What the Kelly criterion is
The Kelly criterion is a staking formula. It says how much of your bankroll to put on a bet, as a share that grows with your edge: the gap between the chance you believe a bet has and the chance its odds imply. No edge, no stake. A bigger edge, a bigger stake.
It comes from a 1956 paper by John L. Kelly Jr., an engineer at Bell Labs, and it answers one precise question: if your estimate of the probability is right, which stake makes a bankroll grow fastest over many bets without ever betting it all? Stake less than Kelly and the bankroll grows more slowly. Stake more and the swings grow faster than the gains; at roughly twice the Kelly stake, the long-run growth is gone.
Everything rests on that first condition, “if your estimate is right”. The calculator above does the arithmetic. Whether your probability is better than the bookmaker’s is the hard part, and the sections below come back to it.
How to use the calculator
- Enter the odds in the format you know: decimal (2.10), fractional (11/10) or American (+110). Switching format converts what you typed.
- Enter your chance of winning, in percent. It is your own estimate, not the one the odds imply; the calculator shows the implied one right below so you can compare.
- Enter your bankroll: the money set aside for betting, nothing more.
- Pick a strategy: full, half or quarter Kelly. The main figure follows your choice, and the row underneath shows all three.
Two lines keep the result honest. If your estimate does not beat the implied chance, the stake is zero and the calculator says so. And when there is an edge, it shows what full Kelly would stake if your real chance were five points lower, which is often enough to turn a good-looking bet into a losing one.
The formula, with an example
With decimal odds, write b for the odds minus 1, p for your chance of winning and q for 1 − p:
Full Kelly stake = (b × p − q) ÷ b, as a share of the bankroll
Your edge is the expected value of each dollar staked, and the break-even chance is the implied one:
Edge = p × odds − 1 · Break-even chance = 1 ÷ odds
Take odds of 2.10 and a chance you estimate at 50%. The odds imply 47.6%, so your edge is 0.50 × 2.10 − 1 = +5%. With b = 1.10, full Kelly is (1.10 × 0.50 − 0.50) ÷ 1.10 = 0.0455, or 4.55% of the bankroll. Half Kelly is 2.27% and quarter Kelly 1.14%. On a $1,000 bankroll, that is $45.45, $22.73 or $11.36.
Now lower the estimate to 45%. The edge becomes 0.45 × 2.10 − 1 = −5.5%, and Kelly stakes nothing. Five points of optimism are the whole difference between a bet the formula backs and one it rejects.
Kelly stakes at a glance
| Odds | Your chance | Implied | Edge | Full Kelly | Half Kelly |
|---|---|---|---|---|---|
| 1.50 | 70% | 66.7% | +5.0% | 10.0% | 5.0% |
| 1.90 | 55% | 52.6% | +4.5% | 5.0% | 2.5% |
| 1.90 | 50% | 52.6% | −5.0% | 0 | 0 |
| 2.10 | 50% | 47.6% | +5.0% | 4.55% | 2.27% |
| 3.00 | 40% | 33.3% | +20.0% | 10.0% | 5.0% |
| 3.00 | 30% | 33.3% | −10.0% | 0 | 0 |
| 5.00 | 24% | 20.0% | +20.0% | 5.0% | 2.5% |
Two things stand out:
- The same edge gives very different stakes. A +5% edge at 1.50 calls for 10% of the bankroll; at 2.10, for 4.55%. Kelly stakes more on short odds because they win more often and swing the bankroll less.
- A 50% chance at 1.90 is a losing bet. It is the classic coin flip with the margin built in, and Kelly answers it with zero.
Why half or quarter Kelly
Full Kelly is the fastest-growing stake in theory and a rough ride in practice. Losing runs are normal, and at full Kelly a few of them in a row can cut a bankroll in half. Our variance simulator shows how far luck alone swings results, even when the edge is real.
The bigger problem is the estimate itself. Overestimate your chance and Kelly makes you overbet, exactly when the bet is worse than you think. Staking a fraction protects against both:
- Half Kelly keeps roughly three quarters of the growth of full Kelly with half the swings, and it forgives a fair amount of optimism in your estimates.
- Quarter Kelly goes further: smaller stakes, much calmer results, still sized by your edge.
That is why most people who use Kelly at all use a fraction of it.
The catch: Kelly needs a real edge
Kelly only ever stakes on bets where your chance beats the one the odds imply. Bookmakers build a margin into every price, so for a typical bet the implied chances of all outcomes add up to more than 100%. Unless you genuinely know better than the market, your real edge is negative and the honest Kelly stake is zero. Our guide to implied probability shows where that margin hides.
Most bettors cannot measure their edge, and the formula cannot do it for them: it takes whatever probability you type and treats it as true. A confident guess goes in, a precise-looking stake comes out. Use the calculator to see what your estimates imply, not as proof that they are right.
Kelly or flat stakes?
Flat staking puts the same unit on every bet, often 1 to 2% of the bankroll. It ignores your edge, which is its strength when you cannot measure one: your stakes never grow because of an overconfident estimate. Kelly varies the stake bet by bet and recalculates it from the current bankroll, so stakes shrink after losses and grow after wins.
If you are not sure you have an edge, flat stakes are the simpler and safer frame. Either way, the stake comes out of a budget you set beforehand. Our guide to bankroll management covers units, limits and why the bankroll should be money you can afford to lose.
Check your estimates against your results
The only way to find out whether your probabilities beat the odds is to track what actually happens. Group your bets by odds range and compare your win rate with the chance those odds imply: if you win 50% of bets priced around 1.90, you are below the 52.6% needed to break even, whatever you estimated at the time.
Over a few dozen bets, luck dominates; it takes hundreds before a win rate says much. Our guide to ROI and yield explains how to read those numbers, and BetTrack keeps them for you: net result, total staked and win rate by period, with ROI, average odds, drawdown and streaks in BetTrack Pro.
Frequently asked questions
Is half Kelly better than full Kelly?
For most people, yes. Half Kelly keeps roughly three quarters of the theoretical growth with half the swings, and it limits the damage when your probability estimate is too optimistic, which is the usual case.
What does it mean when the calculator says zero?
Your estimated chance is at or below the chance the odds imply, so the bet has no edge by your own numbers. The Kelly criterion then stakes nothing, whatever the strategy.
Can I use Kelly on a parlay?
In principle, with the combined odds and the combined chance, which is the product of the chances of each leg. In practice the margin compounds with every leg and small errors in each estimate multiply, so the edge Kelly needs is even harder to have.
Should I recalculate the stake after every bet?
Kelly is a share of your current bankroll, so the stake follows the bankroll: smaller after losses, bigger after wins. Many people instead fix a bankroll for the month and size stakes from it, which keeps betting inside a budget.
How do I know my real chance of winning?
You cannot know it in advance. What you can do is track your bets and compare your win rate at given odds with the chance those odds imply, over hundreds of bets. That record shows whether your estimates have been better than the market.
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