Guide · 7 min read
Kelly Criterion
Optimal stake sizing for value betting
By Lytic · Updated May 2026
What is Kelly Criterion?
Kelly Criterion is a mathematical formula that calculates the optimal fraction of your bankroll to stake on a given bet in order to maximise long-term geometric growth. The formula was published in 1956 by John L. Kelly Jr., a Bell Labs engineer who used information theory to solve the problem of optimal stake sizing under uncertainty.
The Kelly criterion is used today by professional value bettors, quantitative trading funds and hedge funds worldwide. Warren Buffett's investment partner Charlie Munger is a well-known proponent. What all these actors share is the insight that having an edge is not enough — you must also stake the right size in order to realise that edge long term.
The intuition behind Kelly is simple: stake too little and you leave value on the table — growth is unnecessarily slow. Stake too much and variance increases exponentially and the risk of bankroll ruin becomes real, even with positive edge. Kelly finds exactly the point where expected logarithmic growth is maximised — the mathematically optimal answer.
The Kelly formula step by step
The Kelly formula is expressed as a fraction of your total bankroll:
Worked example: You find a bet with decimal odds 2.10. Your estimated true probability for the outcome is 55%.
p = 0.55 q = 0.45
f = (1.10 × 0.55 − 0.45) / 1.10
f = (0.605 − 0.45) / 1.10
f = 0.155 / 1.10 = +5% of bankrollWith a $1,000 bankroll Kelly recommends a stake of $50.
Note that the stake is proportional to your perceived edge: a bet at odds 2.10 with 55% probability gives a 5% stake, while a bet with the same odds but only 52% probability gives a significantly lower Kelly stake. The formula is sensitive to the precision of the probability estimate — that is one of the reasons partial Kelly sizing is used in practice.
Full vs quarter-Kelly
The Kelly formula in its basic form gives full Kelly — the theoretically optimal stake. In practice almost all professional bettors use a fraction of full Kelly. Here is why, and how the three most common alternatives compare:
| Variant | Growth rate | Variance | In practice |
|---|---|---|---|
| Full Kelly (100%) | Fastest possible | Extreme — 50% drawdown common | Theoretical, not recommended |
| Half Kelly (50%) | Square root of full Kelly | Much more stable | Common compromise |
| Quarter-Kelly (25%) | Close to full long-term return | Low, professional standard | Lytic default |
Half Kelly generates approximately the square root of full Kelly's geometric growth rate — you sacrifice some top-end speed but halve the variance. Quarter-Kelly reduces variance further and still preserves 75–80% of full Kelly's long-term value on a sufficiently large sample.
Kelly and EV — the relationship
The Kelly stake is directly proportional to the expected value (EV) of a bet. This is not a coincidence — the formula is mathematically constructed so that bets with higher EV automatically receive a larger recommended stake. This makes Kelly a natural tool for prioritising where you put your capital.
Concrete example: EV +5% at odds 2.00 implies a true probability of 52.5% (not 50%, as the odds implicitly suggest).
f = (1.00 × 0.525 − 0.475) / 1.00
f = 0.525 − 0.475 = 5% of bankrollEV +5% at even money → Kelly 5%. The relationship is linear at odds 2.00.
The most important relationship: if Kelly is negative, EV is negative, and Kelly explicitly tells you not to bet. The formula automatically screens out bets without value — you never need to manually check whether a bet is worth placing.
Practical limitations
Kelly Criterion is a powerful tool, but three practical factors limit how mechanically you can follow it:
1. Maximum stake limits at bookmakers
Soft bookmakers regularly restrict successful bettors and set low maximum stake limits — sometimes $10–$50 per match. Even if Kelly recommends 5% of your bankroll it may be practically impossible to place that stake. The bettor is forced to accept a lower stake, which in practice resembles an even smaller Kelly fraction.
2. Uncertainty in probability estimation
The Kelly formula is only as good as your probability estimate. No model is perfect — sharp bettors expect to be ±3–5% off true probability on individual bets. Full Kelly on a miscalculated probability gives a heavily oversized stake. Partial Kelly sizing is the structural buffer against this uncertainty.
3. Never more than 3–5% of bankroll
As a rule of thumb no single stake should exceed 3–5% of your total bankroll, regardless of what Kelly recommends. Extremely high Kelly stakes signal either an unusually large edge (verify your numbers) or an error in the probability estimate. A hard upper cap protects you against the worst scenario when the model is wrong.
Important reminder: Kelly assumes that your probability estimate is calibrated and independent bet by bet. If you are betting on correlated outcomes — for example multiple bets on the same team in the same round — the Kelly stake should be adjusted downward further to account for the shared risk.
Frequently asked questions about Kelly Criterion
What happens if I overestimate my probability?
The Kelly formula punishes you hard if your probability estimate is too high — it recommends a larger stake than is justified. If you systematically overestimate by 5% full Kelly can lead to ruin long term. Quarter-Kelly acts as a buffer against this uncertainty: a miscalculation that would have wiped out a full-Kelly system is managed without catastrophic consequences. That is the main reason professional bettors almost always use scaled-down Kelly stakes.
Should I calculate Kelly on my total bankroll or per bookmaker?
Always on your total bankroll, not per bookmaker. If you split the bankroll per book and then find the same match at several bookmakers you risk heavily over-betting — you calculate the Kelly stake multiple times on the same event. Your total exposure to one outcome should never exceed what Kelly recommends based on the full capital.
Can the Kelly stake be 0 or negative?
Yes — and that is one of the most important signals Kelly gives you. Zero Kelly means break-even: the odds exactly cover your estimated probability but there is no expected value to extract. Negative Kelly means the odds are worse than your estimated probability — in other words negative EV. Kelly explicitly tells you not to bet. Listen to that signal.
How does Lytic handle Kelly calculations?
Lytic fetches the no-vig probability from Pinnacle for each market and uses it as the estimate of true probability. Kelly stake is calculated per bet and quarter-Kelly (25%) is applied by default — adjustable in settings. You see the recommended stake directly in your currency based on your current bankroll, without doing any manual calculations.
Why do professionals recommend quarter-Kelly?
Uncertainty in probability estimation. Even sharp models can be off ±3–5% on true probability. At full Kelly that margin of error is sufficient to create dangerous drawdowns or in the worst case ruin. Quarter-Kelly preserves most of the long-term growth potential — approximately 75–80% of full Kelly's geometric growth rate — with a fraction of the variance. That is the professional standard for exactly that reason.
Calculate Kelly stake automatically
Lytic calculates the optimal Kelly stake for every bet based on Pinnacle's no-vig odds — so you always know exactly how much to stake.
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