What Is the Kelly Criterion?
The Kelly Criterion is a mathematical formula that determines the optimal bet size to maximize long-term bankroll growth. Developed by John L. Kelly Jr. at Bell Labs in 1956, it has become one of the most important concepts in professional betting and investment.
The Kelly formula answers a fundamental question: “How much should I bet?”
The Kelly Formula
f* = (bp - q) / b
Where:
- f* = fraction of bankroll to bet
- b = decimal odds minus 1 (net odds received)
- p = probability of winning
- q = probability of losing (1 - p)
Alternative Formula (More Intuitive)
Kelly % = (Probability × Odds - 1) / (Odds - 1)
Or simply:
Kelly % = Edge / Odds
How to Use the Kelly Criterion Calculator
Step 1: Enter the Odds
Input the odds for your bet in any format:
- Decimal (e.g., 2.50)
- Fractional (e.g., 3/2)
- American (e.g., +150)
Step 2: Estimate Win Probability
This is the crucial step. Enter your estimated probability of the bet winning (as a percentage).
Important: Your probability estimate must be based on your own analysis, not the implied probability from the odds. If you simply use implied probability, Kelly will always return 0%.
Step 3: Enter Your Bankroll (Optional)
If you want to see the actual dollar amount to stake, enter your total betting bankroll.
Step 4: Choose Kelly Fraction
Select how aggressive you want to be:
- Full Kelly (100%) - Maximum growth, maximum volatility
- Half Kelly (50%) - Reduced volatility, still strong growth
- Quarter Kelly (25%) - Conservative approach, smoother ride
Understanding the Calculator Output
Kelly Percentage
The recommended percentage of your bankroll to stake. A 10% Kelly means betting 10% of your bankroll.
Edge
Your expected profit per unit bet. A 5% edge means you expect to profit $5 for every $100 wagered (on average).
Edge = (Probability × Decimal Odds) - 1
Expected Value (EV)
The mathematical expectation per unit. Positive EV means the bet is profitable long-term.
Implied Probability
What the bookmaker’s odds suggest about the outcome’s probability. Compare this to your estimate to find value.
Optimal Stake
The actual amount to bet based on your bankroll and selected Kelly fraction.
Kelly Criterion Examples
Example 1: Positive Edge Bet
Scenario:
- Odds: 2.50 (decimal)
- Your probability estimate: 45%
- Bankroll: $1,000
Calculation:
b = 2.50 - 1 = 1.50
p = 0.45
q = 0.55
Kelly % = (1.50 × 0.45 - 0.55) / 1.50
Kelly % = (0.675 - 0.55) / 1.50
Kelly % = 0.125 / 1.50
Kelly % = 8.33%
Result:
- Full Kelly stake: $83.30 (8.33% of $1,000)
- Half Kelly stake: $41.65
- Edge: 12.5% (very strong)
Example 2: Close to Fair Odds
Scenario:
- Odds: 2.00 (even money)
- Your probability estimate: 52%
- Bankroll: $1,000
Calculation:
Kelly % = (1.00 × 0.52 - 0.48) / 1.00
Kelly % = 4%
Result:
- Full Kelly stake: $40
- Half Kelly stake: $20
- Edge: 4%
Example 3: No Edge (Don’t Bet)
Scenario:
- Odds: 2.00
- Your probability estimate: 48%
Result:
- Kelly % = -4% (negative)
- Recommendation: Don’t bet
A negative Kelly means you have negative expected value. The calculator will show “No Bet.”
Why Use Kelly Criterion?
Advantages
-
Mathematically Optimal Kelly maximizes the expected logarithm of wealth - proven to maximize long-term growth rate.
-
Bankroll Protection Never suggests betting your entire bankroll (unless you have 100% certainty).
-
Scales with Edge Larger bets for bigger edges, smaller bets for marginal edges.
-
Prevents Overbetting Even with a huge edge, Kelly limits stake to protect against variance.
The Math Behind Long-Term Growth
Over many bets, Kelly betting leads to:
Growth Rate = p × log(1 + bf*) + q × log(1 - f*)
This is maximized exactly at the Kelly fraction.
Fractional Kelly: Managing Volatility
Full Kelly betting can be psychologically challenging due to high variance. Many professional bettors use fractional Kelly:
| Kelly Fraction | Volatility | Growth Rate | Recommended For |
|---|---|---|---|
| Full (100%) | Very High | Maximum | Theoretical/Confident estimates |
| 3/4 Kelly | High | ~94% of max | Experienced bettors |
| Half (50%) | Moderate | ~75% of max | Most bettors |
| Quarter (25%) | Low | ~50% of max | Conservative/Beginners |
Why Half Kelly Is Popular
Half Kelly achieves:
- 75% of the growth rate
- Only 25% of the variance
- Much smoother bankroll trajectory
The trade-off is worth it for most bettors.
Common Kelly Criterion Mistakes
Mistake 1: Overestimating Win Probability
The Problem: Kelly is extremely sensitive to probability estimates. Overestimate by 5% and you’ll massively overbet.
Solution: Be conservative. If you think 55%, use 52-53%.
Mistake 2: Using Implied Probability
The Problem: If you use the bookmaker’s implied probability, your edge is zero (actually negative due to margin).
Solution: Always use YOUR OWN analysis for win probability.
Mistake 3: Betting Full Kelly
The Problem: Full Kelly is optimal theoretically but brutal in practice. A bad run can wipe 50%+ of your bankroll.
Solution: Use Half Kelly or Quarter Kelly.
Mistake 4: Ignoring Bankroll Updates
The Problem: Betting the same amount regardless of bankroll changes.
Solution: Recalculate Kelly stake based on current bankroll for each bet.
Mistake 5: Applying Kelly to Correlated Bets
The Problem: Betting full Kelly on multiple games that could all lose together.
Solution: Reduce Kelly percentage when betting on correlated events.
Kelly Criterion for Different Betting Scenarios
Single Bets
Use the standard formula directly. This calculator handles this case.
Multiple Bets (Same Event)
If betting on multiple outcomes of the same event, reduce total exposure to Kelly of the best single bet.
Parlays/Accumulators
Kelly can be applied but requires the combined probability of all legs. Generally not recommended for parlays.
Live Betting
Recalculate Kelly as odds change during the event. Be cautious as live probability estimation is difficult.
Kelly vs. Flat Betting
| Aspect | Kelly Criterion | Flat Betting |
|---|---|---|
| Stake Size | Varies with edge | Fixed percentage |
| Optimal Growth | Maximum | Suboptimal |
| Variance | Can be high | More consistent |
| Required Skill | Probability estimation | None |
| Bankroll Protection | Built-in | You decide |
When to use Kelly: When you can accurately estimate probabilities and want maximum growth.
When to use Flat: When you can’t estimate probabilities reliably or prefer simplicity.
Advanced Kelly Concepts
Kelly and Bankroll Trajectory
With Kelly betting:
- Your bankroll follows a geometric random walk
- Long-term growth is almost certain (with positive EV bets)
- