Kelly Criterion Calculator
Calculates the mathematically optimal percentage of your bankroll to wager on a positive-EV bet using the Kelly Criterion, with optional fractional Kelly for reduced variance. Use it to maximize long-run growth while controlling ruin risk.
Last updated: May 2026
Compare with similar
About this calculator
The Kelly Criterion is a bankroll management formula derived by John L. Kelly Jr. in 1956 (Bell Labs) that identifies the bet fraction maximizing the long-run logarithmic growth rate of wealth. The core formula is f* = (b × p − q) / b, where b = decimal_odds − 1 (net odds, the profit per unit staked), p = your true win probability (0–1), and q = 1 − p (loss probability). The optimal bet amount is bet = bankroll × KellyFraction × f*. Variables: bankroll (current total), odds (decimal odds offered), winProbability (your estimate, 0–100%), kellyFraction (scaling factor 0.1–1.0). Kelly Fraction below 1 is called 'fractional Kelly' — half-Kelly (0.5) and quarter-Kelly (0.25) are popular because they sacrifice some growth rate in exchange for much lower variance. A positive f* indicates a value bet; a zero or negative result means no edge exists and the formula will recommend a zero or negative stake (which you should interpret as 'do not bet'). Edge cases: Kelly assumes you have a stable, accurate probability estimate — overestimating your edge by even 10% can turn full Kelly from optimal into ruinous. Full Kelly produces aggressive drawdowns (drawdowns of 50%+ are common), which is why even professional bettors typically use 0.25–0.5 Kelly. The formula assumes one bet at a time; for simultaneous correlated bets, the multi-Kelly extension is needed. Real-world bankrolls also face other risks (account closures, exchange suspensions) that Kelly doesn't model.
How to use
Example 1: $1,000 bankroll, decimal odds 2.50, you estimate 50% win probability, using half-Kelly (0.5). Step 1: b = 2.50 − 1 = 1.50. Step 2: f* = (1.50 × 0.50 − 0.50) / 1.50 = (0.75 − 0.50) / 1.50 = 0.25/1.50 ≈ 0.1667 (16.67% of bankroll). Step 3: bet = $1,000 × 0.5 × 0.1667 ≈ $83.33. Verify: edge = 50% − implied 40% = 10 percentage points; half-Kelly on a sizeable edge gives ~8% of bankroll, consistent with conservative pro-style sizing. Example 2: $5,000 bankroll, decimal odds 1.80, 60% win probability, quarter-Kelly. Step 1: b = 0.80. Step 2: f* = (0.80 × 0.60 − 0.40) / 0.80 = (0.48 − 0.40) / 0.80 = 0.10. Step 3: bet = $5,000 × 0.25 × 0.10 = $125. Verify: 5% effective stake of bankroll despite a strong 60% win rate at fair-implied 56% — the Kelly formula correctly scales the bet down for the smaller edge (4 percentage points).
Frequently asked questions
How does the Kelly Criterion help with bankroll management?
Kelly tells you precisely what fraction of your bankroll to wager based on your perceived edge and the odds offered. By betting this exact fraction over and over you maximize the long-term geometric growth rate of your bankroll. Overbetting beyond full Kelly actually reduces long-run growth and increases the risk of ruin nonlinearly. Underbetting is safer but leaves growth on the table. Kelly gives a disciplined, mathematically grounded staking plan rather than gut-feel sizing, and it automatically scales bet size with edge size — bigger edges produce bigger bets, smaller edges smaller bets.
What is fractional Kelly and why do professional bettors use it?
Fractional Kelly means betting only a fraction (commonly 25–50%) of what the full Kelly formula recommends. Full Kelly maximizes expected logarithmic growth but produces aggressive swings — drawdowns of 50%+ are common even with a real edge. Fractional Kelly reduces variance significantly with only a modest reduction in growth rate, making it far more psychologically and practically sustainable. Most professional bettors use quarter-Kelly or half-Kelly to protect their bankroll during inevitable losing streaks. Half-Kelly captures about 75% of full Kelly's growth rate with roughly half the variance, which is widely regarded as the best practical tradeoff.
When does Kelly give a negative bet size, and what does it mean?
A negative Kelly result occurs when (b × p − q) is less than zero, meaning the bet has negative expected value — the bookmaker's edge exceeds your estimated advantage. In this situation the formula tells you not to bet at all, as placing the wager shrinks your bankroll over time. This is one of the most valuable features of the Kelly approach: it doubles as an EV filter, automatically screening out losing propositions. Only bets where you have a genuine edge over the implied probability return a positive Kelly fraction. A common implementation wraps the formula in max(0, …) so that negative values are reported as 'no bet' rather than a negative stake.
What are common mistakes when applying the Kelly Criterion?
Overestimating your win probability is the most expensive mistake — Kelly is exquisitely sensitive to probability accuracy, and a 5-point overestimate (60% when true is 55%) can turn full Kelly from optimal into bankroll-destroying. Forgetting that Kelly assumes one bet at a time leads to overbetting when multiple correlated bets are placed simultaneously. Using Kelly across multiple bookmakers without aggregating your bankroll first overstates effective risk. Ignoring the fixed costs (commission on exchanges, deposit fees) that reduce effective odds inflates the perceived edge. Treating Kelly as a target rather than an upper bound — many bettors stake higher than full Kelly believing more is better, when the math shows the opposite. Finally, applying Kelly to bets where the variance is dominated by tail events (long-shots, longshot parlays) produces unstable results because the normal approximation breaks down.
When should I NOT use the Kelly Criterion?
When you can't reliably estimate your true win probability, Kelly is unusable — without an accurate p, the formula amplifies estimation errors into bankroll destruction. Recreational bettors who treat betting as entertainment should use a fixed flat stake (1–2% of bankroll per bet) rather than variable Kelly sizing. Short-term goals (you need this bankroll to be intact next month) call for far more conservative sizing than even quarter-Kelly. Bets with capped maximum stakes (limited by the book) may force you to bet less than Kelly suggests — that's fine; Kelly is an upper bound. Correlated multi-leg bets like parlays and same-game parlays violate the single-bet assumption — model them as the underlying joint distribution. Sequential live-betting on the same event also violates Kelly's i.i.d. assumption. Finally, with very small bankrolls (under $500) the integer-stake granularity of sportsbooks makes precise Kelly sizing impossible — use flat stakes instead.