Kelly Criterion Calculator
Find your optimal bet size
Enter your estimated win probability and the odds offered. The calculator returns your full Kelly stake and fractional variants — with the formula shown so you can verify every number.
Calculator inputs
Negative = favourite (e.g. -110). Positive = underdog (e.g. +150).
Enter a valid American odds value (not 0).
Your model’s or assessment’s estimated probability this bet wins (1–99).
Enter a win probability between 1 and 99.
Leave blank to see percentages only.
Results
Enter your odds and win probability,
then click “Calculate Kelly stake”.
The formula explained
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula that calculates the optimal fraction of your bankroll to wager on a bet, given your estimated edge and the odds. It was developed by physicist John L. Kelly Jr. at Bell Labs in 1956 and later adopted by gamblers and investors as a bankroll growth strategy.
The core insight of Kelly is that betting too much on even a positive-EV bet will eventually bankrupt you due to variance. Betting too little leaves growth on the table. Kelly finds the mathematically optimal middle point.
The formula produces a percentage of your total bankroll to wager. If Kelly returns 5%, you bet 5% of your current bankroll — not 5% of your starting bankroll. This means stakes shrink during losing runs and grow during winning runs automatically.
In practice, most sports bettors use a fractional Kelly (commonly half-Kelly or quarter-Kelly) to reduce variance while preserving most of the growth benefit.
Kelly Criterion formula
f* = (bp − q) / b- f* = fraction of bankroll to bet
- b = decimal odds minus 1 (net odds received on a win)
- p = your estimated probability of winning
- q = probability of losing (1 − p)
A negative Kelly result means the bet has negative expected value — the formula is telling you not to bet. No amount of positive framing changes a −EV bet into a profitable one over time.
Scenario: NFL game, odds −110 (American), your model estimates a 57% win probability.
−110 American →
100 / 110 + 1 = 1.909b = 1.909 − 1 = 0.909p = 0.57 | q = 1 − 0.57 = 0.43f* = (0.909 × 0.57 − 0.43) / 0.909f* = (0.518 − 0.43) / 0.909f* = 0.088 / 0.909 = 0.097Half Kelly = 4.85% | Quarter Kelly = 2.42%
On a $1,000 bankroll: $48.50 at half-Kelly
Why fractional Kelly?
Full Kelly maximizes long-term growth mathematically, but requires perfectly calibrated probability estimates.
In practice, estimates are imperfect. Half-Kelly gives roughly 75% of the growth with significantly less variance,
which is why most systematic bettors use it as their default.
Kelly variants
Which Kelly fraction should you use?
The right fraction depends on how confident you are in your probability estimates and how much variance you can tolerate emotionally and financially.
| Fraction | Stake size | Variance | Best for | Trade-off |
|---|---|---|---|---|
| Quarter Kelly Conservative | 25% of full Kelly | Very low | Beginners, uncertain models, high-volume bettors | Significantly slower bankroll growth; very forgiving during bad runs |
| Half Kelly Recommended | 50% of full Kelly | Low–moderate | Most systematic bettors with validated models | ~75% of full Kelly growth with ~50% of the variance. Best risk/reward ratio. |
| Three-quarter Kelly | 75% of full Kelly | Moderate | Experienced bettors with high model confidence | Higher growth potential but requires accurate probability estimates |
| Full Kelly Aggressive | 100% of Kelly formula | High | Only with perfectly calibrated models over large samples | Theoretically optimal growth but brutal variance; one bad estimate risks significant bankroll damage |
FAQ
Frequently asked questions
What does a negative Kelly result mean?
A negative Kelly result means the bet has negative expected value at the odds offered given your probability estimate. The formula is telling you to bet zero — or to skip the bet entirely. No fraction of a negative-EV bet is a good bet. Either your probability estimate is too low, or the odds are too short for the edge you see.
How do I estimate win probability accurately?
This is the hardest part of value betting. Common approaches include removing the bookmaker’s margin from their offered odds to get the “true” market probability, using a statistical model (Poisson for soccer, Elo for head-to-head sports), or comparing odds across multiple sharp sportsbooks. Your edge is only as good as the accuracy of your probability estimate.
Can Kelly Criterion be used for parlay bets?
Technically yes, but with difficulty. For a parlay you would multiply the individual probabilities to get the combined win probability, and use the combined decimal odds as your b value. In practice, parlays introduce correlation risk (outcomes are rarely truly independent) which makes the Kelly inputs unreliable. Most professional bettors avoid parlays for this reason.
Does Kelly work for in-play or live betting?
Yes, with the same inputs — current live odds and your estimated win probability at that point in the game. The challenge is that live probability estimates need to update rapidly as the game state changes, and live margins are often wider than pre-match markets. The formula itself works; the difficulty is getting accurate real-time probability estimates fast enough to act on them.
What is the difference between Kelly Criterion and flat staking?
Flat staking means betting the same unit amount (or percentage) on every bet regardless of edge or odds. Kelly scales your stake to the size of your estimated edge — bigger stakes on higher-confidence bets, smaller stakes on marginal edges. Kelly mathematically outperforms flat staking over large samples when your probability estimates are accurate. Flat staking is simpler and performs well enough for recreational bettors who are not trying to size bets by edge.
Want a system that finds the edges for you?
Kelly sizing only works when you have accurate win probabilities to start with. ZCode System uses AI and historical data across NFL, NBA, MLB, NHL, and soccer to generate probability estimates — the inputs Kelly needs.
Affiliate disclosure: we earn a commission if you sign up via this link, at no extra cost to you. We recommend ZCode because it provides probability-based analysis, not just picks.
Responsible gambling notice. The Kelly Criterion is a mathematical tool, not a guarantee of profit. Sports betting involves variance — even correctly sized positive-EV bets lose. Never bet money you cannot afford to lose. If gambling is causing harm: NCPG | BeGambleAware | Gambling Therapy