Kelly Criterion Calculator
Calculate optimal position sizing with the Kelly Criterion. Input bankroll, win probability, and odds to estimate full, half, or custom Kelly stake.
Recommended stake
$704.55
7.05% of bankroll (14.09% Kelly x 50.00% mode)
Expected value / $1 staked
+0.1550
Expected value / recommended stake
$109.20
Implied edge
7.38%
One-trade outcome snapshot
If trade wins
+$775.00
If trade loses
-$704.55
| Sizing mode | Stake fraction | Stake amount |
|---|---|---|
| Full Kelly | 14.09% | $1,409.09 |
| Half Kelly | 7.05% | $704.55 |
| Quarter Kelly | 3.52% | $352.27 |
What is Kelly Criterion?
Kelly Criterion is a capital allocation formula that estimates the fraction of bankroll to risk when you have a measurable edge. It aims to maximize long-term geometric growth while accounting for win rate and payoff ratio.
Core formula: f* = (bp - q) / b. Here f* is optimal stake fraction, b is net odds (decimal odds minus 1), p is win probability, and q = 1 - p.
How to interpret results
A positive Kelly value means you have a theoretical edge. A zero or negative value suggests no bet or no trade under the current assumptions.
Full Kelly is mathematically efficient but can be emotionally and financially volatile. Many traders use half Kelly or quarter Kelly to reduce drawdown depth.
If your win probability estimate is noisy, reduce the fraction. Estimation error is a major reason practical sizing is often smaller than pure Kelly.
Kelly Criterion quick reference
Best for
Repeated decisions with known edge, like system trading or model-driven betting.
Main risk
Overconfident probability assumptions can lead to oversizing and severe drawdowns.
Practical approach
Use fractional Kelly with strict maximum exposure and periodic model recalibration.
Kelly sizing FAQ
Why do many investors avoid full Kelly?
Full Kelly can have deep drawdowns even with a positive edge. Fractional Kelly often improves behavioral consistency and survivability.
Can Kelly work with uncertain probabilities?
Yes, but uncertainty should reduce your stake size. If your model confidence is low, use smaller fractions and tighter risk caps.
Should Kelly replace stop-loss rules?
No. Kelly solves position sizing, not execution risk. Combine sizing with maximum loss rules and portfolio-level exposure limits.