Betting maths guide
What Is the Kelly Criterion?
The Kelly Criterion is a staking formula that estimates how much of your bankroll to stake when you believe you have an edge.
What does the Kelly Criterion mean?
The Kelly Criterion is a mathematical approach to stake sizing. It tries to answer this question:
If I think this bet has value, how much of my bankroll should I risk?
It does this by comparing the odds available with your own estimate of the true probability. If the odds appear better than your estimated chance suggests, the formula may return a positive stake percentage.
The Kelly Criterion formula
For decimal odds, a common version of the Kelly formula is:
Kelly fraction = ((decimal odds − 1) × probability − (1 − probability)) ÷ (decimal odds − 1)
This can also be written as:
Kelly fraction = (decimal odds × probability − 1) ÷ (decimal odds − 1)
The result is the fraction of bankroll suggested by full Kelly. For example, a result of 0.05 means 5% of bankroll.
| Term | Meaning |
|---|---|
| Decimal odds | The odds available for the selection. |
| Probability | Your estimated chance of the selection winning, expressed as a decimal. |
| Kelly fraction | The suggested fraction of bankroll to stake. |
| Bankroll | The betting funds being used for stake sizing. |
Simple Kelly Criterion example
Suppose you have a bankroll of £1,000. You are looking at decimal odds of 3.00 and you estimate the true chance of the selection winning is 40%.
| Bankroll | Decimal odds | Your estimated probability | Full Kelly stake |
|---|---|---|---|
| £1,000 | 3.00 | 40% | £100 |
In this example, the full Kelly fraction is 10%, so the suggested full Kelly stake is £100.
Kelly fraction = (3.00 × 0.40 − 1) ÷ (3.00 − 1)
Kelly fraction = (1.20 − 1) ÷ 2
Kelly fraction = 0.10, or 10%
What is fractional Kelly?
Fractional Kelly means staking only part of the full Kelly amount. For example, half Kelly means staking 50% of the full Kelly suggestion.
Many people prefer fractional Kelly because full Kelly can produce large stakes and big swings when probability estimates are uncertain.
| Kelly type | Full Kelly stake | Actual stake |
|---|---|---|
| Full Kelly | £100 | £100 |
| Half Kelly | £100 | £50 |
| Quarter Kelly | £100 | £25 |
Kelly Criterion and value betting
Kelly staking is closely linked to value betting because the formula only gives a positive stake when your estimated probability is higher than the probability implied by the odds.
For example, decimal odds of 3.00 imply a probability of 33.33%. If you estimate the true chance is 40%, the bet appears to have a positive edge. If you estimate the true chance is only 30%, the Kelly result would be negative.
| Decimal odds | Implied probability | Your estimate | Kelly view |
|---|---|---|---|
| 3.00 | 33.33% | 40% | Positive edge |
| 3.00 | 33.33% | 30% | Negative edge |
Why Kelly staking can be risky
The Kelly Criterion can look precise, but it is only as good as the inputs. In betting, the hardest input is usually your estimated probability.
- Probability estimates can be wrong: a small error can change the suggested stake significantly.
- Full Kelly can be aggressive: it can suggest large stakes when the perceived edge is high.
- Bankroll swings can be uncomfortable: losing runs still happen even with positive expected value.
- Odds can move: the edge may disappear before a bet is placed.
- Limits and restrictions matter: real betting conditions are not always ideal.
Full Kelly vs flat staking
Flat staking means using the same stake size for each bet, such as £10 per bet. Kelly staking changes the stake depending on perceived edge, odds and bankroll.
| Staking method | How stake is chosen | Main risk |
|---|---|---|
| Flat staking | Same stake each time. | May not reflect edge or bankroll size. |
| Full Kelly | Formula based on odds, estimated probability and bankroll. | Can be aggressive if estimates are wrong. |
| Fractional Kelly | A percentage of the full Kelly suggestion. | Still depends on accurate probability estimates. |
Common Kelly Criterion mistakes
Confusing implied probability with true probability
Implied probability comes from the odds. Kelly staking needs your own estimate of the true probability.
Using full Kelly without understanding volatility
Full Kelly can suggest large stakes. Fractional Kelly is often used to reduce stake size and smooth bankroll swings.
Ignoring bookmaker margin
Odds include market pricing and bookmaker margin. It is not enough to look at odds alone.
Thinking Kelly guarantees profit
Kelly staking can help with stake sizing if an edge exists, but it cannot create an edge by itself.
Using money that is not a betting bankroll
Bankroll should mean money set aside for betting risk, not money needed for bills, savings or essential spending.
Kelly Criterion FAQs
What is the Kelly Criterion in simple terms?
The Kelly Criterion is a formula that estimates how much of your bankroll to stake when you believe the odds are better than the true chance of the outcome.
What does a negative Kelly result mean?
A negative Kelly result means the formula does not see a positive edge based on your odds and probability estimate.
What is half Kelly?
Half Kelly means staking half of the full Kelly suggestion.
Does Kelly staking guarantee profit?
No. Kelly staking only sizes stakes based on your inputs. If your probability estimate is wrong, the suggested stake may be wrong too.
Which calculator should I use?
Use the Kelly Criterion Calculator to enter bankroll, odds, estimated probability and fractional Kelly level.