Kelly criterion in sports betting: formula, example and why to use fractional Kelly
The Kelly criterion tells you what share of your bankroll to stake based on your edge: f = (b × p − q) / b, where b is the decimal odds minus 1, p is your estimated probability and q = 1 − p. At odds of 2.20 with a 50% chance, Kelly says stake 8.33% of your bankroll. In practice almost nobody bets full Kelly: people use half or quarter Kelly, because their probabilities are never exact.
What problem Kelly solves
Finding a value bet is only half the job. The other half is deciding how much to put on it. Stake too little and you waste your edge; stake too much and a bad run wipes you out even though your bets had value. Kelly looks for the stake that grows your bankroll fastest over the long run without ever taking it to zero.
The key idea: the bigger your edge, the more you stake; no edge, no bet. If the formula comes out negative, the bet has no value and Kelly says zero.
The Kelly formula, step by step
- Work out b: decimal odds − 1. At 2.20, b = 1.20.
- Estimate p: your true probability, say 0.50.
- Work out q: 1 − p = 0.50.
- Apply the formula: (1.20 × 0.50 − 0.50) / 1.20 = 0.10 / 1.20 = 0.0833.
- Turn it into cash: with a £1,000 bankroll, full Kelly suggests a £83 stake.
A handy shortcut: the top line (b × p − q) is exactly your expected value. So Kelly = expected value / (odds − 1). If you're not yet sure how to get that expected value, start with how to calculate a value bet.
| Probability | Odds | Expected value | Full Kelly | Half Kelly | Quarter Kelly |
|---|---|---|---|---|---|
| 50% | 2.20 | +10% | 8.33% | 4.17% | 2.08% |
| 55% | 2.00 | +10% | 10.00% | 5.00% | 2.50% |
| 30% | 3.80 | +14% | 5.00% | 2.50% | 1.25% |
| 60% | 1.75 | +5% | 6.67% | 3.33% | 1.67% |
Notice that for the same expected value, Kelly stakes less at bigger odds: the chance of losing is higher.
Why full Kelly is dangerous
Kelly gives the optimal stake if your probability is right. It never quite is. If you rate something at 50% and it's really 45%, at 2.20 your true expected value is 0.45 × 2.20 − 1 = −1%. Full Kelly would have had you staking 8.33% of your bankroll on a losing bet.
Full Kelly also produces brutal drawdowns. Seeing your bankroll halved at some point is normal, and very few people can sit through that without abandoning the plan halfway. And if you consistently overrate your edge and stake twice what you should, expected growth drops to zero.
Fractional Kelly: the version people actually use
The fix is to bet a fixed fraction of the Kelly stake. Half Kelly keeps roughly 75% of the long-run growth with about half the volatility. Quarter Kelly grows more slowly, but drawdowns are far easier to live with and estimation errors hurt less.
- Set a cap per bet (say 3–5% of bankroll) even if the formula asks for more.
- If you have several bets running at once, scale stakes down: Kelly assumes bets placed one after another.
- Don't use Kelly until you have a big enough sample backing your probabilities. We cover how big in minimum sample size to evaluate a tipster.
Kelly or level units: which to choose
If you're starting out or don't produce your own probabilities, flat units are simpler and safer; see bankroll management with the units method. Kelly makes sense when you can put a specific probability on each bet and you've already checked with data that your estimates hold up. Even then, be ready for long losing streaks.
If you follow a tipster, look at how they size their stakes. In the Tippium tipsters list you can see the full record and check whether their big-stake picks actually do better than the small ones; if they don't, flattening the stakes is usually the safer move. Many users bet those picks at Stake, a crypto sportsbook with broad markets.
Why the Stake link won't open or shows an error
If you're in a restricted country such as Spain, France, the UK or the US and you tap the Stake link, the site will usually fail to load, stay blank or show a "not available in your country" message. The link isn't broken and neither is your phone: Stake geo-blocks the countries it doesn't accept, based on the IP address you connect from.
How many people connect with Mullvad, step by step
The route many users take is a VPN, an app that makes your connection appear to come from another country. The most common example is Mullvad. Here's how it works, in plain terms:
- Create a Mullvad account. Go to mullvad.net, click to generate an account number and write it down: there's no email or name, that number is your username and password in one.
- Pay for the time you want. It costs about €5 a month and you can pay by card, PayPal or crypto.
- Install the app. Download it for Windows, Mac, Android or iPhone and log in with your account number.
- Pick a server in a country Stake accepts. In Mullvad's location list, choose a country with servers that isn't on Stake's prohibited jurisdictions list, for example Switzerland, Romania, Slovenia or New Zealand. Check that list in the terms first, because it changes.
- Hit "Connect". Wait until the app shows the connection as secure (it turns green).
- Open the Stake link. With the VPN on, use this link to Stake: the site should load normally so you can sign up and deposit.
- Keep the VPN on every time you log in. If you switch it off or change country mid-session, the site will block you again or ask for extra checks.
What Stake's terms say: read this before you deposit
The site loading doesn't mean it's allowed. Clause 14.4 of Stake's terms forbids using a VPN, proxy or false residence details to get around geo-blocking, and under clauses 5.2 and 4.21 Stake can close the account, void bets and withhold the balance, winnings included. On top of that, identity verification (KYC) can ask for an ID and proof of your real address, so the country you live in eventually shows up. If you choose this route, it's at your own risk: only deposit what you're prepared to lose, withdraw often and always check the current terms, because they change.
If you live in a country where Stake is available, you don't need any of this: open Stake here and sign up directly. If you're in a restricted country and don't want that risk, the alternative is a locally licensed bookmaker.
Gamble responsibly: only stake money you can afford to lose and, if betting stops being fun, reach out to a support service in your country.
Kelly criterion FAQs
What if Kelly comes out negative?
Don't bet. A negative figure means that, on your numbers, the bet has no value.
Does Kelly work for accumulators?
You can run it with the combined odds and probability, but the stacked margin and uncertainty make the suggested stake very unreliable.
Half Kelly or quarter Kelly?
If your probabilities come from a model tested over thousands of bets, half Kelly. If you have any doubt, quarter Kelly or less.
18+ only. No staking plan guarantees a profit: please gamble responsibly.