The Kelly Criterion: How Much to Bet When You Have an Edge
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Key takeaways
- Kelly stake = (b × p − q) ÷ b, where b is decimal odds − 1, p your win probability, and q = 1 − p.
- Full Kelly maximizes long-run growth in theory but produces brutal drawdowns, and assumes your probabilities are exact.
- Half Kelly keeps about 75% of the growth with far smaller swings. Quarter Kelly is a common default for market-based edges.
- Betting more than double Kelly is expected to shrink your bankroll over time, even with a real edge.
Finding a +EV bet is half the problem. The other half is deciding how much to put on it. Bet too little and your edge grows your bankroll slowly. Bet too much and a normal losing streak can wipe you out, even when every bet is good.
The Kelly criterion is the standard answer to that problem. It was published in 1956 by John L. Kelly Jr., a researcher at Bell Labs, and was popularized in gambling and investing by the mathematician Edward Thorp. Bill Benter used it to size bets in his Hong Kong horse racing operation, as we describe in his profile.
The formula
An equivalent form that’s easy to remember: Kelly = edge ÷ (decimal odds − 1), where edge = p × decimal odds − 1.
If the result is zero or negative, you have no edge and Kelly says not to bet.
Worked example
Bankroll $5,000. You can bet +110 (decimal 2.10, so b = 1.10). A devigged sharp line says the true probability is 50%.
| Fraction | Share of bankroll | Stake |
|---|---|---|
| Full Kelly | 4.55% | $227.27 |
| Half Kelly | 2.27% | $113.64 |
| Quarter Kelly | 1.14% | $56.82 |
| Eighth Kelly | 0.57% | $28.41 |
Run the numbers: How much of my bankroll should this edge get? Open the Kelly Criterion Calculator
Why Kelly works
Kelly maximizes the long-run growth rate of your bankroll. It does this by betting in proportion to your edge and shrinking bets automatically after losses, since each bet is a share of a smaller bankroll. It also never stakes your whole bankroll on a bet that can lose, so it can’t bust you outright.
The logic runs in both directions. Bet too little and you grow slower than you could. Bet too much and growth slows too, then turns negative:
| Bet size | Long-run growth (vs full Kelly) |
|---|---|
| Quarter Kelly | about 44% |
| Half Kelly | about 75% |
| Full Kelly | 100% |
| 1.5× Kelly | about 75% |
| 2× Kelly | about zero |
| More than 2× Kelly | negative: expected to shrink |
These figures are a close approximation for small edges. They show why overbetting is so costly: at twice Kelly, a genuinely +EV bettor makes no progress on average, and beyond that they lose money despite having an edge.
Why professionals bet a fraction of Kelly
Your probabilities aren’t exact
Kelly assumes you know p. You don’t. You have an estimate from a devigged line or a model. If your true edge is half what you think, full Kelly is really 2× Kelly, which is roughly zero growth. Betting a fraction builds in a margin for error.
Drawdowns are severe
Even when your probabilities are right, full Kelly swings hard. A classic approximation: under full Kelly, the chance your bankroll ever falls to half its starting value is about 50%. Under half Kelly it’s about 12.5%. Under quarter Kelly it’s under 1%.
Bets aren’t independent
On a busy Sunday you may have ten bets open at once, some correlated (a side and a total in the same game). Kelly for each bet in isolation overstates what you should have at risk in total.
For edges derived from sharp market prices, quarter Kelly is a common default. Bettors with long, verified track records sometimes move toward half Kelly.
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- Define your bankroll as money you can afford to lose entirely and that is set aside only for betting.
- Use conservative probabilities. A worst-case devig (see how to devig odds) feeds Kelly a smaller edge.
- Cap single bets, for example at 2% to 3% of bankroll, regardless of what Kelly says.
- Scale down when bets overlap. If several bets are open at once, reduce each one.
- Update your bankroll figure regularly, especially after drawdowns.
When not to use Kelly
Kelly is for bets with outcome risk. It doesn’t apply to:
- Arbitrage, where every outcome wins. Stake size is limited by book limits and capital, not risk.
- Hedged promos, where the value is locked in.
- Bets with no real edge. Kelly returns zero, which is the right answer.
For those, see our guides to arbitrage and bonus bet conversion. For the unhedged +EV bets where Kelly does apply, how big a bankroll you need covers the practical side.
Frequently asked questions
Does Kelly work for parlays?
Yes, if you can estimate the parlay’s true probability. Use the parlay’s combined odds and the product of each leg’s fair probability (adjusted for correlation if the legs are related). Parlay edges are harder to estimate, so use a small fraction.
Should I recalculate my bankroll after every bet?
Kelly assumes you do. In practice, many bettors update their bankroll figure weekly or monthly. Just don’t keep sizing bets off a peak bankroll after a large drawdown.
What if Kelly says to bet more than a book allows?
Bet the maximum the book takes. Limits cap the stake below Kelly all the time, especially on props. Don’t spread one bet across multiple accounts you don’t own.
Get +EV bets flagged against sharp prices
ProfitDuel's EV Matcher and Odds Screener compare US sportsbook prices with the sharpest books in the world and surface bets that beat the fair line.
Start the $1 ProfitDuel trialAffiliate link. The $1, 3-day trial applies to ProfitDuel's Starter plan as listed in September 2026. 21+ and in states where online sports betting is legal.