The Kelly criterion calculator works out the optimal share of your bankroll to stake based on the odds and your own estimate of the outcome probability. Enter the data — the calculator will show what percentage of your bank to stake and will compare the full, half and quarter Kelly strategies.
The Kelly criterion is a mathematical formula that determines the optimal bet size to maximize long-term bankroll growth. The formula was developed by John Kelly in 1956 for information theory problems, but it found wide application in sports betting and investing.
The essence of the method: you should stake exactly the amount that makes the bankroll grow as fast as possible over many repetitions. Stake more — and the risk of ruin rises. Stake less — and your money grows slower than it could.
The Kelly criterion works under two conditions: you estimate the outcome probability correctly, and your estimate differs from the implied probability of the odds. If a bookmaker offers odds of 2.00 (50% probability) and you rate the chances at 55%, Kelly recommends staking a certain percentage of the bank. Read more about bankroll management strategies in the advanced betting strategies section.
The Kelly criterion formula:
f* = (p × b − q) / b
Where:
p = probability of winning
q = 1 − p (probability of losing)
b = odds − 1 (net winnings per unit staked)
f* = optimal bankroll share to stake
If f* is positive, the bet has a positive expected value and Kelly recommends staking. If f* is zero or negative, the bet is unprofitable and should be avoided.
Example: odds of 2.50, your probability estimate — 45%.
b = 2.50 − 1 = 1.50
f* = (0.45 × 1.50 − 0.55) / 1.50 = (0.675 − 0.55) / 1.50 = 0.083
Optimal share = 8.3% of the bankroll
If the calculator shows 0%, the odds do not cover your probability estimate and the bet is unprofitable. To check whether the odds hold value, use the value bet calculator.
The Kelly criterion is a powerful bankroll management tool, but it has both strengths and limitations that are important to consider.
| Advantages | Limitations |
|---|---|
| Maximizes long-term bankroll growth | Requires an accurate probability estimate |
| Mathematically grounded approach | Full Kelly produces high volatility |
| Protects against ruin (stake < 100%) | Ignores bookmaker maximum stake limits |
| Adapts to the size of the bankroll | Hard to estimate probability precisely enough |
In practice most professionals use half or quarter Kelly. This reduces volatility at a small cost in bankroll growth speed. Half Kelly delivers 75% of the full Kelly growth rate with a much smoother ride. More on calculating the bookmaker margin — in our margin calculator.
Let's break the Kelly criterion down on a real example — step by step, with concrete numbers and roubles.
Initial data. A Russian Premier League match: Spartak vs Dynamo. The bookmaker gives odds of 2.10 on a Spartak win. You have analysed the statistics: xG over the last 10 matches, home form, line-ups — and you estimate the probability of a Spartak win at 55%. Your bankroll is ₽30,000.
Step 1: Define the variables.
p = 0.55 (probability of winning)
q = 1 − 0.55 = 0.45 (probability of losing)
b = 2.10 − 1 = 1.10 (net winnings per rouble)
Step 2: Plug them into the formula.
f* = (p * b − q) / b
f* = (0.55 * 1.10 − 0.45) / 1.10
f* = (0.605 − 0.45) / 1.10
f* = 0.155 / 1.10 = 0.141
Step 3: Work out the stake. Full Kelly recommends staking 14.1% of the bankroll — that is 30,000 * 0.141 = ₽4,230. If the bet wins, the bankroll grows to 30,000 + 4,230 * 1.10 = ₽34,653. If it loses, it drops to ₽25,770.
Step 4: Check the sensitivity. This is where the Kelly criterion demands caution. Suppose your estimate was wrong and the real probability is not 55% but 50%. Recalculate:
f* = (0.50 * 1.10 − 0.50) / 1.10 = 0.05 / 1.10 = 0.045
At a 50% probability Kelly recommends only 4.5% — three times less. A 5-percentage-point error in the estimate leads to a threefold change in stake size. That is exactly why professionals prefer fractional Kelly.
Another telling point: if the probability is estimated at 47%, Kelly returns a negative value (−0.024), which means the bet should not be placed — odds of 2.10 do not cover the risks at that probability.
Step 5: Account for multiple outcomes. The classic Kelly formula works with two outcomes — win/lose. But football often has three outcomes (win, draw, loss). In that case use the formula for the specific market: if you bet on the home win at 2.10, then p is the probability of the home win and q is the probability of any other result (draw + away win). The formula stays the same, but the accuracy of your p estimate becomes even more critical.
To control the quality of your probability estimates, keep a spreadsheet: record the probability estimate, the odds, the Kelly stake and the result. After 100 bets compare your average estimated probability with the actual win frequency. If you systematically overestimate probabilities by 3–5 p.p., reduce your Kelly multiplier accordingly. Before running Kelly it is useful to check the bookmaker margin with the margin calculator — a high margin shortens the odds and distorts the optimal share calculation.
The full Kelly criterion is mathematically optimal, but in practice it creates severe bankroll drawdowns. Fractional Kelly is the same formula with the result multiplied by a reducing coefficient.
