Kelly Criterion Calculator 2026
Find the bet size that grows a bankroll fastest, then watch what full, half and quarter Kelly actually do to it over hundreds of bets. One calculator: single bet, several bets at once, and a Monte Carlo growth simulator.
Bet inputs
Bookmaker implied probability: 40.00%
Your honest estimate of how often this bet wins. The edge, and everything below it, is only as good as this number.
Recommended stake
+12.50%
$42
Expected compounding growth of the bankroll per bet at each fraction. Notice half and quarter give up only a little growth for far less risk.
Bankroll growth simulator
This is the part most Kelly calculators skip. We replay the SAME random run of bets at full, half and quarter Kelly so you can see, not just be told, why pros bet a fraction of full Kelly. Each path stakes a constant share of the current bankroll and compounds.
Several bets at once (simultaneous Kelly)
Betting two or three games at the same time is not the same as sizing each one alone, because they share one bankroll. This solves the joint Kelly that maximises long-run growth across all of them together.
Add at least two bets with odds and a win probability to size them together.
The math, briefly
Kelly fraction
Odds 2.50 (b = 1.5) at p = 45%: f* = (1.5·0.45 − 0.55) / 1.5 = 8.33%.
Edge
2.50 × 0.45 − 1 = +12.5%. Positive edge is the only reason to bet at all.
Growth rate
Growth peaks exactly at f*. Bet 2× Kelly and expected growth falls back to zero.
Where
- f* = fraction of bankroll to stake
- b = decimal odds minus 1 (net payout)
- p = your win probability
- q = 1 − p (your lose probability)
How it works
Find your edge
Compare your win estimate with the odds. Beat the implied probability and you have a positive edge. No edge, no bet.
Apply Kelly
The formula turns your edge and the odds into the fraction of bankroll that grows it fastest over the long run.
Scale it down
Most bettors run half or quarter Kelly. You keep most of the growth and cut the swings hard.
Stress test it
Run the simulator to see the spread of outcomes and the drawdowns before you risk a cent.
Full vs half vs quarter Kelly
Why fractional Kelly is the default for serious bettors.
| Fraction | Long-run growth | Variance | Drawdown risk |
|---|---|---|---|
| Full Kelly | Maximum (100%) | High | Deep, frequent |
| Half Kelly | About 75% of max | Moderate | Much shallower |
| Quarter Kelly | About 44% of max | Low | Mild |
Kelly Criterion bet sizing, explained
The Kelly Criterion answers one question: given an edge, what fraction of your bankroll should you stake to grow it as fast as possible without going broke? John Kelly Jr. worked it out at Bell Labs in 1956, and bettors and investors have argued about how much of it to actually use ever since. This calculator gives you the number, then lets you pressure test it.
What the Kelly Criterion is
Kelly maximises the expected growth rate of your bankroll, not the expected profit of a single bet. The difference matters. Flat staking ignores your edge; betting your whole roll on the best spot maximises one bet and ruins you on the bad ones. Kelly sits in between: bigger edge means a bigger slice, and the slice shrinks as the price gets worse. Stake exactly f* and your bankroll compounds at the fastest sustainable rate. Stake more and growth falls; stake double and it drops to zero.
Why almost nobody bets full Kelly
Full Kelly is optimal only if your win probability is exactly right, and it almost never is. Overrate your edge by a few points and full Kelly quietly turns into overbetting, which destroys growth and deepens drawdowns. Half Kelly keeps roughly three quarters of the growth for a fraction of the variance, which is why most professional bettors live there. Quarter Kelly trades more growth for an even smoother ride. The simulator on this page shows the trade plainly.
How to use the Kelly calculator on ToolsGambling
Pick your odds format, type the price your book is offering and your honest win probability, and set your bankroll. The recommended stake updates instantly at whatever Kelly fraction you choose. Add a few bets in the simultaneous section to size a slate of games together. Then run the growth simulator to see the median bankroll, the spread and the drawdown risk for full, half and quarter Kelly on the same luck. It is all free on ToolsGambling.com, with no signup.
A worked example
Bankroll $1,000, decimal odds 2.00, and you rate the bet at 55%. The edge is +10%, full Kelly is 10% ($100), half Kelly is $50. Over a few hundred of these, full Kelly grows the median bankroll fastest but also produces the deepest drawdowns, while half Kelly trails only slightly on growth with far gentler swings. Run it yourself above and the numbers fill in.
Common Kelly mistakes
The big one is trusting your probability. Kelly amplifies a bad estimate in both directions. Others: betting full Kelly on correlated games as if they were independent, ignoring the bookmaker margin baked into the price, and chasing a Kelly fraction above 25%, which usually means your estimate is wrong rather than your edge being huge. Treat the output as a ceiling, not a target.
Kelly terms
- Kelly fraction (f*)
- The share of bankroll Kelly says to stake on a +EV bet: f* = (b·p − q) / b.
- Edge
- Your advantage over the price, odds × your probability − 1. Positive means the bet is worth making.
- Fractional Kelly
- Staking a set fraction of full Kelly (half, quarter) to cut variance while keeping most of the growth.
- Bankroll growth rate
- The expected compounding rate of your bankroll per bet. Kelly maximises it; overbetting lowers it.
- Risk of ruin
- The chance a bankroll falls to a level you treat as broke. With proportional Kelly we measure a deep drawdown instead of a true zero.
- Drawdown
- The worst peak-to-trough fall along a run. Full Kelly produces much deeper drawdowns than fractional Kelly.
- Implied probability
- The win chance baked into the odds, 1 divided by decimal odds. Your edge is the gap between this and your own estimate.
Free betting tools on ToolsGambling.com
On ToolsGambling.com you can use the Kelly calculator for free, just like all our other tools. Pair it with these to find the edge first and size it second.
Value Bet Calculator Risk of Ruin Calculator Bankroll Calculator Odds Converter Implied Probability Calculator
Bet responsibly
Kelly sizes a bankroll you can afford to lose, not your rent. Set limits, never chase losses, and if betting stops being fun, get free, confidential help at BeGambleAware.org.
Kelly Criterion FAQ
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Evgeniy Volkov
Fullstack developer with a background in mathematics. I build the calculators and game-style tools on ToolsGambling with Pixi.js and modern web tech, and every result uses transparent probability formulas you can verify yourself.