Kelly Criterion Betting Calculator
Calculate the mathematically optimal fraction of your bankroll to wager on a bet using the Kelly Criterion. Ideal for bettors who want to maximize long-term bankroll growth while avoiding ruin.
About this calculator
The Kelly Criterion determines the bet size that maximizes the expected logarithm of wealth, which corresponds to maximum long-term growth. The full formula is: f* = (p × b − q) / b, where p is win probability, q = 1 − p is loss probability, and b = decimal odds − 1 (net odds). In this calculator's implementation: Bet = bankroll × kellyFraction × ((p × decimalOdds − 1) / (decimalOdds − 1)). The kellyFraction multiplier (commonly 0.25–0.5 for 'fractional Kelly') reduces volatility at the cost of slightly slower growth. Betting more than the full Kelly fraction increases risk of ruin without improving expected growth. The formula naturally outputs 0 or negative when the bet has no edge, preventing you from wagering on unfavorable lines.
How to use
Suppose your bankroll is $1,000, you estimate a 55% win probability, the decimal odds are 2.00, and you use a half-Kelly fraction of 0.5. Step 1 — p = 55/100 = 0.55; decimalOdds = 2.00. Step 2 — Numerator: (0.55 × 2.00 − 1) = 0.10. Step 3 — Denominator: (2.00 − 1) = 1.00. Step 4 — Full Kelly fraction: 0.10 / 1.00 = 0.10 (10% of bankroll). Step 5 — Apply half-Kelly: $1,000 × 0.5 × 0.10 = $50 recommended bet.
Frequently asked questions
How does the Kelly Criterion maximize long-term betting growth?
Kelly betting maximizes the expected value of the logarithm of your bankroll, which is equivalent to maximizing the geometric growth rate over many bets. Unlike flat betting or fixed-percentage betting, Kelly automatically scales your stake up when you have a large edge and scales it down when your edge is thin. Over thousands of bets, this compounding effect produces significantly larger bankrolls than any fixed staking plan, assuming your probability estimates are accurate.
What is fractional Kelly and why do professional bettors use it?
Fractional Kelly means betting a fixed fraction — typically 25% to 50% — of what the full Kelly formula recommends. Full Kelly produces maximum long-term growth but comes with extreme short-term volatility; drawdowns of 50% or more are mathematically expected. Fractional Kelly dramatically smooths out the variance at only a modest cost to growth rate. Most professional bettors use quarter-Kelly or half-Kelly as a compromise between growth and psychological sustainability.
What happens if my win probability estimate is wrong in the Kelly formula?
The Kelly Criterion is extremely sensitive to the accuracy of your probability estimate. Overestimating your edge even slightly can lead to overbetting, which increases variance and risk of ruin disproportionately. For example, if you input 60% but your true edge is only 52%, you will bet significantly too large. This is why many practitioners use fractional Kelly — it provides a built-in buffer against estimation errors. Regularly tracking your actual win rate versus predicted win rate (known as calibration) is essential for safe Kelly betting.