Kelly Criterion Calculator
Calculate optimal bet size based on edge and bankroll
Calculate Optimal Bet Size
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets. It maximizes the expected logarithm of wealth (bankroll growth) while minimizing the risk of ruin.
The Kelly Formula
f* = (bp - q) / b
- f* = Fraction of bankroll to wager
- b = Net odds received (decimal odds - 1)
- p = Probability of winning
- q = Probability of losing (1 - p)
Example: If you have a 55% chance of winning at 2.00 odds:
b = 2.00 - 1 = 1.00
p = 0.55, q = 0.45
f* = (1.00 × 0.55 - 0.45) / 1.00 = 0.10 = 10%
On a $1,000 bankroll, bet $100
How Kelly Criterion Works
Estimate Win Probability
Determine your true probability of winning the bet. This requires skill, research, and accurate handicapping.
Compare to Implied Probability
Calculate the bookmaker's implied probability from the odds. If your estimate is higher, you have an edge.
Calculate Optimal Bet Size
Use the Kelly formula to determine what percentage of your bankroll to wager for maximum growth.
Apply Fractional Kelly
Most pros use half or quarter Kelly to reduce volatility while still growing the bankroll efficiently.
Fractional Kelly: Risk Management
While full Kelly maximizes growth rate, it can lead to significant bankroll swings. Most professional bettors use fractional Kelly:
🎯 Full Kelly (100%)
Pros: Maximum growth rate
Cons: High volatility, requires perfect probability estimates
Use case: Only if extremely confident in estimates
📊 Half Kelly (50%)
Pros: 75% of full Kelly growth, much lower volatility
Cons: Slower growth than full Kelly
Use case: Standard for most professional bettors
🛡️ Quarter Kelly (25%)
Pros: Low volatility, forgiving of estimate errors
Cons: Slower bankroll growth
Use case: Conservative approach for beginners
🔒 Eighth Kelly (12.5%)
Pros: Very low risk, minimal drawdowns
Cons: Slowest growth
Use case: Extremely risk-averse bettors
⚠️ Important Considerations
🎲 Probability Estimation
Kelly Criterion is only as good as your probability estimates. Overestimating your win probability leads to overbetting and bankroll erosion.
📉 Negative Kelly
If Kelly comes out negative, it means you have no edge. Don't bet! The bookmaker's odds are better than your win probability.
💰 Bankroll Swings
Even with an edge, expect losing streaks. Full Kelly can experience 50%+ drawdowns. Use fractional Kelly to smooth volatility.
🔄 Recalculate Often
As your bankroll changes, so does your optimal bet size. Recalculate Kelly after significant wins or losses.
📊 Multiple Bets
If betting on correlated events, the Kelly percentages don't simply add up. Advanced portfolio theory is needed.
⏱️ Long-Term Focus
Kelly is designed for long-term growth. Short-term results will vary widely. Stick to the system through variance.
Kelly Criterion Best Practices
Start Conservative
Begin with quarter or eighth Kelly until you're confident in your probability estimation skills. It's better to grow slowly than to bust.
Track Your Results
Keep detailed records of your bets, estimated probabilities, and outcomes. This helps calibrate your future estimates.
Never Overbet Kelly
Betting more than full Kelly actually decreases your expected growth rate and increases risk of ruin dramatically.
Consider Opportunity Cost
Don't bet just because Kelly is positive. If the expected growth is tiny, it may not be worth the risk and effort.
Adjust for Correlation
If placing multiple bets, reduce Kelly percentage for each bet to account for correlation and total portfolio risk.
Study Probabilities
The Kelly Criterion assumes you know the true probability. Invest time in learning to estimate probabilities accurately.
Frequently Asked Questions
What is a good Kelly percentage to bet?
Most professional bettors aim for Kelly percentages between 1-5% of their bankroll per bet. If full Kelly suggests betting more than 10%, it's a sign of either a very strong edge or potentially overestimated win probability. Many pros use half Kelly (betting 50% of the suggested amount) to reduce variance while still capturing most of the growth potential.
Should I use full Kelly or fractional Kelly?
Fractional Kelly is almost always the better choice. Half Kelly gives you 75% of the growth rate with significantly less volatility and is the industry standard among professional bettors. Quarter Kelly is ideal for beginners or when you're uncertain about your probability estimates. Full Kelly is only appropriate when you have extremely accurate probability estimates and can tolerate 50%+ drawdowns.
What does a negative Kelly percentage mean?
A negative Kelly percentage means you have no edge on this bet—the bookmaker's implied probability is better than your estimated win probability. Kelly Criterion recommends not placing this bet at all. In fact, a negative Kelly technically suggests you should bet the other side if possible. Never force a bet when Kelly is negative; wait for opportunities where you have a genuine edge.
How accurate does my win probability estimate need to be?
The Kelly Criterion is highly sensitive to probability estimates. A small error can lead to significant overbetting or underbetting. This is why fractional Kelly is so popular—it provides a buffer against estimation errors. If your estimates are off by even 5%, full Kelly can lead to overbetting and potential ruin. Track your predictions over time to calibrate your accuracy before using higher Kelly fractions.
Can I use Kelly Criterion for parlays and accumulators?
Yes, but you need to calculate the combined probability of all legs winning together. Multiply the individual win probabilities for each leg, then use the parlay odds in the Kelly formula. Be extra conservative with parlays because small errors in individual leg probabilities compound significantly. Most Kelly practitioners avoid parlays altogether or use quarter Kelly at most due to the compounded uncertainty.
How often should I recalculate my Kelly bet size?
Recalculate your Kelly bet size whenever your bankroll changes significantly—typically after each betting session or at least daily. Since Kelly uses a percentage of your current bankroll, your absolute bet sizes should grow after winning streaks and shrink after losing streaks. This automatic adjustment is one of Kelly's key features for protecting against ruin while maximizing growth.
What's the difference between Kelly Criterion and flat betting?
Flat betting uses the same fixed amount for every bet regardless of edge, while Kelly dynamically adjusts bet size based on your edge and bankroll. Kelly mathematically maximizes long-term growth when you have accurate probability estimates, but requires more discipline and calculation. Flat betting is simpler and less sensitive to estimation errors. Many recreational bettors prefer flat betting, while serious bettors with proven edges often use Kelly.
Does Kelly Criterion work for casino games?
For most casino games, Kelly Criterion will recommend not betting at all because the house edge means you have negative expected value. The only casino scenarios where Kelly applies are advantage play situations like card counting in blackjack or exploiting promotional offers. If you're playing standard casino games, Kelly will always return a negative or zero percentage because the math is against you.