Kelly Criterion Calculator
Find the optimal fraction of your bankroll to risk on each bet given your win rate and win-to-loss ratio. Includes the safer half- and quarter-Kelly variants most professionals actually use.
Results
With your inputs, full Kelly says risk 25.00% of your bankroll per bet, but the recommendation is quarter kelly — i.e. 6.25% per bet. The conservative recommendation is because Kelly inputs (win rate, avg win, avg loss) are usually estimated, not known exactly, and small overestimates of edge cause severe overbetting. Your edge is 37.50% with a payoff ratio of 1.50×.
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Frequently asked questions
How the Kelly criterion works
John Kelly Jr. derived the formula at Bell Labs in 1956 to maximize the long-term geometric growth rate of capital under repeated favorable bets. Edward Thorp later applied it to blackjack and to portfolio management. The intuition: if you bet too small, you grow slowly; if you bet too big, occasional losses compound and your bankroll goes to zero. There is a unique fraction in between that maximizes long-run growth — that fraction is Kelly.
The formula in plain English
For a discrete bet with two outcomes, f* = p − (1 − p) / b. Here p is your probability of winning, and b is the ratio of average win to average loss. The expression p − (1 − p) / b is your edge per dollar risked, expressed as a fraction.
Concrete example: if you win 55% of the time, with average wins of $150 and average losses of $100, then p = 0.55, b = 1.5, and f* = 0.55 − 0.45 / 1.5 = 0.55 − 0.30 = 0.25. Full Kelly says bet 25% of your bankroll on this opportunity. Half Kelly says 12.5%; quarter Kelly says 6.25%.
Why most professionals use a fraction of Kelly
The full Kelly formula assumes you know your edge exactly. In practice, you estimate it from a sample of past trades, and the estimate is noisy. Overestimating your edge by 20% can cause severe overbetting that destroys the long-run advantage. Half-Kelly captures about 75% of the long-term growth rate with substantially lower volatility and a much lower probability of large drawdowns. Quarter-Kelly is even more conservative — about 50% of full- Kelly growth with a much smoother equity curve. Almost no one runs full Kelly in real money management for this reason.
When Kelly does NOT apply
- Single-shot decisions. Kelly maximizes long-term growth across many bets. For a one-time decision, the right answer depends on your utility function, not on Kelly.
- Multiple correlated bets. Single-bet Kelly assumes one bet at a time. If you have multiple positions running simultaneously, you should size each smaller — divide by the number of independent bets, more if they are correlated.
- Continuous returns. For a strategy that produces a continuous return stream (not discrete win/loss outcomes), use the continuous-Kelly formula:
f* = mean(returns) / variance(returns). The QuantOracle API supports this viamode=continuous. - Non-stationary edge. If your edge changes over time (markets adapt, strategies decay), the static Kelly fraction is wrong. Re-estimate often, and use a smaller fraction than the textbook formula suggests.