Kelly Criterion Calculator
Calculate the optimal bet size to maximize your long-term bankroll growth. The Kelly Criterion helps you determine exactly how much to wager based on your edge and bankroll size.
Free Kelly Criterion Calculator
Table of Contents
How to Use the Kelly Criterion Calculator
The Kelly Criterion calculator helps you determine the optimal bet size to maximize your long-term bankroll growth. It's a powerful tool for serious bettors who want to optimize their stake sizing based on their edge. First, use our odds value calculator to identify positive expected value bets.
Bankroll
Enter your total betting bankroll in dollars. This is the amount of money you have available for betting. The Kelly Criterion will calculate what percentage of this bankroll you should wager on the current bet.
Bookmaker Odds
Enter the odds offered by the sportsbook in American format (like +150 or -200). These are the odds you'll receive if your bet wins. The calculator uses these odds to determine the potential payout relative to your stake. Use our betting odds calculator to convert between different odds formats.
Win Probability
Enter your assessed probability that this bet will win, as a percentage. This should be based on your analysis, research, or models. Be honest and realistic—overestimating your probability will lead to betting too much.
Fractional Kelly
Choose between Full Kelly, Half Kelly, Quarter Kelly, or Third Kelly. Full Kelly maximizes growth but creates high volatility. Most bettors use Half or Quarter Kelly to reduce risk while still benefiting from optimal bet sizing.
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. in 1956 while working at Bell Labs. Originally designed for information theory and gambling, it has become one of the most respected methods for determining optimal bet sizing in both betting and investing. The Kelly Criterion calculator helps you apply this formula to your betting strategy.
The core principle is simple: when you have an edge (a positive expected value), the Kelly Criterion tells you exactly what percentage of your bankroll to wager to maximize long-term growth. It balances the desire for growth with the need to protect your bankroll from ruin. First, identify value bets using our odds value calculator.
Unlike fixed bet sizing or flat betting, the Kelly Criterion adjusts your stake based on your edge. When you have a larger edge, you bet more. When your edge is smaller, you bet less. This dynamic approach theoretically maximizes the geometric growth rate of your bankroll over time. Calculate your optimal bet size with our Kelly Criterion calculator.
Key Benefits
The Kelly Criterion provides several advantages: it maximizes long-term growth, prevents over-betting, automatically adjusts stake size based on edge, and protects against bankroll ruin when used correctly. It's mathematically proven to be optimal for maximizing logarithmic utility.
Important Considerations
The Kelly Criterion assumes you can accurately assess probabilities, that you have an edge, and that you can place many bets over time. It doesn't account for psychological factors, bankroll constraints, or the fact that you might not have unlimited betting opportunities.
Understanding the Kelly Formula
The Kelly Criterion formula is: f* = (bp - q) / b
Where:
- f* = The fraction of your bankroll to bet (the Kelly percentage)
- b = The net odds (decimal odds - 1). For American odds +150, decimal is 2.50, so b = 1.50
- p = Your probability of winning (as a decimal, so 55% = 0.55)
- q = Your probability of losing (1 - p, so if p = 0.55, then q = 0.45)
Example Calculation
Let's say you have a bankroll of $10,000, the bookmaker offers +150 odds, and you assess a 55% win probability. Use our betting odds calculator to convert between odds formats.
First, convert +150 to decimal: 2.50, so b = 1.50
p = 0.55, q = 0.45
f* = (1.50 × 0.55 - 0.45) / 1.50
f* = (0.825 - 0.45) / 1.50
f* = 0.375 / 1.50 = 0.25
So you should bet 25% of your bankroll, which is $2,500.
However, most bettors would use Half Kelly (12.5% = $1,250) or Quarter Kelly (6.25% = $625) to reduce volatility. Our Kelly Criterion calculator makes these calculations easy.
When Kelly Gives Negative Results
If the Kelly formula gives you a negative number, it means the bet has negative expected value. You shouldn't place this bet at all. The Kelly Criterion only works when you have a positive edge—when your assessed probability is higher than the bookmaker's implied probability.
Full Kelly vs Fractional Kelly
One of the most important decisions when using the Kelly Criterion is whether to use Full Kelly or a fractional version. This choice significantly impacts both your growth potential and your risk exposure.
