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Updated April 20, 2026 · Investing · Educational use only ·

Kelly Criterion Calculator

Optimal bet sizing.

Calculate the Kelly Criterion optimal bet size for positive expected value bets, from win probability, payoff multiple, and bankroll.

What this tool does

The Kelly Criterion sizes bets as a fraction of your bankroll to maximise expected log wealth growth over time. This calculator takes your estimated win probability, the amount you'd gain if you win, and the amount you'd lose if you don't — then computes both the full Kelly fraction and the half Kelly fraction. Full Kelly represents the mathematically aggressive sizing; half Kelly applies a safety buffer by halving that fraction. The result shows what percentage of your bankroll each approach suggests risking per bet. Win probability has the largest influence on the output; smaller changes to payoff amounts affect sizing less dramatically. A trader testing a strategy with a 55% win rate and known payoff structure might use this to model bet sizes. Note that the calculation assumes consistent payoffs and probabilities, doesn't account for transaction costs or changing market conditions, and is for educational illustration only.


Enter Values

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Formula Used
Optimal fraction
Win/loss ratio
Win probability
Loss probability

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Disclaimer

Results are estimates for educational purposes only. They do not constitute financial advice. Consult a qualified professional before making financial decisions.

Kelly Criterion calculates optimal bet size to maximise long-term geometric growth: f* = (bp - q) / b, where b = win/loss ratio, p = win probability, q = loss probability. Used by Warren Buffett, Ed Thorp, professional gamblers and sports bettors. Tells you how much of capital to risk per opportunity.

Example: 60% win probability, win 200 / lose 100 (2:1 ratio). Kelly = (2 × 0.60 - 0.40) / 2 = 0.40 = 40% of bankroll. Aggressive but mathematically optimal for long-term growth. Most professionals use Half Kelly (20% in this example) - sacrifices some growth for dramatically lower volatility and drawdown risk.

Kelly limitations: assumes you know exact probabilities (rarely true in markets). Over-betting (above Kelly) causes ruin even with positive edge. Half Kelly is standard practice - retains 75% of growth at 25% of volatility. Kelly is impossible without edge: if expected value is negative (no edge), Kelly returns negative or zero - don't bet. Kelly is for repeated bets, not one-time decisions.

A worked example

Try the defaults: win probability of 60%, win payoff of 200, loss amount of 100. The tool returns 40.00%. You can adjust any input and the result updates as you type — no submit button, no reload. That's the real power here: seeing how sensitive the output is to one or two assumptions.

What moves the number most

The result responds to Win Probability %, Win Payoff, and Loss Amount. Not every input has equal weight. Adjusting one input at a time toward extreme values shows which ones move the result most.

The formula behind this

Kelly fraction = (b×p - q) / b. Half Kelly = full Kelly / 2 (recommended for safety). Everything the calculator does is shown in the formula box below, so you can check the math against your own spreadsheet if you want.

Using this well

What this doesn't capture

Steady-rate math ignores real-world volatility. Actual returns are lumpy; sequence-of-returns risk matters most in drawdown; fees and taxes drag on compound growth; and behaviour changes in drawdowns can reduce outcomes below the projection. The number represents one scenario rather than a forecast.

Example Scenario

60% win, ££200 vs ££100 payoffs = 40.00% of bankroll.

Inputs

Win Probability %:60
Win Payoff:£200
Loss Amount:£100
Expected Result40.00%

This example uses typical values for illustration. Adjust the inputs above to match a specific situation and see how the result changes.

Sources & Methodology

Methodology

This calculator computes the Kelly fraction, a formula from probability theory that models optimal bet sizing relative to bankroll. It applies the formula f* = (bp − q) / b, where b is the ratio of win payoff to loss amount, p is win probability as a decimal, and q is loss probability (1 − p). The result expresses the fraction of bankroll to wager on a single bet. The calculator assumes constant odds, independent outcomes, and a fixed bankroll across successive bets. It does not account for transaction costs, market impact, liquidity constraints, or the practical difficulty of executing fractional positions. Results are mathematical outputs only and do not incorporate risk tolerance, time horizon, or portfolio context. The calculator also offers a half-Kelly variant, which applies the full Kelly result divided by two.

Frequently Asked Questions

Why use Half Kelly?
Full Kelly maximises geometric growth but with massive volatility (50%+ drawdowns common). Half Kelly: ~75% of growth at ~25% of volatility. The math: utility function shows risk-adjusted return optimised at fractional Kelly. Most professional sports bettors and quant traders use 25-50% of full Kelly.
What if I overestimate edge?
Over-betting Kelly causes guaranteed long-term ruin even with positive edge. If true edge is 3% but you size for 6%, you'll go broke despite winning expected value. Always size below Kelly when uncertain about true probability - safety margin is more valuable than optimal growth in real markets.
Kelly for stocks?
Stocks are continuous (not binary win/lose). Need different formulation: f = (E[r] - r_f) / σ². For S&P 500: 7% expected return, 4% baseline, 16% volatility = (0.07-0.04) / 0.16² = 117% allocation. Hence why people leverage stocks 2x. But that ignores fat tails - real Kelly for stocks much lower (50-100% with margin of safety).
Negative Kelly = don't bet?
Yes - if Kelly returns 0 or negative, expected value is non-positive. Don't bet. Casino games (negative EV) all give negative Kelly. Most retail trading strategies (after fees and slippage) give negative Kelly. Only bet when you have demonstrable positive expected value with statistical confidence.

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