Smarter Than Free calculator
Kelly Criterion Calculator
Full, half and quarter Kelly from win probability and decimal odds (or win/loss payoff ratio). Stake for a bankroll. Warns on negative edge.
Calculator
What is the Kelly criterion formula for decimal odds?
f* = p − (1−p)/(decimal−1). Stake = f* × bankroll. Negative f* means no bet.
Why use half Kelly?
Full Kelly assumes your probability is exact. Estimation error and variance make half or quarter Kelly the usual practical choice.
What happens if you bet more than Kelly?
You take more risk for less growth. In the table below, 2 × Kelly compounds at −0.099% a bet against 1.844% at full Kelly, so an edge can compound to nothing purely through oversizing.
How much growth do you give up with half Kelly?
Surprisingly little. In this example half Kelly stakes half as much and keeps 75% of the full Kelly growth.
What if your win probability is wrong?
Sizing for 55% when the truth is 50%, at odds of 2.2: full Kelly compounds at −0.088% a bet, while half Kelly still manages 0.415%. Same mistake, smaller stake, different outcome.
Can you use Kelly for trading?
Yes, with p as your hit rate and b as average win ÷ average loss. Backtests can flatter both numbers, and trades are not always independent, so fractional Kelly matters even more.
Win probability 55% at decimal odds 2.2: what stake size does to growth
Growth per bet is the long-run compound rate at that stake, from the Kelly growth formula. Assumes the 55% is exactly right, which is generous.
| Stake | % of bankroll | Growth per bet |
|---|---|---|
| Quarter Kelly | 4.38% | 0.804% |
| Half Kelly | 8.75% | 1.380% |
| Full Kelly | 17.50% | 1.844% |
| 1.5 × Kelly | 26.25% | 1.368% |
| 2 × Kelly | 35.00% | −0.099% |
| 2.5 × Kelly | 43.75% | −2.646% |
The formula
For decimal odds: b = decimal − 1, q = 1 − p Full Kelly fraction f* = p − q/b = p − (1−p)/(decimal−1) Or with win/loss ratio b = amount won net per 1 risked: f* = p − q/b Half / quarter Kelly = f*/2 or f*/4. Stake = f × bankroll.
Worked example
Win probability 55%, decimal odds 2.2 (b = 1.2).
f* = 0.55 − 0.45/1.2 = 0.175 = 17.5% of bankroll.
Half Kelly = 8.75%. On a £1,000 bankroll that is £87.50.
Methodology
How it calculates
- Full Kelly fraction from win probability and decimal odds (or payoff ratio b), then half and quarter Kelly.
- Stake = fraction × bankroll when a bankroll is entered.
Formula
For decimal odds: b = decimal − 1, q = 1 − p Full Kelly fraction f* = p − q/b = p − (1−p)/(decimal−1) Or with win/loss ratio b = amount won net per 1 risked: f* = p − q/b Half / quarter Kelly = f*/2 or f*/4. Stake = f × bankroll.
Assumptions
- Assumes a known edge. Estimation error makes fractional Kelly the usual practical choice.
Edge cases
- Negative or zero edge => Kelly fraction and stake are 0 (no bet).
- Half / quarter Kelly are f*/2 and f*/4.
Sources
None. Pure maths; no external rate or spec feed.
FAQ
Why use half Kelly?
Full Kelly is loud. Estimation error and variance make fractional Kelly the usual practical choice.
Popular variants
Same maths, aimed at a specific search. Pre-filled where it helps.
Not financial advice. This calculator is for education only. Double-check results before you make money decisions. Past moves do not predict future ones.