Quick answer: the Kelly criterion tells you what share of your bankroll to stake when you have an edge: stake = (p × d − 1) ÷ (d − 1), where d is the decimal odds and p your chance of winning. At odds of 2.20 with a 50% chance, full Kelly is 8.33% of your bankroll. Most bettors stake half or a quarter of that, because the formula is only as good as your estimate of p.
The stake is a share of your current bankroll, so work it out again before every bet. The answer is only as good as your win chance: if you overestimate it, Kelly tells you to bet too much. With no edge, the right stake is zero.
How to use the Kelly criterion calculator
- Enter your bankroll, the money you have set aside for betting, not your savings.
- Pick the odds format and enter the odds. Decimal (2.20), fractional (6/5) and American (+120 or −150) all work. Our odds calculator converts between them.
- Enter your chance of winning as a percentage. This is your own estimate, not the bookmaker’s. The “break-even” figure shows the chance the odds imply: you need to beat it to have an edge.
- Choose a Kelly fraction. Half Kelly is the default because it gives up little growth for much smaller swings (see the table below).
- Work it out again before every bet, using your bankroll at that moment. Kelly stakes go down after losses and up after wins.
What is the Kelly criterion?
It is a rule for sizing bets so that your bankroll grows as fast as possible over many bets, without ever staking it all. John L. Kelly Jr., a researcher at Bell Labs, published it in 1956 in a paper called “A New Interpretation of Information Rate” in the Bell System Technical Journal. The mathematician Edward Thorp then used it to size his bets when counting cards at blackjack, and later in sports betting and investing.
The idea is simple: bet more when your edge is bigger, bet nothing when you have no edge, and always bet a share of what you have now rather than a fixed amount. Because the stake shrinks after losses, full Kelly never bets you down to zero in theory, but it can still give you deep drawdowns along the way.
Kelly criterion formula
d is the decimal odds, b = d − 1 the net odds (your profit per 1 staked), p your chance of winning and q = 1 − p your chance of losing:
| What you want | Formula |
|---|---|
| Full Kelly stake (share of bankroll) | f* = (b × p − q) ÷ b |
| Same thing with decimal odds | f* = (p × d − 1) ÷ (d − 1) |
| Your edge (expected profit per 1 staked) | p × d − 1 |
| Break-even chance at these odds | 1 ÷ d |
| Fractional Kelly stake | k × f* (half Kelly: k = 0.5) |
| What a negative f* means | No edge: don’t bet |
Put simply, full Kelly is your edge divided by the net odds. A 10% edge at odds of 2.20 (net odds 1.2) gives 10% ÷ 1.2 = 8.33%.
Kelly criterion example
You think a tennis player has a 50% chance of winning, and a bookmaker offers 2.20. The odds imply a break-even chance of 1 ÷ 2.20 = 45.45%, so if you are right you have an edge of 0.50 × 2.20 − 1 = 10%.
| Share of bankroll | Stake from £1,000 | |
|---|---|---|
| Full Kelly | 8.33% | £83.33 |
| Half Kelly | 4.17% | £41.67 |
| Quarter Kelly | 2.08% | £20.83 |
If the bet wins at half Kelly, your bankroll rises to £1,050 and the next half Kelly stake on a similar bet is £43.75. If it loses, you have £958.33 and the next stake is £39.93.
Why do most bettors use half Kelly?
Because you get most of the growth with much smaller swings. For small edges, betting a fraction k of the Kelly stake gives roughly k × (2 − k) of the full Kelly growth rate: about 75% at half Kelly and about 44% at quarter Kelly. Our own figures for the example above (odds 2.20, a true 50% chance, £1,000 bankroll) show the same pattern:
| Stake size | Share of bankroll | Growth per bet | Share of full Kelly growth | Typical bankroll after 100 bets |
|---|---|---|---|---|
| Quarter Kelly | 2.08% | 0.18% | 44% | £1,200 |
| Half Kelly | 4.17% | 0.31% | 75% | £1,366 |
| Full Kelly | 8.33% | 0.41% | 100% | £1,514 |
| 1.5 × Kelly | 12.50% | 0.31% | 75% | £1,366 |
| 2 × Kelly | 16.67% | 0.00% | 0% | £1,000 |
| 2.5 × Kelly | 20.83% | −0.52% | below zero | £592 |
“Typical” is the median result: half of players would do better and half worse. Two things stand out. Betting 1.5 times Kelly grows your money no faster than half Kelly, but with far bigger swings. And at twice Kelly the growth rate falls to zero, so you take all the risk for no long-run gain. Overbetting hurts more than underbetting.
