Kelly Criterion
A formula that determines the theoretically optimal bet size to maximize long-term growth rate, based on win probability and payoff ratio.
What the Kelly Criterion Is
The Kelly Criterion is a mathematical formula for calculating the optimal fraction of capital to risk on a bet or trade, maximizing the long-term geometric growth rate of an account. It was developed by John L. Kelly Jr. at Bell Labs and published in the *Bell System Technical Journal* in 1956. The formula was later adapted for financial markets by Ed Thorp, who used it to beat casinos and manage the Princeton Newport Partners hedge fund.
The Formula
f* = (bp - q) / b
Where:
- f* = fraction of capital to risk
- b = ratio of average win to average loss (the payoff ratio)
- p = probability of winning
- q = probability of losing (1 - p)
Example: 55% win rate, 1:1.5 risk-reward (b = 1.5)
f* = (1.5 × 0.55 - 0.45) / 1.5 = 0.25 (25% of capital)
Why Full Kelly Is Dangerous
Full Kelly sizing maximizes long-term growth but produces extreme drawdowns. In trading:
- Drawdowns of 50–80% are common under full Kelly
- It assumes perfect knowledge of your edge (which traders rarely have)
- Overestimating your win rate by just 5% can lead to catastrophic over-sizing
As Ed Thorp wrote in *A Man for All Markets* (Random House, 2017): "full Kelly is the boundary between aggressive growth and almost-certain ruin. Most practitioners should stay well below it."
Fractional Kelly in Practice
Most professional traders and fund managers use a fraction of the Kelly recommendation:
- Half Kelly (f*/2): Captures approximately 75% of the growth rate with significantly lower drawdowns
- Quarter Kelly (f*/4): Much smoother equity curve, lower returns, approximately 50% of optimal growth
The reduction accounts for uncertainty in edge estimates and the psychological reality of large drawdowns.
Kelly vs. Fixed Fractional
Fixed fractional sizing (e.g., always risk 2%) is simpler but doesn't adapt to your edge. Kelly adjusts position size to your actual win rate and payoff ratio, putting more capital behind stronger edges. The downside: Kelly requires accurate estimates of your strategy parameters. Bad inputs produce bad sizing.
Testing Kelly with Simulation
Before applying Kelly sizing, run your parameters through Monte Carlo simulation to see the drawdown distribution. The Risk of Ruin Calculator lets you test different risk levels. RangeSight provides full simulation with real volatility data.
Key Takeaway
A formula that determines the theoretically optimal bet size to maximize long-term growth rate, based on win probability and payoff ratio. Use RangeSight Studio's Monte Carlo simulator to model kelly criterion with 10,000 simulated paths and real market volatility.
This explains the concept.
But how kelly criterion affects your specific strategy depends on your parameters, position sizing, and market conditions.
Test your strategy to see how consistent it actually is → Run survival test
See the full distribution with real market data
10,000 Monte Carlo paths. P5/P50/P95 scenarios. Real ticker volatility.
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