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Your selected Kelly stake is $500 (5% of bankroll). 100% up to €300, no wagering - use code STARS1 · Weekly reload + free spins · $20 minimum deposit
Compare this stake size with CasinoStarsKelly Criterion Calculator
Calculate full, half, and quarter Kelly stake sizes from your bankroll, estimated win probability, and decimal odds. A non-positive result means no bet.
Kelly criterion calculator quick answer
The Kelly stake is bankroll multiplied by (b × p - q) / b, where b is decimal odds minus 1, p is your estimated win probability, and q is 1 minus p. If the result is zero or negative, the Kelly answer is no bet. Many bettors use half or quarter Kelly because probability estimates are rarely exact.
- A $1,000 bankroll, 55% win estimate, and 2.00 decimal odds produce a 10% full Kelly stake: $100.
- Half Kelly would stake $50 in that example; quarter Kelly would stake $25.
- The formula only has an edge if your win estimate is higher than the break-even probability implied by the odds.
- Kelly assumes repeated bets, changing bankroll size, and an honest probability estimate. It cannot repair a bad forecast.
Kelly betting calculator examples
These examples use the bankroll available before the bet. Full Kelly is the mathematical growth-maximizing fraction under the stated assumptions; the smaller fractions reduce exposure to estimation error.
| Bankroll | Win estimate | Decimal odds | Full Kelly | Half Kelly | Quarter Kelly |
|---|---|---|---|---|---|
| $1,000 | 55% | 2.00 | $100.00 | $50.00 | $25.00 |
| $2,000 | 45% | 2.50 | $166.67 | $83.33 | $41.67 |
| $500 | 30% | 4.00 | $33.33 | $16.67 | $8.33 |
| $1,000 | 50% | 1.90 | $0 (no edge) | $0 | $0 |
Full, half, and quarter Kelly compared
Fractional Kelly changes the amount staked, not your underlying edge. Use the smallest fraction that still fits your confidence in the probability estimate and your tolerance for losing streaks.
| Method | Stake calculation | Best fit | Main trade-off |
|---|---|---|---|
| Full Kelly | 100% of the calculated Kelly stake | Rare cases with a well-tested probability model | Highest theoretical growth and the sharpest swings. |
| Half Kelly | 50% of the calculated Kelly stake | A practical default when the model has some uncertainty | Less growth in exchange for a smaller sizing mistake. |
| Quarter Kelly | 25% of the calculated Kelly stake | Noisy markets, small samples, or cautious bankroll plans | Slowest growth, but least exposed to an inflated edge estimate. |
| No bet | 0% when Kelly is zero or negative | Your estimate does not beat the offered price | Skipping the bet protects the bankroll from negative expected value. |
Kelly gives you a ceiling, not permission to trust a weak estimate
Kelly is most useful when it stops a bet. The formula compares your probability estimate with the price on offer. If the estimate does not clear the break-even probability, the answer is zero. That is a pass, not an invitation to round the stake up because you like the pick.
The difficult input is not bankroll or decimal odds. It is win probability. A move from 53% to 55% at even money changes full Kelly from 6% to 10% of bankroll. That four-point sizing jump comes entirely from the forecast. If the model is new, the sample is thin, or the market has changed, half or quarter Kelly leaves more room for being wrong.
Kelly also expects the stake to move with the bankroll. Win, and the next dollar stake rises. Lose, and it falls. The 100-bet projection in the calculator uses that rebalancing assumption, constant odds, and independent outcomes. It is a mathematical comparison, not a promise about the next season or betting card.
Treat bonuses separately. A no-wagering cash bonus may increase usable bankroll once its terms are satisfied. A locked balance with rollover, game restrictions, or a maximum-bet rule is not equivalent to cash. Read the offer terms first, then decide how much of that balance belongs in the bankroll input.
Sources and methodology
- J. L. Kelly Jr., A New Interpretation of Information Rate (1956): The original Bell System Technical Journal paper that introduced the growth-optimal criterion.
Kelly Criterion questions
How do you calculate a Kelly stake?
Convert decimal odds to net odds with b = decimal odds - 1. Set p to your estimated win probability and q to 1 - p. Full Kelly is (b × p - q) / b. Multiply that fraction by the current bankroll to get the stake amount.
What does a negative Kelly result mean?
A negative result means your estimated win probability does not beat the break-even probability in the price. The practical Kelly stake is zero. Do not turn the negative number into a smaller positive bet; the formula is telling you to pass.
Is half Kelly better than full Kelly?
Full Kelly maximizes theoretical long-run growth only when the probability and odds inputs are accurate. Half Kelly stakes half as much and gives up some theoretical growth, but it is less punishing when your edge estimate is too optimistic. That makes it a more practical default for many bettors.
Can I use the Kelly criterion for sports betting?
Yes, if you can estimate the true win probability independently from the sportsbook odds. Enter the bankroll, your own probability estimate, and the available decimal odds. For correlated bets or several open positions, size the group conservatively rather than treating every wager as independent.
What is quarter Kelly?
Quarter Kelly is 25% of the full Kelly stake. If full Kelly says to risk 8% of bankroll, quarter Kelly risks 2%. It is useful when the sample is small, the market is volatile, or you want more protection from probability error.
Should a bonus be included in the Kelly bankroll?
Only include funds you can actually stake and withdraw under the offer terms. A locked bonus with wagering requirements is not the same as cash. Check game eligibility, rollover, maximum-bet rules, and expiry before treating any bonus amount as usable bankroll.
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