Kelly Criterion Calculator
The fraction of a bankroll to stake for maximum long-run growth, with half-Kelly and the break-even probability.
Results
What this tool does
John Kelly, working at Bell Labs in 1956 on the capacity of a noisy telephone line, derived the bet size that maximises the long-run growth rate of a bankroll. The answer depends only on the edge and the odds, and it has two hard lessons built in: bet more than Kelly and you grow more slowly while risking ruin, and if the edge is negative no stake at all is the only correct answer.
Formula
f* = (b p - q) / b
Variables
| Symbol | Meaning | Unit |
|---|---|---|
bb | Net odds received (b to 1) | — |
pp | Probability of winning | % |
bk | Bankroll | — |
FF | Kelly fraction | % |
HF | Half Kelly | % |
ST | Stake | — |
EG | Edge | % |
BE | Break-even probability | % |
Worked example
- Net odds received (b to 1)2
- Probability of winning40 %
- Bankroll1000
- Kelly fraction10.0000 %
- Half Kelly5.0000 %
- Stake100.00
- Edge20.0000 %
- Break-even probability33.3333 %
Limitations
- This is an informational calculator, not personalised financial advice. Rates, fees, taxes and contract conditions vary between institutions and countries.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Frequently asked questions
Why do people use half Kelly?
Because full Kelly maximises long-run growth only if your estimate of the probability is exactly right, and it is violently volatile even then — drawdowns of half the bankroll are routine. Betting half the Kelly fraction gives about three quarters of the growth with far smaller swings, and it forgives an overestimated edge instead of ruining you for it. A negative fraction means there is no bet worth making.