Kelly Criterion Calculator

Work out the Kelly stake - the share of your bankroll to bet - from the decimal odds and your estimated win probability.

The Kelly criterion is a mathematical formula that determines the optimal stake for each bet to maximize long-term bankroll growth, scaling your wager proportionally to your edge over the odds.

What Is the Kelly Criterion?

The Kelly criterion is a mathematical formula used to determine the ideal proportion of your bankroll to stake on a bet. It calculates the exact fraction of your funds to risk in order to maximize long-run growth while minimizing the risk of ruin. The formula stakes more aggressively when your probability edge over the odds is larger, and stakes nothing when there is no edge.

Unlike fixed-stake betting, which treats every bet the same regardless of your confidence, Kelly adjusts your stake to match the strength of your edge. This means a high-confidence bet receives a bigger slice of your bankroll, while a weak-edge bet receives barely anything. In theory, over hundreds of bets, the Kelly criterion grows wealth faster than any other staking strategy.

However, Kelly is also aggressive. Full Kelly can recommend large stakes when you have a significant edge, which creates large swings in your bankroll. For this reason, many professional bettors use a fraction of it — such as half-Kelly — to reduce volatility while still benefiting from edge-based staking. The Kelly criterion sets the stake that maximises the long-run growth of a bankroll. It stakes more when your edge is larger and nothing when there is no edge. Full Kelly is aggressive and swingy, so many bettors use a fraction of it, such as half-Kelly, to smooth the ride.

How Kelly Criterion Is Calculated

The Kelly criterion uses a straightforward mathematical formula. Let b equal the decimal odds minus one (the profit return). Let p equal your estimated win probability as a decimal, and q equal one minus p (the loss probability). The Kelly fraction f is then calculated as: f = (b × p − q) / b. Once you have the fraction, multiply it by your current bankroll to find your stake.

For example, with decimal odds of 2.10, your calculation begins with b = 1.10. If you believe your win probability is 52 percent (0.52 as a decimal), then q = 0.48. Substituting into the formula: f = (1.10 × 0.52 − 0.48) / 1.10 = 0.0836, or 8.36%.

A critical feature: if the Kelly fraction is zero or negative, the formula says stake nothing. This occurs when you have no edge or a negative edge. The break-even probability (where f reaches zero) is calculated as 1 divided by the decimal odds. At odds of 2.10, the break-even probability is 47.6%. Below this probability, your edge vanishes and Kelly recommends no stake.

Many bettors also use a fraction of Kelly — half-Kelly is most common. Half-Kelly simply means taking half of the Kelly fraction. If full Kelly recommends 8.36%, half-Kelly recommends 4.18%. This reduces volatility without abandoning the edge-based principle.

What the Calculator Shows You

This Kelly criterion calculator takes three inputs: your estimated win probability, the decimal odds offered, and your bankroll. It then computes the exact Kelly fraction as a percentage and translates that into a euro stake for your current bankroll size.

The calculator displays both the full Kelly stake and the half-Kelly stake side by side, so you can see the difference in size. It also shows the Kelly fraction itself — the mathematical result before bankroll multiplication — so you understand the proportional edge the formula has identified. If your estimated probability yields a zero or negative Kelly fraction, the calculator will show zero stake, confirming that no edge exists at those odds.

By entering different probabilities, you can observe how Kelly sensitivity works: a small shift in your confidence level can produce a large shift in recommended stake. This illustrates why honest probability estimation is critical and why many bettors prefer half-Kelly’s smoother ride.

Worked Example

Imagine you have a bankroll of EUR 1000 and are offered a bet at decimal odds of 2.10. You estimate your win probability at 52 percent. Let us work through the Kelly calculation step by step.

First, calculate b: 2.10 − 1 = 1.10.

Second, express your probability as a decimal: 52% = 0.52. Therefore, q = 1 − 0.52 = 0.48.

Third, apply the formula: f = (1.10 × 0.52 − 0.48) / 1.10 = 0.0836. This equals 8.36% as a percentage.

Fourth, multiply the Kelly fraction by your bankroll to find your stake: 0.0836 × 1000 = EUR 83.64. This is your full Kelly stake.

If you prefer half-Kelly to reduce swings, take half of the fraction: 4.18%. On a €1000 bankroll, that gives EUR 41.82.

So the Kelly criterion recommends a full Kelly stake of EUR 83.64 or a half-Kelly stake of EUR 41.82 on this bet. Over many similar bets, staking in this manner — proportional to your edge — should grow your bankroll faster than a fixed-stake approach.

Kelly Fraction by Probability

The Kelly fraction responds sharply to small changes in your estimated probability. Below is a reference table showing how the Kelly fraction grows as your probability increases, using odds of 2.10 and a bankroll of EUR 1000.

