Kelly Criterion Calculator
Find the mathematically optimal percentage of your bankroll to bet on any outcome using the Kelly Criterion. Use it to maximize long-run growth while controlling ruin risk.
About this calculator
The Kelly Criterion is a bankroll management formula developed by John L. Kelly Jr. in 1956 that identifies the bet fraction maximizing the logarithm of expected wealth growth. The core formula is: f* = (b × p − q) / b, where b = decimal odds − 1 (net odds), p = win probability, and q = 1 − p (loss probability). The optimal bet amount is then: Bet = Bankroll × KellyFraction × f*. The Kelly Fraction (often 0.25–0.5) scales the full Kelly stake down to a 'fractional Kelly', reducing variance while sacrificing some growth rate. A positive f* indicates a value bet; a negative result means the bet has negative expected value and should not be placed. Over many bets, full Kelly maximizes geometric growth but can cause large drawdowns, which is why fractional Kelly is widely preferred.
How to use
Example: You have a $1,000 bankroll, decimal odds of 2.50, a 50% win probability, and you want to use half-Kelly (fraction = 0.5). Step 1: Calculate b = 2.50 − 1 = 1.50. Step 2: Compute 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: Apply fractional Kelly: Bet = $1,000 × 0.5 × 0.1667 ≈ $83.33. Your optimal stake is roughly $83.
Frequently asked questions
How does the Kelly Criterion help with bankroll management in sports betting?
The Kelly Criterion tells you precisely what fraction of your bankroll to wager based on your perceived edge and the odds offered. By betting this exact fraction, you maximize the long-term growth rate of your bankroll geometrically rather than arithmetically. Overbetting beyond full Kelly actually reduces long-run growth and increases the risk of ruin, while underbetting is safer but leaves growth on the table. It gives bettors a disciplined, mathematically grounded staking plan rather than relying on intuition.
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% or more are common even with an 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.
When does the Kelly Criterion give a negative bet size, and what does that 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 is telling you not to bet at all, as placing the wager will shrink 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 should return a positive Kelly fraction.