- Kelly fraction = (1.10 × 0.52 − 0.48) / 1.10 = (0.572 − 0.48) / 1.10 = 0.0836
- Full Kelly stake = $1,000 × 0.0836 = $83.60
That is aggressive for one bet. Half-Kelly ($41.80) gives most of the growth with much less drawdown variance.
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Frequently Asked Questions
What if my probability estimate is wrong?
Overestimating your edge is the biggest risk with Kelly. If your true edge is half what you think it is, full Kelly will severely over-stake and you'll lose money long-term. This is why half-Kelly or quarter-Kelly is the practical choice.
Why use half-Kelly?
Half-Kelly captures ~75% of the long-term growth of full Kelly but with much lower drawdown variance. It's the standard "I have an edge but I'm not 100% sure of my probability" stake size.
What if Kelly recommends a negative stake?
Negative Kelly means your estimated probability is at or below the implied probability of the odds - i.e. no edge. Don't bet. The calculator clamps to $0.
Can I use Kelly for parlays?
Yes - use the combined parlay odds and your estimated probability that all legs hit. The Kelly stake will be very small because parlay hit rates are low.
What about correlated bets?
Kelly assumes independence. For correlated bets (e.g. two outcomes that might happen together), you need fractional or multi-bet Kelly. Stick to single bets for simplicity.
Is Kelly used by professional sports bettors?
Yes - sized at 0.25× to 0.5× full Kelly. The full Kelly variance is brutal even for confirmed edges, so fractional Kelly is the industry standard.