What if your win chance is wrong?
This is the real danger. Say the player’s true chance is 50%, but you think it is 55%. Full Kelly then tells you to stake 17.5% instead of 8.33%, more than twice the right amount, and your typical bankroll after 100 such bets falls from £1,000 to about £916. Using half Kelly on the same wrong estimate stakes 8.75%, close to the true Kelly stake, and the typical bankroll grows to about £1,513.
That is why half or quarter Kelly is the usual advice: it protects you from your own overconfidence. A good starting point for p is the bookmaker’s fair probability with the margin removed, which our no vig calculator works out. If you can’t say why your estimate is better than that, you probably don’t have an edge.
Can you use the Kelly criterion at a casino?
Not on normal casino games, because the house edge means you never have an edge. A bet on red in European roulette wins 18 times in 37 and pays even money (decimal odds 2.00): 18/37 × 2 − 1 = −2.70%, so the Kelly stake is zero. The same is true of slots and baccarat, and of roulette betting systems: no way of sizing bets turns a negative edge into a positive one, as our gambler’s fallacy guide explains.
The famous exception is blackjack card counting, where the edge swings in the player’s favour when many high cards are left in the shoe. That is where Thorp first used Kelly sizing in practice, raising bets only when the count was in his favour.
What the coin flip experiment showed
In a 2016 experiment by Victor Haghani and Richard Dewey, 61 people were given $25 and 30 minutes to bet on a coin they were told would land heads 60% of the time, with winnings capped at $250. Kelly says to bet 20% of your money on heads every time (2 × 0.6 − 1). Even with a known edge, 28% of the players went bust and the average payout was just $91, mostly because they bet far too much on single flips.
Limits of the Kelly criterion
- It needs your true chance of winning, which you never know exactly. Errors upwards are the expensive ones.
- It is for one bet at a time. Several bets running at once, or bets that depend on each other, need smaller stakes than the single-bet formula gives.
- Swings are big even when it works. Full Kelly can halve your bankroll on the way to long-run growth, so plan for losing runs.
- Bookmakers limit winners. Accounts that win regularly often get lower maximum stakes, which caps Kelly sizing in practice.
- It assumes you only care about long-run growth. If you need the money for something else, bet less, or not at all.
More betting tools: the arbitrage calculator, matched betting calculator, each way calculator and accumulator calculator.
How we checked this
We built the calculator ourselves and tested it in a browser against every example on this page. The growth rates, median bankrolls and the roulette edge are our own calculations from the standard formulas. Everything else comes from at least two independent sources:
- Kelly formula, no-edge and overestimation risk: Wikipedia and TopEndSports.
- Kelly’s 1956 paper and Bell Labs: Wikipedia (John L. Kelly Jr.) and TopEndSports.
- Thorp using Kelly for blackjack card counting: Thorp’s 1997 paper and Wikipedia (Edward O. Thorp).
- Half Kelly giving about 75% of the growth, and zero growth at twice Kelly: William Ziemba in Wilmott magazine and TopEndSports, plus our own maths.
- The coin flip experiment: Haghani and Dewey (Elm Wealth) and Wikipedia.
Last checked: 9 October 2026. Betting is for adults (18+) only. The Kelly criterion doesn’t create an edge, it only sizes bets when you already have one, and no staking plan can promise a profit. If betting stops being fun, our responsible gambling guide lists ways to set limits, and our gambling budget calculator helps you plan.
Kelly criterion calculator FAQs
What is the Kelly criterion formula?
Full Kelly stake = (b × p − q) ÷ b, where b is the net odds (decimal odds − 1), p your chance of winning and q = 1 − p. With decimal odds d it is (p × d − 1) ÷ (d − 1).
What is half Kelly?
Staking half of the full Kelly amount. For small edges it keeps about 75% of the long-run growth with far smaller swings, and it protects you if you overestimate your chance of winning.
What does a negative Kelly number mean?
That you have no edge at those odds: your chance of winning is below the break-even chance of 1 ÷ odds. The right stake is zero.
Is the Kelly criterion good for sports betting?
It is a sound way to size bets if your probability estimates really are better than the market’s. Most bettors use half or quarter Kelly because their estimates are uncertain.
Does the Kelly criterion work for casino games?
Not for normal casino games. The house edge means you never have an edge, so Kelly always says stake nothing. Blackjack card counting is the well-known exception.
