Kelly Criterion Calculator
Calculate optimal bet sizes for maximum long-term growth
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About the Kelly Criterion
The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets to maximize the logarithm of wealth. In sports betting, it helps calculate what percentage of your bankroll you should wager based on your edge.
The Formula
Where:
b = decimal odds - 1 (the net odds)
p = your probability of winning
q = your probability of losing (1 - p)
When to Use Kelly
- When you have a positive expected value (+EV)
- When you can accurately estimate probabilities
- When you're focused on long-term bankroll growth
Most professional bettors use a "fractional Kelly" approach (typically ¼ or ½ of the calculated Kelly stake) to reduce volatility.
Learn more about Kelly Criterion in our comprehensive guide.
How To Use This Calculator
Follow these steps to get the most out of the Kelly Criterion calculator:
Enter American Odds: Input the odds offered by your sportsbook in American format (e.g., +150 for favorites or -110 for underdogs).
Estimate Your Probability: Enter your estimated probability of the bet winning as a percentage (e.g., 55%). This should be your honest assessment based on research, models, or analysis.
Input Your Bankroll: Enter the total amount of your betting bankroll. This should be money you've specifically allocated for sports betting.
Select Kelly Fraction: Choose what fraction of the full Kelly recommendation you want to use. Most bettors use 1/4 or 1/2 to reduce variance.
Analyze the Results: Review the recommended bet size, your edge percentage, and whether the bet has positive expected value.
Pro Tip: Managing Your Betting Portfolio
When using Kelly to manage multiple bets, keep the total percentage of your bankroll at risk to a reasonable level. Many professionals aim to never have more than 20-30% of their bankroll in play at any given time, regardless of what individual Kelly calculations might suggest.
Remember that the Kelly Criterion assumes you can bet the same opportunity repeatedly over time. For one-off or rare betting opportunities, you might want to be even more conservative with your sizing.
Frequently Asked Questions
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. while working at Bell Labs in 1956. It calculates the optimal size of a series of bets to maximize long-term wealth growth. In sports betting, it helps determine what percentage of your bankroll you should risk based on your perceived edge.
How does the Kelly Criterion work for sports betting?
The Kelly Criterion considers both the odds offered by the sportsbook and your estimated probability of winning. It calculates the optimal stake size that balances the potential for growth with protection from ruin. Bets with a larger edge receive larger recommended bet sizes, while negative EV bets always get a zero recommendation.
What is Fractional Kelly?
Fractional Kelly is a more conservative approach where you bet a fraction of what the full Kelly formula recommends. For example, Half-Kelly (50%) means wagering half of the calculated percentage. This reduces variance and risk of ruin, which is why many professional bettors use Half or Quarter Kelly instead of the full amount.
Why does Kelly Criterion recommend zero bet size for negative EV bets?
The Kelly formula is designed to maximize long-term bankroll growth. Since negative expected value bets will lose money in the long run, the mathematically optimal amount to wager on them is always zero, regardless of the odds or stake size.
How accurate do my probabilities need to be for Kelly Criterion?
For Kelly Criterion to be effective, your probability estimates must be reasonably accurate. Overestimating your edge can lead to overbetting and potential bankroll damage. This is another reason why many bettors use Fractional Kelly—it provides some protection against probability estimation errors.
Can I use Kelly Criterion for parlays and other exotic bets?
The Kelly formula works best for single wagers with two possible outcomes. While it can be adapted for parlays and other exotic bets, the calculations become more complex. For these bet types, you need to accurately calculate the true probability of the combined events, which is often difficult.
Advanced Kelly Criterion Concepts
Advantages of Kelly Criterion
Mathematically Optimal: Kelly betting is proven to grow your bankroll faster than any other strategy in the long run, assuming accurate probability estimates.
Dynamic Sizing: Automatically adjusts bet size based on your edge—larger edges get larger bets.
Bankruptcy Protection: Proper Kelly betting mathematically eliminates the possibility of complete ruin, as bet sizes decrease as your bankroll decreases.
Compounding Growth: As your bankroll grows, so do your bet sizes, enabling exponential growth over time.
Limitations of Kelly Criterion
Variance: Full Kelly betting can lead to significant bankroll swings, which can be psychologically difficult to handle.
Probability Estimation: The strategy is only as good as your probability estimates. Overconfidence can lead to overbetting.
Practicality: Kelly often recommends very small bet sizes (1-3% of bankroll), which may be impractical for some bettors.
Multiple Simultaneous Bets: The basic Kelly formula doesn't account for correlation between concurrent bets, which requires more complex calculations.
Kelly Criterion in Professional Betting
Most professional sports bettors use some form of the Kelly Criterion to size their bets, but virtually none use full Kelly. Professionals typically use fractional Kelly approaches (1/4 to 1/2 Kelly) to reduce variance while still capturing most of the growth benefits. This is sometimes called "Kelly-informed" betting.
Even legendary bettors and hedge fund managers like Bill Benter (horse racing) and Ed Thorp (blackjack, investments) have advocated for fractional Kelly approaches—using the formula as a ceiling rather than an exact prescription. This approach helps manage the inevitable errors in probability estimation while maintaining disciplined bankroll management.