What question does Kelly answer?
Suppose you believe a bet is good value. The next question is how much of a dedicated betting bank to risk. Too little produces slower growth when the edge is real. Too much makes losses disproportionately damaging.
The Kelly criterion chooses the fraction that maximises expected logarithmic bankroll growth under its assumptions. That is a long-run mathematical objective, not a target for next month’s profit or a guarantee against severe drawdowns.
The starting bank in these examples is money separately set aside for betting, not savings needed for bills. The figures illustrate the arithmetic; they are not a recommendation to bet that amount.
The formula, in ordinary numbers
For a simple win-or-lose bet: full Kelly fraction = (decimal odds × win probability − 1) ÷ (decimal odds − 1). Use probability as a decimal: 55% becomes 0.55. If the result is zero or negative, this back-bet calculation calls for no stake.
The formula assumes the stated payout, a probability you can rely on, and losses limited to the stake. Bets with pushes, commissions or different settlement outcomes need those features incorporated; do not silently apply the two-outcome formula to them.
Illustrative £1,000 bank, odds 2.00 and an estimated 55% win chance. Each fraction uses the same uncertain estimate.
The fragile input is your probability
If you size at 55% but the true chance is 52%, the original 10% stake is 2.5 times the full Kelly fraction justified by that true chance. At these numbers it has negative expected log growth, even though the bet itself still has positive expected value.
If the real chance is 48%, reducing the stake does not make the bet profitable. Fractional Kelly reduces exposure to estimation error; it does not repair a wrong forecast.
Swipe the table sideways to see every column.
| Actual chance | Actual EV | Full Kelly if known |
|---|---|---|
| 55% | +10% | 10% of bank |
| 52% | +4% | 4% of bank |
| 50% | 0% | No positive stake |
| 48% | −4% | No back bet |
A 4% fall in bankroll needs a 4.17% gain to recover. A 50% fall needs a 100% gain. This asymmetry is why stake size matters even when average returns look attractive.
Why people use fractions of Kelly
Half, quarter and one-tenth Kelly multiply the calculated fraction by 0.5, 0.25 and 0.1. Smaller fractions generally trade some growth potential for smaller swings when the assumed edge is correct. They can still lose money and suffer long drawdowns.
There is no universal fraction that becomes safe just because the market is tennis or player props. Probability uncertainty, long odds, liquidity, simultaneous bets and your ability to tolerate losses all matter. Treat calculator presets as scenarios, not rules you must follow.
- Start with a credible estimate
A personal hunch written as 60% is still a hunch. Test probability calibration before treating the number as stake-sizing evidence.
- Apply a fraction and an exposure limit
Consider money already at risk in other bets. A series of individually modest stakes can add up to substantial exposure.
- Recalculate from the current bank
After a loss the same percentage means a smaller cash stake. Do not increase it to chase the previous balance.
Three bets can share one underlying risk
A striker to score, have two shots on target and take a penalty are not independent opportunities. Minutes, injury and the same match events can affect all three. Applying a full standalone Kelly stake to each does not account for that relationship.
The same problem arises with several bets on one tennis match. A proper portfolio calculation needs the joint outcome probabilities. A simple single-bet calculator does not provide that. Keep total exposure visible rather than adding every suggested stake together.
Try an error test before a stake test
- Enter the actual odds
Use what you can place now, not a price that disappeared when the tip was published.
- Enter an estimated probability
Be explicit about where the estimate comes from and its uncertainty.
- Move the estimate-error slider
In our calculator, the stake stays based on your belief while the simulated outcomes use a lower probability. See how the picture changes.
- Read the drawdowns
The median finish is only one summary. Read the losing scenarios and risk of the bank being halved too.
Kelly versus a simpler stake
Without credible probabilities, a Kelly output is false precision. A small, predefined staking budget can be easier to monitor, although no staking plan turns negative-value bets into positive-value ones. Doubling after losses escalates exposure; it does not change the underlying price.
Swipe the table sideways to see every column.
| Approach | What it does | Main limitation |
|---|---|---|
| Fixed cash stake | Same cash amount per bet | Becomes a larger share of a shrinking bank |
| Fixed percentage | Cash stake follows the current bank | Does not distinguish stronger and weaker edges |
| Fractional Kelly | Uses odds and estimated probability | Sensitive to a wrong probability and correlated bets |
Where the idea comes from
J. L. Kelly’s 1956 paper linked information to the growth rate of capital. The useful lesson for a bettor is to treat stake size and probability quality together. A sophisticated fraction cannot compensate for an untested input.