Three variants of fractional Kelly:
| Strategy | Multiplier | Example (at f* = 14.1%) | Growth rate | Max drawdown |
|---|---|---|---|---|
| Full Kelly | 1.0 | ₽4,230 (14.1%) | 100% | 50–70% |
| Half Kelly | 0.5 | ₽2,115 (7.05%) | 75% | 25–40% |
| Quarter Kelly | 0.25 | ₽1,058 (3.53%) | 56% | 12–20% |
| One-tenth Kelly | 0.1 | ₽423 (1.41%) | 34% | 5–8% |
Half Kelly is the golden middle for most bettors. The growth rate drops by 25%, but the maximum drawdown shrinks by almost half. On a ₽30,000 bankroll the difference between full and half Kelly over 100 bets will be 10–15% of the final capital, while the stress levels are incomparable.
When to use which variant:
An important principle: use one fractional Kelly variant consistently rather than switching between full and fractional depending on your mood. Inconsistent staking destroys the formula's edge. Recalculate the bankroll and therefore the stake size after every 10–20 bets, not after each individual one.
Fractional Kelly over the long run — an example. Suppose the bankroll is ₽20,000. You place half-Kelly bets on events with average odds of 2.00 and an average edge of 5 p.p. (your probability estimate is 55% against an implied 50%). Full Kelly recommends 10%, half Kelly — 5%, i.e. ₽1,000 per bet. After a run of 20 bets at a 60% strike rate (12 wins, 8 losses) the bankroll will be about ₽24,000. With full Kelly the result would be around 26,000, but in a run of 5 straight losses (the probability of such a run is about 3%) full Kelly would draw the bank down to 12,000, while half Kelly would only fall to 16,000. The difference in psychological comfort is enormous.
Another nuance: when the bankroll is recalculated after a losing run, Kelly automatically reduces the stake size. This is built-in protection against ruin — the formula never recommends staking your last money. But it only works with disciplined adherence to the formula, without "chasing losses" with doubled stakes. An alternative approach to risk management is hedging, where you lock in profit with a bet on the opposite outcome instead of relying on the long run.
The Kelly criterion and value betting are two tools that work together. A value bet answers the question "should I bet?", and Kelly — "how much should I stake?". One without the other loses its meaning.
What a value bet is. A bet has value when your estimate of the outcome probability is higher than the implied probability of the odds. If a bookmaker offers 2.50 (implied probability 40%) and you rate the outcome at 45%, the 5 p.p. difference is the value. A detailed calculation — in the value bet calculator.
How Kelly uses value. In the Kelly formula f* = (p*b − q) / b the numerator (p*b − q) is the expected value of the bet. If it is positive, the bet is a value bet. The size of f* is proportional to the degree of value: the bigger the edge, the larger the recommended share.
Consider three bets with the same odds of 2.00 but different degrees of value:
| Probability estimate | Value (difference) | Kelly (f*) | With a ₽20,000 bank |
|---|---|---|---|
| 52% | +2 p.p. | 4.0% | ₽800 |
| 55% | +5 p.p. | 10.0% | ₽2,000 |
| 60% | +10 p.p. | 20.0% | ₽4,000 |
A clear pattern emerges: Kelly increases the stake in proportion to the edge. With minimal value (2 p.p.) it recommends a modest 4%, and with a serious edge (10 p.p.) — already 20%. This is logical: more value — more reason to take risk.
A practical workflow:
To track the profitability of a series of bets, use the ROI calculator. A positive ROI over 200+ bets confirms that your probability estimation system works, and you can gradually raise the fractional Kelly multiplier — for example, from quarter to half.
A typical mistake: Kelly without value. Some beginning bettors apply the Kelly formula to bets that are not value bets. They take the implied probability from the odds (for example, 50% at odds of 2.00) and plug that same figure into the formula. The result — Kelly shows 0%, because there is no edge. The Kelly formula only works when value is present: the difference between your estimate and the bookmaker's estimate must be positive.
A second point — simultaneous bets. Classic Kelly is designed for sequential bets (one after another). If you place 3–5 bets in a single day, the total risk can exceed a comfortable level. In such cases divide the recommended Kelly share by the number of simultaneous bets or use a more conservative multiplier.
Over 500+ bets the Kelly criterion shows an advantage over flat betting: the stake size adapts to the value. On favorites at 1.50 Kelly recommends 5–10% of the bankroll; on underdogs at 4.00 — 2–3%. Variance under Kelly is higher than under flat betting, but the bankroll grows faster. Losses over short runs are normal; the strike rate stabilizes at 300+ bets. Before applying it, check the margin in the margin calculator — with a high commission the bookmaker's line shortens the odds, and Kelly may recommend stakes that are too large.
Disclaimer: a responsible attitude to betting
The information on this page is for informational purposes only. By betting on sports with bookmakers, you risk your own money. Profytball is not a gambling operator and is not responsible for possible losses. Always treat betting as entertainment, not as a way to make money. Play responsibly!
If you feel that gambling is becoming a problem, seek help from specialists.
