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Kelly Criterion Calculator: Full and Fractional Stakes
Use a probability estimate that you supply. Examine the full Kelly fraction, a reduced fraction and an optional upper cap; this does not validate the probability or recommend a real-money bet.
How it works & examplesUnderstand the calculation
Kelly sizes an assumed edge; it does not discover one
Kelly uses your probability estimate and the offered odds to calculate a bankroll fraction. At decimal odds of 2.00 and an assumed 55% win chance, full Kelly gives 10% of bankroll. Half Kelly would scale that to 5%. The calculation changes immediately if the 55% assumption changes.
Position sizing depends on both the offered price and your estimated win chance; validate the price component in Betting Odds Calculator: Decimal, Fractional, US.
The most important input is therefore not bankroll size but the credibility of the probability estimate. A price-implied probability is not independent evidence of an edge. Fractional Kelly reduces the modeled stake, not the possibility of loss or estimation error. A zero recommendation means the entered assumptions do not support a positive stake in this model.
Maths & verification
Calculate full Kelly, fractional Kelly, expected value and a capped illustration from your own win probability and decimal odds. No predictions.
Try the simulator below. Input values stay in your browser; no account or money is involved.
Model assumptions: No. Virtual games use declared teaching models. Verify any actual operator’s payout rules independently.
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How to use the tool
Explore the Kelly fraction without treating a personal probability guess as a verified edge.
- Enter decimal odds, a hypothetical budget and your own win probability estimate.
- Choose how much of full Kelly to illustrate and an optional maximum budget share.
- Review expected value, break-even chance and the capped model allocation.
Understanding your result
Full Kelly = max(0,(p × decimal odds − 1)/(decimal odds − 1)). The selected fraction scales it down; the risk cap limits the final budget share. Negative or zero expected value yields zero.
Scope and limitations
Probability estimates are uncertain; Kelly can exaggerate losses when those estimates are wrong. This does not recommend bets or account for variance, correlations, limits or taxes.
Before you rely on the result
- How the calculation works
Formulas, assumptions, rounding and model limits are documented on the methodology page.
- Check the current inputs
Use the odds, RTP, fees, bonus terms or other values currently shown by the operator or market.
Kelly criterion: edge, bankroll fraction and fractional Kelly
Kelly sizes a stake from your own estimated win probability and the offered odds. It does not estimate the probability for you.
With decimal odds d, let b = d − 1, p = estimated win probability and q = 1 − p. Full Kelly fraction = (b × p − q) / b. If the result is zero or negative, the model says no positive Kelly stake.
Worked example at decimal odds 2.20
At 50% estimated win probability, b = 1.20. Full Kelly = (1.20 × 0.50 − 0.50) / 1.20 = 8.33% of bankroll.
| Kelly setting | Bankroll fraction | Stake on 1,000 bankroll |
|---|---|---|
| Full Kelly | 8.33% | 83.33 |
| Half Kelly | 4.17% | 41.67 |
| Quarter Kelly | 2.08% | 20.83 |
Kelly is extremely sensitive to probability error
If your probability estimate is too high, Kelly can recommend an oversized bet. Fractional Kelly reduces exposure to model error and drawdown, but it does not turn a poor probability estimate into an edge.
Several open bets change total bankroll exposure
Single-bet Kelly assumes the stake is sized against the current bankroll in isolation. Applying full Kelly independently to several correlated or simultaneous bets can risk more of the bankroll than intended. This calculator does not solve portfolio Kelly.
Worked example
At decimal odds 2.20 and your own assumed win chance of 50%, full Kelly is 8.33% of budget. A 25% Kelly fraction is about 2.08%; on 1,000 illustrative units that is 20.83.
Would the amount be correct if the probability were actually 40%?
No. Expected value would be negative and the same model would return zero.
Questions about this calculation
Does Kelly calculate my true chance of winning?
No. You must supply that chance independently; the calculator only applies algebra to your input.
Why is the calculated amount zero?
The entered chance does not exceed the break-even probability for the quoted odds.
When is Kelly Criterion Calculator: Full and Fractional Stakes the right tool?
Explore the Kelly fraction without treating a personal probability guess as a verified edge.
How should I read the result from Kelly Criterion Calculator: Full and Fractional Stakes?
Full Kelly = max(0,(p × decimal odds − 1)/(decimal odds − 1)). The selected fraction scales it down; the risk cap limits the final budget share. Negative or zero expected value yields zero.
What can Kelly Criterion Calculator: Full and Fractional Stakes not tell me?
Probability estimates are uncertain; Kelly can exaggerate losses when those estimates are wrong. This does not recommend bets or account for variance, correlations, limits or taxes.