Kelly Criterion in Betting: Formula, Examples and Fractions

The Kelly criterion is a staking formula: it tells you what share of your bankroll to bet so that the bankroll grows as fast as possible in the long run, given your edge and the odds. In decimal odds, Kelly stake = (p × odds − 1) ÷ (odds − 1), where p is the true probability of winning; if the result is zero or negative, you do not bet.

The formula is only as good as p. In practice that means two things: you need a reliable fair price to estimate p, and you should stake a fraction of what the formula says, because your estimate of p is never exact.

Definition. The Kelly criterion (John L. Kelly Jr., 1956) is the bet size, as a fraction of the current bankroll, that maximises the expected logarithm of wealth, which is the long-run growth rate of the bankroll. Fractional Kelly means staking a fixed fraction of that amount, for example a quarter (¼ Kelly) or a half (½ Kelly).

What is the Kelly criterion formula?

Three equivalent ways to write it, all for a single bet with decimal odds:

The third form is the one value bettors use. If you already know the expected value of a bet, divide it by the net odds. A +5% bet at 2.00 gives 5% ÷ 1.00 = 5% of the bankroll; the same +5% at 4.00 gives 5% ÷ 3.00 = 1.67%. Longer odds mean a smaller Kelly stake for the same edge, because the bet loses more often.

Two consequences follow straight from the formula:

• No edge, no bet. If p × odds ≤ 1 (EV of zero or less), Kelly says stake nothing.
• The stake scales with the bankroll. Kelly is a percentage of what you have now, so stakes shrink after losses and grow after wins.

How do you calculate a Kelly stake? A worked example

A real move from Pinnacle Terminal, 28 October 2026, about 09:37 Madrid time (CET): ITF Women Poitiers, Leonard v Hesse, games handicap Leonard −3.5. Pinnacle's price fell from 1.826 to 1.543 and the limit went up as it fell; the terminal labelled the move Limit-backed. The fair price on that line, with the margin removed by the Power method, was 1.631.

Suppose a slower bookmaker still offered 1.75 on the same line (an illustrative price, not a recorded one).

1. True probability. p = 1 ÷ 1.631 = 61.3%.
2. Expected value. EV = 1.75 ÷ 1.631 − 1 = +7.3%.
3. Full Kelly. f = 7.3% ÷ (1.75 − 1) = 9.7% of the bankroll. Check with the classic form: (0.613 × 1.75 − 1) ÷ 0.75 = 0.097.
4. Fractional Kelly. ½ Kelly = 4.9%; ¼ Kelly = 2.4%. On a €1,000 bankroll, ¼ Kelly is about €24.

Nearly 10% of the bankroll on one tennis handicap is a lot, and that is the point of the example: full Kelly gets large quickly when the edge looks big. The Kelly calculator does steps 2 to 4 from the bankroll, your odds, the fair odds and the fraction you choose. For step 1, the devig calculator turns Pinnacle's two or three prices into a fair price.

Where does the probability come from?

Kelly does not find bets; it sizes them. The input p has to come from somewhere, and for most value bettors it comes from the sharp market:

• Pinnacle's no-vig price. Remove Pinnacle's margin from all outcomes of a market and invert the fair price: 1 ÷ 1.631 = 61.3%. Why Pinnacle is the usual reference is covered in Pinnacle as a sharp reference price.
• Your own model. A rating or Poisson model gives p directly. Models are usually less accurate than a sharp closing price, so they deserve a smaller fraction.
• The devig method matters. Different methods give different fair prices, especially on long odds, and Kelly magnifies the difference. Power is a reasonable default for favourite–longshot markets; see devig methods.

The quality of p is also why the move itself matters. A price that has just dropped with a rising limit is a different input from a price that drifted on a thin market, even if the fair number on screen is the same.

Why do most bettors use fractional Kelly?

Because full Kelly assumes p is exact, and it is not. Three reasons, with numbers.

1. Overbetting hurts more than underbetting. Growth per bet is a hill: it peaks at full Kelly and falls on both sides, but it falls to zero at about twice Kelly. For a +3% bet at 2.00 (full Kelly = 3% of bankroll), our calculation of the expected log growth gives:

Half Kelly keeps three quarters of the growth rate at half the stake size. Doubling the stake gives up all of it.

2. Errors in p push you past Kelly without you noticing. In the tennis example, if the true fair price were 1.70 rather than 1.631, the real edge would be +2.9% and the real Kelly stake 3.9%. Staking the 9.7% you calculated would be about 2.5 × the true Kelly, which our calculation puts at negative expected growth. A quarter of your estimate (2.4%) would still be below the true Kelly.

