Kelly Criterion
/KEL-ee kry-TEER-ee-uhn/
The Kelly Criterion is a mathematical formula for optimal bet sizing that maximizes the long-term growth rate of your bankroll. Originally developed by John Kelly at Bell Labs in 1956, the formula calculates the ideal percentage of your bankroll to wager based on your estimated edge and the offered odds. By betting proportionally to your advantage, Kelly avoids both the risk of overbetting, which can lead to ruin, and the inefficiency of underbetting, which leaves profit on the table. Because full Kelly assumes perfectly accurate probability estimates and can produce volatile swings, most professional bettors use fractional Kelly at 25-50% of the recommended amount.
Example
You estimate a 55% win probability on a bet offered at -110 odds (decimal 1.91). The Kelly formula yields: (0.55 x 1.91 - 0.45) / 1.91 = 4.7% of your bankroll. If your bankroll is $10,000, full Kelly recommends a $470 bet, while half-Kelly would be $235. Now consider a stronger edge: you estimate 60% at +100 odds (decimal 2.0). Kelly says: (0.60 x 2.0 - 0.40) / 2.0 = 40% of bankroll—an aggressively large bet that illustrates why fractional Kelly is so important in practice. Overestimating your edge by even a few percentage points can lead to dangerously large recommended bet sizes.
Common Questions
Should I use full Kelly?
Should I use full Kelly?
Most professionals strongly recommend against using full Kelly. While it maximizes theoretical long-term growth, it assumes your probability estimates are perfectly accurate, which they never are in practice. A 2-3% error in your estimated win probability can significantly change the optimal bet size and lead to overbetting. Fractional Kelly at 25-50% of the full recommendation provides a much smoother ride, reduces drawdowns substantially, and still captures the majority of the growth benefits with far less risk of ruin.
What's the Kelly formula?
What's the Kelly formula?
Kelly % = (bp - q) / b, where b equals the decimal odds minus 1, p is your estimated win probability, and q is the loss probability (1 - p). For example, at -110 odds, b = 0.91. If p = 0.55 and q = 0.45, then Kelly % = (0.91 x 0.55 - 0.45) / 0.91 = 5.5%. A negative result means you have no edge and should not bet at all. Our Kelly calculator handles this math automatically and also shows fractional Kelly recommendations.
How does Kelly compare to flat betting?
How does Kelly compare to flat betting?
Flat betting means wagering the same fixed amount on every bet regardless of your perceived edge. It's simple and safe but doesn't optimize growth because it treats a 51% edge the same as a 60% edge. Kelly Criterion adjusts your stake based on how large your advantage is—betting more when your edge is bigger and less when it's smaller. Over thousands of bets, Kelly produces significantly faster bankroll growth than flat betting, but it requires accurate probability estimates and discipline to handle the larger swings that come with variable bet sizing.