Kelly Criterion Calculator
Find the growth-optimal bet size from win probability and payoff, with half and quarter Kelly. Educational only, not trading or investment advice.
Quick answer
The Kelly criterion gives the bankroll fraction that maximises long-run growth: f* = p - (1 - p) / b, where p is the win probability and b the win/loss ratio. Half and quarter Kelly scale that stake down.
Kelly Criterion Calculator
Amount won per 1 lost.
Total payout per 1 staked.
Full Kelly (f*)
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Half Kelly
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Quarter Kelly
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Expected Value per 1 Staked
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Growth per Bet at Full Kelly
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Full Kelly Stake
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Break-even Win Probability
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Expected growth per bet (%) vs fraction staked (%)
Educational only. This is not trading, betting or investment advice.
Growth by Fraction of Kelly
| Fraction of Kelly | Stake (% of bankroll) | Growth per bet | Bets to double |
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Assumptions & method
- Kelly fraction f* = p − (1 − p) ÷ b, where p is the win probability and b the amount won per 1 lost. With decimal odds, b = odds − 1.
- Expected value per 1 staked = p·b − (1 − p). A bet with f* ≤ 0 has no positive edge and the stake should be zero.
- Growth per bet g(f) = p·ln(1 + b·f) + (1 − p)·ln(1 − f); bets to double = ln 2 ÷ g when g > 0. These are expected values, not guarantees.
- Assumes repeated independent bets with fixed probability and payoff, losing the full stake on a loss, and reinvesting the whole bankroll each time.
- Not included: estimation error in p and b, costs, taxes, limits on bet size, or correlated bets. Educational only, not trading or investment advice.
Results are estimates based on the figures you enter. They are not guarantees and not financial advice.
Sizing a bet for long-run growth
The Kelly criterion answers one question: if you could repeat the same bet many times, what fraction of your bankroll should you stake to make it grow fastest over the long run? The answer depends on your win probability and on how much you win relative to what you lose. Stake too little and you grow slowly; stake too much and volatility drags growth down, even to zero or below. This calculator gives the full, half and quarter Kelly fractions, the expected growth per bet, and a curve showing how growth changes with stake size. It relies on probabilities you supply, which are uncertain, so it is an illustration, not a betting plan.