3. Drawdowns at full Kelly are deep. We simulated 20,000 runs of 1,000 bets, each with a true +3% edge at 2.00 (seed fixed, 31 October 2026):

Published research points the same way. Uhrín, Šourek, Hubáček and Železný (Czech Technical University, 2021) tested staking rules on 16,000 NBA games priced at Pinnacle's closing line and 32,000 football matches priced at Pinnacle's opening line, using models that were slightly less accurate than Pinnacle. Plain full Kelly ended in ruin (the bankroll falling below 0.01% of the start) in 100% of their 1,000 simulated runs in both sports; fractional Kelly, with the fraction tuned on training data, had 0% ruin. Their abstract concludes that "an adaptive variant of the popular 'fractional Kelly' method is a very suitable choice across a wide range of settings".

Our runs above assume the edge is real and exact. With the same 1,000 bets and no edge, full Kelly sizing on an imagined +3% left 68% of runs below the start, against 54% at ¼ Kelly. A smaller fraction does not create an edge; it limits the damage when you are wrong about having one. Our variance simulator runs this kind of test on your own numbers.

When does Kelly not apply as written?

• Several bets at the same time. Kelly assumes one bet, settled before the next. With ten open bets, ten separate Kelly stakes can add up to a large share of the bankroll. Cap the total exposure, or scale each stake down.
• Correlated bets. Two bets on the same match (a handicap and a total, for example) are not independent. Treat them as one position.
• Limits. The formula may ask for more than a bookmaker accepts. The limit wins; do not spread the rest across worse prices to reach the number.
• Exchange commission. On an exchange, use the odds after commission in the formula, not the displayed odds; see sharp bookmakers list for how commission changes the effective price.
• Very small edges at long odds. The stake is tiny and the variance huge. Many bettors set a minimum EV or a maximum price before Kelly is even considered.

Kelly vs flat staking

Flat staking means betting the same amount (or the same percentage) on every bet. It ignores the size of the edge, so a +1% bet gets the same stake as a +8% bet. Kelly gives more to better bets and less to long shots. A common middle ground is capped fractional Kelly: ¼ Kelly with a maximum of 2-3% of the bankroll per bet. Whatever you choose, write it down before you bet; see betting discipline and positive EV betting.

How Pinnacle Terminal handles this

Pinnacle Terminal supplies the two numbers Kelly needs from the sharp side: Pinnacle's current price and its fair price (Power devig by default, with other methods available), updated as the line moves. It grades every pre-match move 0–10 and labels it, so you can see whether the price behind your p is a Limit-backed drop (Pinnacle raised the limit as the odds fell), a Big move (the odds dropped and Pinnacle closed the market), a Sharp drop (about 20% or more below the recent high), a Downtrend, a Rebound towards the opener or a Standard move. Live in-play football drops are shown and filtered, not graded. Telegram alerts follow the rules each user sets. The terminal does not size stakes or place bets: you take the fair price to the Kelly calculator or your own sheet. See Pinnacle dropping odds.

FAQ

What is the Kelly criterion in simple terms?

A formula that says what share of your bankroll to stake on a bet with an edge: bet more when the edge is bigger and the odds shorter, nothing when there is no edge. In decimal odds: (p × odds − 1) ÷ (odds − 1).

What fraction of Kelly should I use?

Most bettors use between a quarter and a half. Half Kelly keeps about 75% of full Kelly's growth rate with much smaller drawdowns; a quarter is safer when your probabilities come from a model or a thin market.

Is the Kelly criterion good for sports betting?

It is a sound sizing rule when you have a reliable estimate of the true probability, such as a sharp no-vig price. It is dangerous when that estimate is too high, because overbetting reduces long-run growth and deepens drawdowns. That is why fractional Kelly is the norm.

What happens if I bet more than Kelly?

Long-run growth falls, and at about twice the Kelly stake it drops to zero; beyond that the bankroll is expected to shrink even though each bet has a positive edge.

Can the Kelly stake be negative?

The formula can return a negative number, which means the bet has negative expected value. Kelly's answer is to stake nothing.

Try it

Get Pinnacle's live price and fair odds on every line, with each pre-match move graded 0–10 and Telegram alerts on your own rules: start the Pinnacle Terminal 7-day free trial. Nothing is charged before day 8.

Sources

• J. L. Kelly Jr., "A New Interpretation of Information Rate", Bell System Technical Journal 35(4), 1956, pp. 917–926.
• M. Uhrín, G. Šourek, O. Hubáček and F. Železný, "Optimal sports betting strategies in practice: an experimental review", Czech Technical University in Prague, arXiv:2107.08827, 2021 (read 31 October 2026).
• Leonard v Hesse prices: Pinnacle Terminal capture, 28 October 2026. Growth and drawdown figures: our own calculation and simulation, 31 October 2026 (20,000 runs × 1,000 bets).

18+ · Bet responsibly. Kelly sizes a bet you have already judged to have an edge; it does not make a bet more likely to win.