Kelly Criterion Calculator
Calculate the mathematically optimal position size for trading and prediction markets. Includes full Kelly, half Kelly, and quarter Kelly recommendations.
What Is the Kelly Criterion?
The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. at Bell Labs in 1956 that determines the optimal percentage of capital to risk on a bet or trade when you have a quantifiable edge. It maximises the long-term geometric growth rate of your account while theoretically preventing ruin.
In trading and prediction markets, the Kelly Criterion answers the question: given my win rate and average win/loss ratio, how much of my account should I risk on each trade?
Where:
f* = optimal fraction of capital to risk
p = probability of winning
q = probability of losing (1 − p)
b = ratio of average win to average loss
Worked Examples
Win rate: 55%. Average win: $200. Average loss: $100. b = 200/100 = 2.
f* = (0.55 × 2 − 0.45) / 2 = 32.5% (full Kelly)
Half Kelly: 16.25%. Quarter Kelly: 8.1%
On a $10,000 account, quarter Kelly = $812 per trade
You believe an event has 60% probability. Contract trades at $0.40. Payoff: $1 if correct, $0 if wrong.
p = 0.60. b = (1-0.40)/0.40 = 1.5. q = 0.40.
f* = (0.60 × 1.5 − 0.40) / 1.5 = 33.3% (full Kelly)
Quarter Kelly: 8.3% of prediction market portfolio
Why Use Fractional Kelly?
Full Kelly maximises long-term growth rate but creates extreme volatility. A full Kelly portfolio can experience 50%+ drawdowns during losing streaks. In practice, most professional traders and prediction market participants use fractional Kelly:
| Kelly Fraction | Growth Rate | Max Drawdown | Volatility | Recommendation |
|---|---|---|---|---|
| Full (100%) | Maximum | Very high (50%+) | Extreme | Theoretical only |
| Half (50%) | ~75% of max | Moderate (25-35%) | High | Aggressive traders |
| Quarter (25%) | ~50% of max | Low (12-18%) | Manageable | Most traders |
| Tenth (10%) | ~20% of max | Very low (5-8%) | Low | Conservative |
Quarter Kelly is the most commonly recommended fraction because it captures approximately 50% of the maximum possible growth rate while reducing drawdowns to manageable levels. Vector Ridge's Polymarket Strategy Guide recommends 25–50% Kelly for prediction market position sizing.
Kelly Criterion Limitations
- Requires accurate probability estimates — if your win probability estimate is wrong, Kelly gives incorrect sizing. Overestimating your edge leads to over-sizing.
- Assumes independent bets — correlated positions (e.g., multiple political bets in the same election) should be treated as a single risk unit, not independent Kelly calculations.
- Does not account for partial wins/losses — the basic formula assumes binary outcomes. For trades that can hit partial take-profit or be closed early, the calculation is approximate.
- Full Kelly is too aggressive for real trading — always use fractional Kelly (25–50%) in practice.
Related Tools
- Polymarket Calculator — Kelly sizing + arbitrage detection for prediction markets
- Risk Reward Calculator — calculate R:R and required win rate
- Position Size Calculator — multi-asset position sizing
- Implied Probability Calculator — convert odds to probability for Kelly input
- Polymarket Strategy Guide — Kelly applied to prediction markets
A formula for optimal bet sizing: f* = (p×b - q) / b. Maximises long-term growth given your win rate and payoff ratio. Developed by John Kelly at Bell Labs in 1956.
Using 25-50% of the full Kelly recommendation to reduce volatility. Quarter Kelly achieves ~50% of max growth with much lower drawdowns. Recommended for real trading.
Kelly determines what % of your prediction market portfolio to allocate per contract based on your edge (difference between your assessed probability and market price). Use the Polymarket Calculator for automated sizing.
Full Kelly creates extreme volatility (50%+ drawdowns). Your probability estimates are never perfectly accurate. Fractional Kelly provides most of the growth with far less risk. Quarter Kelly is the professional standard.