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Kelly Criterion Calculator
Calculate a theoretical stake from your bankroll, decimal odds and estimated win probability.
Kelly stake calculator
Explore a stake size based on your own probability estimate and a spending cap.
The amount allocated to this model.
The price offered for your selection.
Your estimate, not the implied probability.
An upper limit applied after the Kelly fraction.
Instant calculation
- Calculated stake
- US$50.00
- Share of bankroll
- 5.00%
- Break-even probability
- 50.00%
- Expected return on stake
- +10.00%
Compare fractions before your cap
- Full Kelly
- US$100.00
- Half Kelly
- US$50.00
- Quarter Kelly
- US$25.00
The model depends on an accurate probability estimate. A smaller fraction or cap reduces exposure but cannot prevent losses. The cap is a modelling input, not a spending recommendation.
Calculated on your device. No sign-up.
How the Kelly criterion works
Kelly sizes each bet as a percentage of your bankroll, scaled to your edge: the bigger the gap between your estimated probability and the probability implied by the odds, the larger the stake. The formula is(b·p − q) ÷ bwhere b = decimal odds − 1, p = your win probability and q = 1 − p.
Full Kelly grows a bankroll fastest in theory but swings hard and punishes over-confident estimates. Most bettors use half or quarter Kelly to cut the volatility.
Worked example
You estimate a 55% chance at odds of 2.00, bankroll $1,000.
b = 1.00, p = 0.55, q = 0.45 → full Kelly = (1×0.55 − 0.45) ÷ 1 = 10%.
Full Kelly stake = $100. Half Kelly = $50. These are formula outputs based on the assumed 55% probability, not a guarantee that the bet has an edge.
Frequently asked questions
What is the Kelly criterion?
The Kelly criterion is a formula that sets your stake as a fraction of your bankroll based on your edge and the odds. Under ideal assumptions, it maximises expected long-term logarithmic bankroll growth. It depends on accurate probabilities and does not guarantee profit or prevent losses. The formula is (b·p − q) ÷ b, where b = decimal odds − 1, p = your win probability and q = 1 − p.
Why use half or quarter Kelly?
Full Kelly is mathematically optimal but very volatile, and it is unforgiving if your probability estimate is too high. Betting a fraction — half or quarter Kelly — reduces the calculated stake and volatility, at the cost of lower theoretical growth.
What does a negative Kelly result mean?
A negative result means the bet has no positive expected value at those odds and probability, so Kelly recommends staking nothing. Only bet when your estimated probability is higher than the odds imply.