About the Kelly Criterion Calculator
The Kelly criterion answers a simple question: if you have an edge, what fraction of your capital should you risk on each bet or trade to grow your wealth fastest over the long run? Risk too little and you leave growth on the table; risk too much and the swings drag your compounded growth down — beyond roughly twice the Kelly fraction (exactly twice for small edges), growth turns negative even though each bet has a positive expected value.
This Kelly criterion calculator takes your probability of winning and the size of a typical win relative to a typical loss, and returns the full Kelly fraction, the fraction after applying a safety multiplier (half or quarter Kelly), the amount to stake from your bankroll, your edge per unit risked and the expected logarithmic growth per bet. The chart shows how growth rises and then falls as the stake grows.
For trading, the "loss" is the amount you lose when your stop is hit, so the fraction is the share of your account to put at risk on the trade, not the position size. Kelly assumes your probabilities are accurate; because real-world estimates are uncertain, most practitioners use half Kelly or less.
With the default inputs, the recommended stake (% of bankroll) is 5%. Change any value above to recalculate instantly.
How to use the kelly criterion calculator
- 1Enter your estimated probability of winning each bet or trade.
- 2Enter the average win and average loss in the same units (or the net odds and 1).
- 3Choose full, half or quarter Kelly.
- 4Enter your bankroll to see the dollar amount to risk.
Formula and method
Kelly maximizes the expected logarithm of wealth, which is the same as maximizing the long-run compound growth rate. For a bet that wins b times the stake with probability p and loses the stake otherwise, setting the derivative of g(f) to zero gives f* = p − q ÷ b, where q = 1 − p is the probability of losing. The edge p·b − q is the expected profit per unit risked.
The growth curve is flat near the optimum and asymmetric: betting half Kelly keeps about three-quarters of the maximum growth rate with much smaller drawdowns, while betting about twice Kelly brings growth to roughly zero (the exact break-even stake, shown in the notes, is a little higher when the payoff ratio is large). A negative f* means you have no edge and should not bet. The calculator caps the stake at 100% of the bankroll.
- f*
- Kelly fraction of bankroll to risk
- p
- Probability of winning
- q
- Probability of losing (1 − p)
- b
- Net payoff per unit risked (win ÷ loss)
Worked examples
Even-money bet with a 55% win rate, half Kelly
With b = 1 and p = 0.55, Kelly is 0.55 − 0.45 ÷ 1 = 10% of the bankroll. Half Kelly stakes 5%, or $500 of $10,000, for expected log growth of about 0.375% per bet — three-quarters of the 0.50% available at full Kelly.
Trend-following trader: 40% winners, 3:1 payoff
Winning only 40% of the time but making three times the loss on winners gives b = 3 and f* = 0.40 − 0.60 ÷ 3 = 20%. The edge is 60 cents per dollar risked.
High win rate, small winners, quarter Kelly
Average wins are 80% of average losses, so b = 0.8 and f* = 0.60 − 0.40 ÷ 0.8 = 10%. Quarter Kelly risks 2.5%, or $1,250 per trade.
No edge
A 45% chance of winning an even-money bet has a negative edge of −10%. Kelly is negative, so the growth-maximizing stake is zero.
Frequently asked questions
What is the Kelly criterion formula?+
For a simple bet, f* = p − q ÷ b, where p is the probability of winning, q = 1 − p, and b is the net amount won per unit staked. It gives the fraction of your bankroll that maximizes long-run growth.
Why do people use half Kelly?+
Full Kelly produces large drawdowns and is very sensitive to overestimating your edge. Half Kelly achieves about 75% of the growth rate with roughly half the volatility, which is why many professional bettors and traders prefer it.
How do I use the Kelly criterion for trading?+
Use your historical win rate for p and your average win divided by your average loss for b. The result is the share of your account to risk per trade — the loss if your stop is hit — not the total position size.
What does a negative Kelly percentage mean?+
It means the bet has a negative expected value at your estimates, so the growth-optimal stake is zero. A negative result can sometimes be read as a signal to take the other side, if that is possible at the same odds.
What happens if I bet more than Kelly?+
Growth slows and volatility rises. At roughly twice the Kelly fraction the expected compound growth rate falls to zero, and beyond that you are expected to lose money over time even with a positive edge per bet.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.