Calculate a Bankroll-Based Stake
Choose flat percentage staking or a Kelly method, enter the required inputs and set a maximum percentage of bankroll that any single calculated stake may use. The cap is applied after the raw staking calculation.
How Each Method Works
Flat percentage
Flat percentage staking uses the same selected percentage of the current bankroll regardless of the probability estimate. It is simple to audit and does not require a probability input.
Raw stake = bankroll × flat stake percentageFull Kelly
Full Kelly calculates the stake from decimal odds and your estimated probability. If the Kelly fraction is zero or negative, the raw stake is zero.
Kelly fraction = ((decimal odds − 1) × p − (1 − p)) ÷ (decimal odds − 1)Half Kelly
Half Kelly uses 50% of the full Kelly stake before the maximum stake cap is applied.
Raw stake = bankroll × positive Kelly fraction × 0.50Quarter Kelly
Quarter Kelly uses 25% of the full Kelly stake before the maximum stake cap is applied.
Raw stake = bankroll × positive Kelly fraction × 0.25Maximum stake cap
The cap is applied after the selected method calculates its raw stake. It does not alter the staking formula; it limits the final amount used for a single calculation.
Suggested stake = lower of raw stake or bankroll × maximum stake capMethods Comparison
| Method | Stake basis | Main trade-off |
|---|---|---|
| Flat percentage | A fixed percentage of the current bankroll. | Simple and consistent, but it does not adjust the stake when the estimated edge changes. |
| Full Kelly | 100% of the positive Kelly fraction. | Produces the largest Kelly-based stake and is the most sensitive to probability-estimation error. |
| Half Kelly | 50% of the positive Kelly fraction. | Produces a smaller stake than full Kelly while retaining the same probability-based sizing logic. |
| Quarter Kelly | 25% of the positive Kelly fraction. | Produces smaller stakes than half or full Kelly, including when the probability estimate is accurate. |
Worked Example
Assume a bankroll of 1,000, decimal odds of 2.10, an estimated win probability of 52% and a maximum stake cap of 5%.
For full Kelly, b = 2.10 − 1 = 1.10, p = 0.52 and q = 0.48. The Kelly fraction is:
((1.10 × 0.52) − 0.48) ÷ 1.10 = 0.083636...The raw full Kelly stake is therefore 8.36% of the bankroll, or 83.64. The 5% cap allows a maximum stake of 50.00, so the suggested stake is reduced to 50.00 and the result shows Cap applied: Yes.
At decimal odds of 2.10, a 50.00 stake has a potential profit of 55.00 and a total return of 105.00 if the bet wins.
Main Risks
- Probability error: Kelly staking is only as reliable as the estimated probability entered. The calculator does not validate that estimate, and an overly optimistic input can produce an oversized raw stake.
- Price changes: decimal odds affect Kelly sizing, potential profit and total return. Recalculate the stake if the available price changes.
- Per-bet cap: the maximum stake cap limits a single calculated stake. It does not measure the combined exposure of several open or correlated bets.
- Bankroll definition: stake percentages are meaningful only when the bankroll represents funds specifically allocated to betting.
- Variance: a positive Kelly stake does not imply that an individual bet will win. Losing sequences remain possible even when the probability estimate is accurate.
- Fractional Kelly: half Kelly and quarter Kelly reduce stake size, but they do not correct an inaccurate probability estimate or an unfavourable price.
FAQ
Why is estimated probability hidden for flat percentage staking?
Flat percentage staking does not use a win-probability estimate. Its raw stake depends on bankroll and the selected flat percentage. Decimal odds are still required to calculate potential profit and total return.
Why can a Kelly method return a zero stake?
A Kelly result is zero when the entered odds and estimated probability do not produce a positive Kelly fraction. Negative fractions are treated as zero rather than as a negative stake.
What does “raw stake before cap” mean?
It is the stake calculated by the selected method before the maximum stake cap is applied. It shows whether the cap changed the final suggested stake.
Does the maximum stake cap change the Kelly calculation?
No. The calculator first computes the raw Kelly or flat stake and then compares it with the maximum amount permitted by the cap. The lower amount becomes the suggested stake.
What is the difference between full, half and quarter Kelly?
Full Kelly uses the entire positive Kelly fraction. Half Kelly uses 50% of it, while quarter Kelly uses 25%. The fractional versions therefore produce smaller stakes from the same odds and probability estimate.
Does this calculator predict whether a bet will win?
No. It calculates stake size from the values entered. It does not predict an event, verify the probability estimate or guarantee a profitable outcome.