Full Kelly (1.0x)
Full Kelly maximizes the theoretical growth rate of your bankroll. However, it creates extreme volatility with large swings in your bankroll. You'll experience significant drawdowns, and if your probability assessments are even slightly off, you can lose substantial amounts. Most professional bettors avoid Full Kelly due to the psychological and practical challenges.
Half Kelly (0.5x)
Half Kelly is the most popular choice among serious bettors. It provides about 75% of Full Kelly's growth rate while reducing volatility by half. This creates a much more stable bankroll growth pattern that's easier to manage psychologically. Half Kelly is often considered the sweet spot between growth and risk.
Quarter Kelly (0.25x)
Quarter Kelly provides about 50% of Full Kelly's growth rate but with much lower volatility. This conservative approach is ideal if you're less confident in your probability assessments, have a smaller bankroll, or prefer more stable growth. It's also useful when you're just starting with the Kelly Criterion.
Third Kelly (0.33x)
Third Kelly offers a middle ground between Half and Quarter Kelly. It provides about 67% of Full Kelly's growth with moderate volatility. This can be a good option if you want more growth than Quarter Kelly but less risk than Half Kelly.
Choosing the Right Fraction
The right fractional Kelly depends on several factors:
- Confidence in your edge: If you're very confident in your probability assessments, you might use Half Kelly. If less confident, use Quarter Kelly.
- Bankroll size: Larger bankrolls can handle more volatility, so you might use a higher fraction. Smaller bankrolls benefit from more conservative sizing.
- Psychological tolerance: Can you handle large swings? If not, use a lower fraction.
- Betting frequency: If you place many bets, you can use a higher fraction because variance evens out. With fewer bets, use a lower fraction.
Kelly Criterion Examples
Example #1: Strong Edge on Underdog
You're analyzing an NBA game where the underdog is offered at +200 odds. After thorough research, you believe this team actually has a 40% chance of winning, not the 33.3% that +200 odds imply. First, verify this is a value bet using our odds value calculator.
Using the calculator:
- Bankroll: $10,000
- Odds: +200
- Win Probability: 40%
- Fraction: Half Kelly
The calculator shows:
- Kelly Percentage: 20%
- Half Kelly: 10%
- Recommended Bet: $1,000
This is a strong edge, so the Kelly Criterion recommends betting 10% of your bankroll (with Half Kelly). This balances growth potential with risk management. Calculate payouts using our betting odds calculator.
Example #2: Small Edge on Favorite
A favorite is offered at -150 odds. The bookmaker's implied probability is 60%. You assess the probability at 62%, giving you a small but positive edge. Check the expected value with our odds value calculator before using the Kelly Criterion.
Entering into the calculator:
- Bankroll: $10,000
- Odds: -150
- Win Probability: 62%
- Fraction: Half Kelly
The calculator reveals:
- Kelly Percentage: 3.33%
- Half Kelly: 1.67%
- Recommended Bet: $167
With a small edge, the Kelly Criterion recommends a much smaller bet size. This protects your bankroll while still allowing you to benefit from the positive expected value over time. Use our odds value calculator to identify value bets before using the Kelly Criterion.
Example #3: Negative Expected Value
You're considering a bet at -110 odds where you assess the win probability at 50%. The bookmaker's implied probability is 52.4%.
Calculation:
- Odds: -110
- Win Probability: 50%
- Kelly Percentage: -4.55% (negative!)
The negative Kelly percentage indicates this bet has negative expected value. You shouldn't place this bet at all. The Kelly Criterion correctly identifies that this bet will lose money over time, even though it might win occasionally.
Advantages and Limitations of the Kelly Criterion
Advantages
- Mathematically Optimal: The Kelly Criterion is proven to maximize long-term bankroll growth when you have an edge.
- Automatic Adjustment: It automatically adjusts your bet size based on your edge—larger edges mean larger bets, smaller edges mean smaller bets.
- Prevents Over-Betting: It prevents you from betting too much, which protects your bankroll from ruin.
- Prevents Under-Betting: It also prevents you from betting too little when you have a strong edge, ensuring you maximize growth.
