Kelly criterion calculator for sports betting
Enter the odds, the probability you estimate and your bank. The calculator gives you the full and fractional Kelly stakes and tells you whether there is an edge.
What the Kelly criterion is
The Kelly criterion is a formula for deciding how much of your bank to stake when you believe you have an edge. It was published in 1956 and aims to maximise long-term capital growth: stake more the bigger your edge, and nothing if you have none.
Its weak point is that it starts from something nobody knows exactly: the true probability of the outcome. The odds are on your screen, but the probability is your own estimate. If that estimate is wrong, so is the stake.
The formula
f = (b × p − q) ÷ b
- f: share of the bank to stake
- b: decimal odds minus 1
- p: estimated probability of winning
- q: probability of losing, that is, 1 − p
If the result is zero or negative, there is no edge and the formula says not to bet. The calculator shows this as €0.
A worked example
Odds of 2.10, estimated probability of 50% and a €1,000 bank.
- b = 2.10 − 1 = 1.10
- f = (1.10 × 0.50 − 0.50) ÷ 1.10 = 0.0455, or 4.55% of the bank
- Full Kelly: €45.45
- 1/2 Kelly: €22.73
- 1/4 Kelly: €11.36
The expected value of this bet is 5%: 0.50 × 2.10 − 1 = 0.05. That is what you would make on average per euro staked if your 50% were correct.
Why almost nobody uses full Kelly
Full Kelly is only optimal if you know the exact probability. Since you do not, it tends to overbet, and losing runs can take a very large part of the bank. That is why it is common to use a fraction such as 1/2 or 1/4: you grow more slowly, but drawdowns are noticeably smaller and you cope better with your own estimation errors.
We compare this method with flat and percentage staking in the bankroll management guide.
Common mistakes
- Overestimating the probability. This is the main failure. Moving from 50% to 55% in the example above triples the stake. A little overconfidence is expensive.
- Treating the odds as the true probability. Odds include the bookmaker’s margin. Check it with the implied probability calculator.
- Applying Kelly to simultaneous bets without adjusting. The formula assumes one bet at a time. With several at once, adding up their stakes can expose too much of the bank.
- Not recalculating the bank. Kelly applies to your current bank, not the starting one. If it falls, the stake falls too.
To know whether your estimates are worth anything you need data: compare your odds with the closing ones, as explained in the guide to CLV, and measure your real yield on a large sample.
Frequently asked questions
What fraction of Kelly should I use?
There is no single answer. The less sure you are of your probabilities, the smaller the fraction should be. Many bettors use between 1/4 and 1/2 precisely because their estimates are not exact.
What does it mean when Kelly gives €0?
That with the odds and probability you entered there is no edge: the expected value is zero or negative. The formula says not to bet.
Does Kelly guarantee I will not go broke?
No. It is a way of sizing stakes, not a guarantee. If your probabilities are badly estimated you can still lose money, and betting always carries risk.
Does it work for parlays?
You can apply it using the total odds and the joint probability, but estimating that probability is even harder and any error is multiplied. It is more reliable on single bets.