Kelly Criterion Calculator
Calculate the mathematically optimal position size to maximize long-term portfolio growth.
Formula
Where b = average win / average loss (odds), p = win probability, q = 1 − p (loss probability). f* is the fraction of bankroll to risk per trade.
An equivalent form: win probability minus the ratio of loss probability to the win/loss ratio. Positive values indicate an edge; negative means no edge.
The average expected dollar return per trade. Kelly only recommends a positive position when EV is positive — when you have a genuine edge.
Examples
- Win rate (p) = 45% = 0.45, Loss rate (q) = 0.55
- Average win (W) = $200, Average loss (L) = $100
- Odds (b) = W/L = 200/100 = 2.0
- Kelly f* = (2.0 × 0.45 − 0.55) / 2.0 = 0.35 / 2.0 = 0.175
- Half-Kelly (recommended) = 0.175 / 2 = 0.0875
- Win rate (p) = 65% = 0.65, Loss rate (q) = 0.35
- Average win (W) = $50, Average loss (L) = $50
- Odds (b) = 50/50 = 1.0
- Kelly f* = (1.0 × 0.65 − 0.35) / 1.0 = 0.30
- Half-Kelly = 0.30 / 2 = 0.15
- Win rate (p) = 40% = 0.40, Loss rate (q) = 0.60
- Average win (W) = $100, Average loss (L) = $100
- Odds (b) = 100/100 = 1.0
- Kelly f* = (1.0 × 0.40 − 0.60) / 1.0 = −0.20
- Negative Kelly → no edge, do not trade this strategy
Key Concepts
What is the Kelly Criterion?
The Kelly criterion is a formula for determining the optimal fraction of your bankroll to bet or invest on each opportunity. Developed by John Kelly Jr. at Bell Labs in 1956, it maximizes the long-term geometric growth rate of wealth. It's used by professional gamblers, traders, and hedge fund managers.
Why Use Half-Kelly?
Full Kelly assumes your estimates of win rate and payoff ratio are perfectly accurate — they never are. Half-Kelly (betting half the Kelly fraction) sacrifices about 25% of the growth rate but dramatically reduces volatility and drawdowns. Most practitioners use fractional Kelly (½ to ¼) in real trading.
The Kelly Edge Requirement
A negative Kelly fraction means you have no edge — you're expected to lose money over time. The Kelly criterion only recommends a positive position size when your expected value is positive. If Kelly says 0% or negative, don't trade that strategy until you find a genuine edge.
Kelly and Ruin Risk
Full Kelly can lead to very aggressive position sizes (30%+ of bankroll per trade), resulting in severe drawdowns before the long-term growth materializes. Using fractional Kelly greatly reduces the probability of ruin while still capturing most of the long-term growth benefit.
Estimation Error Problem
The biggest limitation of Kelly is that it requires accurate estimates of win probability and payoff ratio. In trading, these are estimated from historical data and can change. Overestimating your edge leads to overbetting, which is more destructive than underbetting — another reason to use fractional Kelly.
Kelly for Crypto Trading
Crypto markets have fat-tailed distributions, meaning extreme moves occur more often than normal distribution assumes. Standard Kelly doesn't account for this. Conservative traders in crypto often use quarter-Kelly or even eighth-Kelly to survive the frequent large moves that characterize these markets.
How to Apply the Kelly Criterion to Trading
The Kelly criterion solves a fundamental problem in trading: given a strategy with a known edge, what's the optimal position size? Too small and you leave growth on the table; too large and you risk catastrophic drawdowns or ruin. Kelly provides the mathematically optimal answer for maximizing long-term compounded returns.
To use Kelly, you need two inputs from your trading history: your win rate (percentage of profitable trades) and your payoff ratio (average winning trade divided by average losing trade). The formula then outputs a fraction of your bankroll to risk on each trade. A full Kelly fraction of 20% means you should risk 20% of your current bankroll per trade.
In practice, most traders use half-Kelly or quarter-Kelly. The growth rate with half-Kelly is about 75% of full Kelly, but the volatility is halved. This is almost always a better tradeoff because it accounts for estimation error in your win rate and payoff ratio, and it makes the strategy psychologically tolerable during inevitable losing streaks.
Frequently Asked Questions
What win rate and payoff ratio should I use?
Use your actual historical trading data. Calculate win rate from at least 50–100 trades, and measure the average dollar amount of winning vs losing trades. Be conservative with estimates — overstating your edge leads to overbetting, which is far more dangerous than underbetting.
Is full Kelly too aggressive?
Almost always, yes. Full Kelly assumes perfect knowledge of your edge and leads to very volatile equity curves. In practice, half-Kelly or quarter-Kelly is standard. Even professional sports bettors and hedge fund managers rarely use more than half-Kelly.
What if I get a negative Kelly value?
A negative Kelly fraction means the strategy has a negative expected value — you expect to lose money. Do not trade this strategy. Re-examine your entry/exit rules, risk management, and edge. The Kelly criterion is telling you the math doesn't support taking the bet.
Does Kelly account for fees and slippage?
Only if you include them in your win/loss calculations. Your average win and average loss should be net of all fees, commissions, and slippage. If your average win is $100 before fees but $90 after, use $90. This gives a more conservative and realistic Kelly fraction.