Kelly Criterion Calculator
Estimate full Kelly, half Kelly and quarter Kelly stakes from your bankroll, decimal odds and personal win-probability estimate.
Calculator inputs
How to use the Kelly Criterion calculator
The Kelly Criterion calculator estimates a theoretical stake size from three inputs: your bankroll, the decimal odds available and your own estimate of the probability that the bet will win. It then shows the full Kelly recommendation together with more conservative half-Kelly and quarter-Kelly alternatives.
Enter your bankroll, add the decimal odds and provide your estimated win probability. The calculator measures whether the price suggests a positive mathematical edge. If the estimated edge is zero or negative, the recommended Kelly stake is zero. The result is educational and depends entirely on the accuracy of the probability you enter.
What is the Kelly Criterion?
The Kelly Criterion is a mathematical staking method designed to maximise long-term logarithmic bankroll growth when the bettor has a genuine edge and can estimate probabilities accurately. Instead of using the same stake for every bet, Kelly changes the stake according to the size of the perceived advantage.
A larger edge produces a larger suggested stake, while a small edge produces a smaller stake. If the entered probability does not exceed the break-even probability implied by the odds, the Kelly result is zero. This prevents the formula from recommending a stake when there is no theoretical positive expectation.
Edge-sensitive
The recommended percentage increases when the estimated advantage becomes larger.
Bankroll-based
The stake is calculated as a percentage of current bankroll rather than a fixed amount.
Probability-dependent
The method is only as reliable as the probability estimate entered by the user.
Kelly Criterion formula explained
For decimal odds, the Kelly fraction can be written as follows:
f* = (b × p − q) ÷ bIn this formula, b is the decimal odds minus 1, p is your estimated probability of winning and q is the probability of losing, calculated as 1 minus p.
The Kelly fraction is multiplied by the bankroll to produce the theoretical full-Kelly stake.
Bankroll × Kelly fractionEstimated probability, implied probability and edge
Decimal odds can be converted into a basic implied probability by dividing 100 by the odds. Odds of 2.20 imply approximately 45.45% before accounting for bookmaker margin. If you estimate the real win probability at 50%, the difference suggests a theoretical positive edge.
The calculator also shows estimated edge using the expression probability multiplied by decimal odds minus 1. In percentage terms:
(Estimated probability × Decimal odds − 1) × 100A positive result means your probability estimate exceeds the break-even point. A negative result means the entered price is not high enough relative to your estimate. This is not proof that the bet is genuinely profitable; it only describes the relationship between the numbers you entered.
Full Kelly vs half Kelly vs quarter Kelly
Full Kelly uses the complete fraction produced by the formula. It offers the highest theoretical long-term growth when probabilities are accurate, but it can also create large swings and deep drawdowns. Because real-world probability estimates are uncertain, many bettors use fractional Kelly instead.
| Method | Stake size | Volatility | Main use |
|---|---|---|---|
| Full Kelly | 100% of calculated fraction | Highest | Theoretical maximum growth with highly accurate inputs |
| Half Kelly | 50% of calculated fraction | Moderate | Balance between growth and protection from estimation error |
| Quarter Kelly | 25% of calculated fraction | Lower | More conservative staking when confidence is limited |
Fractional Kelly does not make a poor probability estimate correct, but it reduces the financial impact of being wrong. This is why half Kelly and quarter Kelly are often preferred in practical betting environments.
Kelly Criterion calculator examples
Example 1: positive edge
Assume a bankroll of €1,000, decimal odds of 2.20 and an estimated win probability of 50%. The decimal profit multiple is 1.20. The Kelly fraction is approximately 8.33%, producing a full-Kelly stake of €83.33. Half Kelly suggests €41.67, while quarter Kelly suggests €20.83.
| Input or result | Value |
|---|---|
| Bankroll | €1,000 |
| Decimal odds | 2.20 |
| Estimated probability | 50% |
| Full Kelly | 8.33% / €83.33 |
| Half Kelly | €41.67 |
| Quarter Kelly | €20.83 |
| Estimated edge | 10% |
Example 2: no positive Kelly stake
Suppose the odds are 1.80 and your estimated win probability is 50%. The break-even probability at 1.80 is about 55.56%, so the entered probability does not indicate a positive edge. The calculator returns a Kelly stake of zero.
