Kelly Calculator for Betting
Calculate the optimal Kelly bet size for sports betting based on edge and odds. Enter values for instant results with step-by-step formulas.
Formula
f* = (bp - q) / b
Where f* is the optimal fraction of bankroll to wager, b is the net decimal odds (decimal odds minus 1), p is the probability of winning, and q is the probability of losing (1 - p). The result is multiplied by the chosen Kelly fraction (e.g., 50% for half Kelly) for risk management.
Worked Examples
Example 1: NFL Point Spread Bet
Problem: You have a $1,000 bankroll and estimate a 55% win probability on a point spread bet at decimal odds of 1.91 (-110). What is the optimal bet size?
Solution: Net odds (b) = 1.91 - 1 = 0.91\nWin probability (p) = 0.55, Loss probability (q) = 0.45\nFull Kelly: f* = (0.91 x 0.55 - 0.45) / 0.91 = (0.5005 - 0.45) / 0.91 = 0.0555 = 5.55%\nOptimal bet: $1,000 x 5.55% = $55.50\nEV per bet: (0.55 x 0.91) - 0.45 = 0.0505 = 5.05%\nHalf Kelly (recommended): 2.78% = $27.75
Result: Full Kelly: $55.50 (5.55%) | Half Kelly: $27.75 | EV: +5.05% per bet
Example 2: Underdog Value Bet
Problem: Bankroll of $5,000. You estimate a 35% chance on a bet paying decimal odds of 3.50 (+250). Using half Kelly.
Solution: Net odds (b) = 3.50 - 1 = 2.50\nFull Kelly: f* = (2.50 x 0.35 - 0.65) / 2.50 = (0.875 - 0.65) / 2.50 = 0.09 = 9.0%\nHalf Kelly: 4.5% = $5,000 x 4.5% = $225\nEV per bet: (0.35 x 2.50) - 0.65 = 0.225 = 22.5%\nImplied probability: 1/3.50 = 28.6% (your edge: 6.4%)
Result: Full Kelly: $450 (9.0%) | Half Kelly: $225 | EV: +22.5% | Edge: 6.4%
Frequently Asked Questions
What is the Kelly Criterion and how does it apply to betting?
The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. at Bell Labs in 1956 that determines the optimal percentage of your bankroll to wager on a bet with a positive expected value. The formula is f* = (bp - q) / b, where f* is the fraction of bankroll to bet, b is the net decimal odds (decimal odds minus 1), p is the probability of winning, and q is the probability of losing (1 - p). In sports betting, if you believe a team has a 55% chance of winning at decimal odds of 2.00 (even money), the Kelly formula suggests betting 10% of your bankroll. The beauty of Kelly staking is that it maximizes the long-term growth rate of your bankroll while mathematically preventing total ruin since bet sizes shrink proportionally as your bankroll decreases.
Why do most professional bettors use fractional Kelly?
Most professional sports bettors and advantage gamblers use fractional Kelly, typically between 25% and 50% of the full Kelly recommendation, for several important practical reasons. First, the Kelly Criterion assumes you know the exact probability of winning, but in reality probability estimates contain uncertainty and error. Overbetting due to overestimated edge is far more damaging than underbetting. Second, full Kelly produces extreme bankroll volatility with drawdowns of 50% or more being common, which is psychologically difficult to endure. Half Kelly produces approximately 75% of the long-term growth rate with significantly reduced variance and maximum drawdown. Third, fractional Kelly provides a margin of safety against estimation errors. Professional bettors consistently report that quarter to half Kelly provides the best real-world balance between growth and emotional sustainability.
What happens if the Kelly formula gives a negative number?
A negative Kelly value means the bet has a negative expected value, and you should not place the wager at all. This occurs when the implied probability from the odds is higher than your estimated true probability of winning. For example, if a bet offers decimal odds of 2.00 (implied 50% chance) but you estimate only a 45% probability of winning, the Kelly formula returns a negative value: (1 x 0.45 - 0.55) / 1 = -0.10. Negative Kelly essentially means the bookmaker has the edge, not you. In practice, most bets offered by sportsbooks have negative expected value, which is how bookmakers profit. Only bet when your analysis suggests the true probability exceeds the implied probability by a meaningful margin, ideally producing a Kelly fraction of at least 1-2% to justify the effort and emotional energy of placing the wager.
How does the Kelly Criterion relate to expected value in sports betting?
Expected value (EV) and the Kelly Criterion are complementary concepts in sports betting mathematics. EV tells you whether a bet is profitable on average: EV = (probability x net odds) - (1 - probability). A positive EV means the bet is worth making over many repetitions. However, EV alone does not tell you how much to bet. That is where Kelly comes in. The Kelly Criterion optimizes bet sizing to maximize the geometric growth rate of your bankroll given a known positive EV. Importantly, a higher EV does not always mean a larger Kelly bet. A bet with moderate EV but high probability might warrant a larger Kelly stake than a long-shot with higher EV but lower probability. Kelly accounts for both the edge and the odds, balancing potential profit against risk of loss to produce mathematically optimal bankroll growth over time.
How does Kelly Criterion work for betting?
The Kelly Criterion calculates the optimal bet size to maximize long-run bankroll growth: f = (bp − q) / b, where b = net odds, p = probability of winning, q = probability of losing. For a 55% win probability at even money: f = (1 × 0.55 − 0.45) / 1 = 10% of bankroll. Over-betting the Kelly fraction increases ruin risk; under-betting is safer but grows slower.
Can I share or bookmark my calculation?
You can bookmark the calculator page in your browser. Many calculators also display a shareable result summary you can copy. The page URL stays the same so returning to it will bring you back to the same tool.