- Objective Approach: It removes emotion from bet sizing decisions, using mathematics instead of gut feelings.
Limitations and Considerations
- Requires Accurate Probability Assessment: The Kelly Criterion only works if you can accurately assess probabilities. Overestimating your edge leads to over-betting.
- High Volatility with Full Kelly: Full Kelly creates extreme bankroll swings that many bettors can't handle psychologically.
- Assumes Many Bets: The Kelly Criterion works best over many bets. With few betting opportunities, variance can dominate results.
- Doesn't Account for Bankroll Constraints: It might recommend bet sizes that exceed your available bankroll or that you're not comfortable with.
- No Consideration of Opportunity Cost: It doesn't account for other betting opportunities you might have.
- Requires Discipline: You must stick to the Kelly recommendations even after losses, which can be psychologically difficult.
Best Practices
To get the most from the Kelly Criterion:
- Use fractional Kelly (Half or Quarter) to reduce volatility
- Be conservative in your probability assessments—it's better to underestimate your edge than overestimate it
- Track your results and compare your assessed probabilities to actual outcomes
- Adjust your Kelly fraction based on your confidence level and bankroll size
- Don't use Kelly for bets where you don't have a clear edge
- Consider your psychological tolerance for volatility when choosing your fraction
Frequently Asked Questions About Kelly Criterion
The Kelly Criterion is a mathematical formula that determines the optimal bet size to maximize long-term bankroll growth when you have an edge. Developed by John L. Kelly Jr. in 1956, it calculates what percentage of your bankroll to wager based on your probability of winning and the odds offered. It's mathematically proven to maximize the geometric growth rate of your bankroll over time. Use our Kelly Criterion calculator to determine optimal bet sizes. First, identify value bets using our odds value calculator.
The Kelly formula is: f* = (bp - q) / b, where f* is the fraction of bankroll to bet, b is the net odds (decimal odds - 1), p is your probability of winning, and q is your probability of losing (1 - p). For example, with +150 odds (b = 1.50) and a 55% win probability (p = 0.55, q = 0.45): f* = (1.50 × 0.55 - 0.45) / 1.50 = 0.25, meaning you should bet 25% of your bankroll. Most bettors use Half Kelly (12.5%) or Quarter Kelly (6.25%) to reduce volatility. Our Kelly Criterion calculator does all these calculations automatically. First, identify value bets using our odds value calculator.
Most bettors should use fractional Kelly (Half or Quarter) rather than Full Kelly. Full Kelly maximizes growth but creates extreme volatility with large bankroll swings. Half Kelly provides about 75% of Full Kelly's growth with half the volatility, making it the most popular choice. Quarter Kelly offers even more stability with about 50% of the growth. Choose based on your confidence in your probability assessments, bankroll size, and psychological tolerance for volatility.
A negative Kelly percentage means the bet has negative expected value—your assessed probability is lower than the bookmaker's implied probability. You shouldn't place this bet at all. The Kelly Criterion only works when you have a positive edge. If you consistently get negative results, you may be underestimating probabilities or the bookmaker's odds may not offer value.
Your probability assessment needs to be more accurate than the bookmaker's implied probability on average. However, the Kelly Criterion is sensitive to overestimation—if you consistently overestimate your edge, you'll bet too much and risk bankroll ruin. It's better to be conservative and underestimate your edge slightly. Track your bets and compare your assessed probabilities to actual outcomes to improve your accuracy over time.
The Kelly Criterion works best when you have a clear edge and can place many bets over time. It's ideal for value betting situations where you've identified positive expected value. However, you shouldn't use it for recreational bets, bets where you don't have an edge, or situations where you can't accurately assess probabilities. Also, if Kelly recommends bet sizes you're not comfortable with, consider using a smaller fraction or a different bankroll management strategy.
Fixed bet sizing means betting the same amount (or percentage) on every bet regardless of your edge. Kelly Criterion adjusts your bet size based on your edge—larger edges mean larger bets, smaller edges mean smaller bets. This dynamic approach theoretically maximizes growth, while fixed sizing is simpler but doesn't optimize for growth. Kelly is more complex but potentially more profitable for bettors who can accurately assess probabilities.
