What is the Kelly Criterion?
The Kelly Criterion (also known as the Kelly Strategy or Kelly Bet) is a mathematical formula for optimal bet sizing developed by John L. Kelly Jr. at Bell Labs in 1956. Originally designed for information theory, it was quickly adopted by gamblers, investors, and traders as the definitive answer to the question: “How much should I bet?”
The formula maximizes the long-term geometric growth rate of your capital. Unlike fixed position sizing, Kelly dynamically adjusts your bet size based on the strength of your edge, ensuring you never overbet (risking ruin) or underbet (leaving growth on the table).
The Kelly Criterion Formula
f* = (b × p − q) / b
Equivalently: f* = p − (q / b)
For example, if your win rate is 55% (p = 0.55) and your average win is 1.5 times your average loss (b = 1.5), the Kelly fraction is:
Why Use Our Kelly Strategy Calculator?
Full & Fractional Kelly
Calculate both the mathematically optimal Full Kelly and the practically recommended Fractional Kelly. Adjust the fraction from 1% to 100% to find the risk level that matches your tolerance.
Growth Simulation
Visualize how your bankroll grows over 100 bets at Full Kelly, Half Kelly, and Double Kelly. See firsthand why overbetting destroys returns even with a genuine edge.
Kelly Curve
The Kelly Curve plots expected growth rate against bet size, revealing the optimal peak and the danger zone where overbetting turns a winning strategy into a losing one.
Risk-Aware Metrics
Beyond bet size, view expected value per bet, geometric growth rate, edge percentage, and estimated doubling time. Make informed decisions with a complete picture of your strategy's risk-reward profile.
How to Use This Kelly Strategy Calculator
- 1
Choose Your Input Mode
Use Basic mode if you know your win rate and win/loss ratio directly. Use Advanced mode to enter average win and loss amounts in dollars — the calculator will derive the ratio automatically.
- 2
Enter Your Win Rate
Input the percentage of trades or bets you expect to win. Use historical data from at least 100 trades for a reliable estimate. Be conservative — overestimating your win rate leads to overbetting.
- 3
Set Your Win/Loss Ratio
Enter how much you win on average relative to how much you lose. A ratio of 1.5 means your average win is 1.5 times your average loss. In Advanced mode, enter dollar amounts and the ratio is calculated for you.
- 4
Adjust the Kelly Fraction
Most professionals use 25-50% of Full Kelly. The default is 50% (Half Kelly), which captures 75% of the optimal growth rate while dramatically reducing drawdowns and volatility.
- 5
Analyze the Results
Review the optimal bet size, key metrics, growth simulation, and Kelly curve. Use the growth chart to compare Full Kelly vs. Half Kelly vs. Double Kelly, and the Kelly curve to understand the relationship between bet size and expected growth.
Understanding Kelly Criterion Metrics
- Full Kelly Percentage: The mathematically optimal fraction of your bankroll to bet. Maximizes long-term growth but produces significant drawdowns. Most traders find Full Kelly too aggressive for real-world use.
- Fractional Kelly: A reduced version of Full Kelly (e.g., Half Kelly = 50%). Sacrifices some growth for dramatically smoother equity curves. Half Kelly achieves approximately 75% of the Full Kelly growth rate.
- Expected Value (EV): The average profit per dollar wagered. A positive EV means you have a mathematical edge. The higher the EV, the stronger your advantage.
- Geometric Growth Rate: The expected rate at which your bankroll compounds per bet. This is the metric Kelly maximizes. A higher growth rate means faster capital accumulation.
- Edge Percentage: Your expected return expressed as a percentage. An edge of 5% means you expect to earn $0.05 for every $1.00 risked, on average.
- Doubling Time: The estimated number of bets required to double your bankroll at the Kelly-optimal bet size. Lower is better, but remember this is an expected value — actual results will vary.
Full Kelly vs. Fractional Kelly
While Full Kelly is theoretically optimal, it assumes perfect knowledge of your win rate and win/loss ratio — something no trader has in practice. Here is how different Kelly fractions compare:
| Kelly Fraction | Growth Rate | Drawdown Risk | Best For |
|---|---|---|---|
| 25% Kelly | ~44% of optimal | Very Low | Conservative traders, uncertain edge |
| 50% Kelly (Half) | ~75% of optimal | Moderate | Most traders (recommended) |
| 100% Kelly (Full) | 100% (maximum) | High | Precise edge estimates only |
| 200% Kelly (Double) | 0% (zero growth) | Extreme / Ruin | Never recommended |
Practical Tips for Using the Kelly Criterion
- Use Conservative Estimates: Always underestimate your win rate and win/loss ratio. Real markets are noisier than backtests suggest. A 2-3% haircut on your win rate provides a useful safety margin.
- Start with Half Kelly: Unless you have thousands of trades confirming your edge, Half Kelly (50%) is the most practical starting point. It captures most of the growth with far less volatility.
- Recalculate Regularly: Your win rate and average win/loss ratio change over time as market conditions evolve. Update your Kelly inputs monthly or quarterly using your most recent trade data.
- Cap Maximum Position Size: Even if Kelly suggests a large bet, many traders cap individual positions at 5-10% of their portfolio to limit concentration risk and account for model uncertainty.
- Combine with Stop Losses: Kelly tells you how much to risk, not where to place your stop. Use Kelly for position sizing and technical analysis for stop-loss placement to create a complete risk management framework.
Disclaimer: This Kelly Strategy Calculator is for educational and informational purposes only. The Kelly Criterion assumes known probabilities and fixed payoff ratios, which are approximations in real markets. Past trading performance does not guarantee future results. Position sizing carries inherent risk, including the potential loss of capital. Always consult with a qualified financial advisor before making investment decisions.