Kelly Criterion Calculator
Calculate the optimal bet or position size given your win probability and payout.
How this is calculated
The Kelly formula is f* = (p × b − q) / b, where p is your win probability, q is 1 − p, and b is your win multiple. When win and loss multiples differ, the generalised form f* = (p × win − q × loss) / (win × loss) is used instead. The result is the fraction of your bankroll that maximizes long-run geometric growth.
If the calculated fraction comes out negative, the bet has negative expected value and Kelly recommends staking nothing. Because real-world edge estimates are rarely perfectly accurate, most practitioners bet a fraction of full Kelly — commonly half — to reduce volatility and protect against overestimating their edge.
Frequently asked questions
- What is the Kelly Criterion?
- A formula that calculates the optimal fraction of your bankroll to bet or invest in a favorable opportunity, in order to maximize the long-run geometric growth rate of your capital. Developed by John Kelly at Bell Labs in 1956, it is used in gambling, sports betting, and position sizing for trading.
- Why use half-Kelly instead of full Kelly?
- Full Kelly maximizes long-run growth but comes with large swings in bankroll value, and is very sensitive to overestimating your true edge. Half-Kelly gives up some growth rate in exchange for significantly less volatility and more protection against estimation error — a trade-off most practitioners consider well worth it.
- What is the "win multiple"?
- How many dollars you receive per dollar wagered if you win, not counting your original stake. A "2.0" win multiple (2:1 odds) means a $100 bet that wins pays out $200 in profit, on top of getting your $100 stake back.
- Can Kelly be used for stock trading?
- Yes, though estimating a reliable win probability and payout ratio for a trading strategy is much harder than for a game with known odds. Many traders use a fraction of Kelly (often much less than half) specifically because their edge estimates carry meaningful uncertainty.
- What happens if I bet more than the Kelly fraction?
- Betting above full Kelly ("over-betting") actually reduces your long-run growth rate, not just your risk — beyond a certain point, more aggressive sizing makes both the ride rougher and the destination worse. This is one of Kelly's more counter-intuitive results.
- Is Kelly appropriate for a full investment portfolio?
- The classic formula assumes a single repeated bet with known, fixed odds — real portfolios involve many correlated positions with uncertain and changing probabilities, so Kelly is better used as a sizing principle (bet less when your edge or confidence is smaller) than a literal formula for portfolio construction.
- What does negative expected value mean?
- If your expected value per bet is negative, there is no bet size that makes the wager profitable in the long run — the mathematically optimal Kelly fraction is 0%, meaning you should not take the bet at all, regardless of how good the odds look on any single try.
- Can I use this in my own app?
- Yes — every calculator on Stupidly Clever has a matching REST API and MCP tool that runs the same underlying logic.