Example 3: probability overconfidence
If a bettor enters 65% when the real probability is closer to 50%, the formula may recommend a dangerously large stake. Kelly is especially sensitive to overconfidence because stake size rises rapidly as the perceived edge increases.
Common Kelly Criterion mistakes
- Guessing probability without evidence. The formula is not a substitute for a forecasting process.
- Using full Kelly with uncertain inputs. Full Kelly can create large drawdowns when estimates are noisy.
- Ignoring bookmaker margin. Market odds may include overround and may not represent fair probability.
- Using the same edge estimate repeatedly. Different matches and markets require separate evaluation.
- Applying Kelly to correlated bets without adjustment. Multiple related positions can produce more total exposure than intended.
- Increasing probability to justify a preferred bet. Inputs should be set before emotional attachment to an outcome.
- Failing to update bankroll. Kelly is based on current bankroll, so stake amounts should change as bankroll changes.
Kelly staking and bankroll management
Kelly is a bankroll-growth framework, not permission to take uncontrolled risk. A mathematically positive edge can still lose, and long losing sequences remain possible. The formula assumes repeated opportunities, accurate probabilities and consistent execution over time.
Practical safeguards include using fractional Kelly, applying a maximum stake cap, separating betting funds from personal money, tracking every wager and reviewing probability calibration. If your estimated 60% selections win only 48% over a meaningful sample, the input process needs revision.
Kelly Criterion versus flat staking
| Feature | Kelly staking | Flat staking |
|---|---|---|
| Stake size | Changes with edge and bankroll | Usually fixed as a constant amount or unit |
| Input requirement | Requires a probability estimate | Does not require an explicit probability |
| Volatility | Can be high, especially at full Kelly | Usually easier to control |
| Main risk | Overestimating edge | Using the same stake on unequal opportunities |
Related bankroll and value guides
Use Kelly only after estimating probability carefully
The calculator can size a theoretical stake, but it cannot create an edge. Explore the Academy for probability, value betting and bankroll-management guides.
Related betting tools
Kelly Criterion Calculator FAQ
What is the Kelly Criterion?
The Kelly Criterion is a mathematical staking method that sizes a bet according to bankroll, odds and estimated edge.
What does a zero Kelly result mean?
It means the entered probability does not create a positive theoretical edge at the entered odds.
Should I use full Kelly?
Full Kelly can be volatile and highly sensitive to probability errors. Many bettors prefer half Kelly or quarter Kelly.
What is half Kelly?
Half Kelly uses 50% of the full Kelly stake, reducing volatility and the impact of estimation error.
What is quarter Kelly?
Quarter Kelly uses 25% of the full Kelly stake and is a more conservative fractional-Kelly approach.
Does Kelly guarantee bankroll growth?
No. Growth depends on accurate probability estimates, repeated opportunities and disciplined execution.
Why is probability accuracy important?
Kelly converts the estimated edge directly into stake size, so overestimating probability can produce an excessive recommendation.
Can Kelly recommend more than 100% of bankroll?
Extreme inputs can produce very large fractions. In practice, bettors often apply fractional Kelly and strict maximum stake caps.
Does this calculator remove bookmaker margin?
No. It uses the decimal odds and probability exactly as entered.
Can I use Kelly for accumulators?
The formula can be applied to combined odds, but estimating the true probability of an accumulator is difficult and correlations may matter.
Can I use American or fractional odds?
This page accepts decimal odds. Convert other formats with the Odds Converter first.
How often should bankroll be updated?
Kelly stakes should be based on current bankroll, so the bankroll figure should be updated as results change.
Is Kelly better than flat staking?
Neither method is automatically better. Kelly may improve theoretical growth with accurate probabilities, while flat staking is simpler and less sensitive to forecasting error.
Is my data stored?
No. The calculation runs locally in your browser and does not require registration.
Is Kelly suitable for beginners?
Beginners should first understand implied probability, value and bankroll risk. Fractional Kelly is generally less aggressive than full Kelly.