Notice that at 48%, the stake is tiny (EUR 7.30) because your edge is nearly zero. At 52%, it rises to EUR 83.60. By 60%, Kelly recommends EUR 236.40 — more than one-fifth of your bankroll. This sensitivity to probability is both the strength and the danger of Kelly: small errors in your probability estimate lead to large errors in your stake.

Full Kelly vs Half-Kelly

Full Kelly maximizes theoretical long-run growth but creates large swings in your bankroll. Half-Kelly reduces both the upside and the downside, making the ride smoother. Here is how they compare on the worked example.

Full Kelly stakes EUR 83.64; half-Kelly stakes EUR 41.82. Over time, full Kelly will grow your bankroll faster — in theory. But it also exposes you to larger drawdowns. If you hit a losing streak, full Kelly can shrink your bankroll more painfully than half-Kelly. For this reason, professional bettors often adopt half-Kelly or quarter-Kelly as a compromise between growth and comfort.

When Kelly Can Lead You Astray

The Kelly criterion is mathematically sound, but it relies entirely on honest input. If you overestimate your win probability — even slightly — Kelly will recommend an oversized stake, and you risk a catastrophic loss.

Kelly needs an honest probability. The break-even point here is 1 / 2.10 = 47.6%; below that the fraction turns negative and Kelly says stake nothing. Overstate your edge and full Kelly can recommend a punishing stake, which is why half-Kelly or smaller is common in practice. Suppose you genuinely have a 52% edge on the odds of 2.10, but you overestimate and give yourself more credit than you deserve. Kelly would then recommend a much larger stake than the 8.36% you truly deserve. If your actual edge is only 52%, you have inflated your stake, setting yourself up for unnecessary losses.

This is why many bettors regard full Kelly as too aggressive for real-world use. Probability estimation is difficult, and overconfidence is common. Using full Kelly assumes you know your edge with near-perfect accuracy. For most bettors, this assumption does not hold. A miscalibrated Kelly stake can turn what should be a modest loss into a severe one.

Additionally, Kelly assumes you can stake any fraction of your bankroll and that you can repeat the bet indefinitely. In practice, bookmakers set minimum stakes, bet limits may change, and market conditions shift. Kelly also ignores the psychological impact of large swings, which can prompt emotional decisions that violate the system.

When Kelly Makes Sense

Kelly makes the most sense in scenarios where you can estimate your probability with reasonable accuracy, have a large bankroll relative to bet size, and plan to place many similar bets over time.

If you are a professional sharp bettor or serious amateur who has developed edge through research and historical performance tracking, Kelly helps you scale your stakes to match your confidence. Rather than betting the same amount on every wager, Kelly lets you be aggressive when you have a strong edge and conservative when your edge is weak. This proportional approach accelerates bankroll growth compared to fixed-stake betting.

Kelly also works well in markets where you can find consistent mispricings. In sports betting, if you have developed a model or heuristic that consistently outperforms the market odds, Kelly helps you capitalise on that edge in the long run. The mathematical guarantee of Kelly — that no other strategy grows wealth faster in the limit — becomes relevant when you are placing dozens or hundreds of bets over months and years.

Kelly is also valuable as a teaching tool. Even if you do not stake a full Kelly fraction, understanding the formula reveals how your edge directly controls your stake size. It pushes you to think carefully about probability. It shows graphically why a small confidence increase justifies a large stake increase. For serious bettors, this insight alone is worth learning Kelly, even if you ultimately use half-Kelly or a smaller fraction to manage risk.

Common Mistakes

Feeding in an inflated probability, which oversizes the stake, is the most common mistake. Bettors often overestimate their edge, leading to oversized Kelly stakes and unnecessary losses. Honest self-assessment of your probability is essential.

Using full Kelly when your probability is only a rough estimate is another mistake. Unless you have backtested your predictions or have strong historical evidence, you should use half-Kelly or smaller to hedge against estimation error.

Staking anything when the fraction is zero or negative is a critical error. If your probability falls below the break-even point, Kelly says stake nothing. Ignoring this signal is a form of gambling against the odds.

Finally, recalculating the fraction on a bankroll you have not updated is a common oversight. Kelly must be recalculated on your current bankroll, not a historical bankroll. If your bankroll shrinks after a loss, your next Kelly stake must be proportionally smaller.

Kelly vs Fixed Stake

Fixed-stake betting treats every wager the same, regardless of your edge. Kelly adjusts your stake to match your confidence. Over a long series of bets, Kelly’s proportional approach grows wealth faster than fixed stakes — provided your probability estimates are honest.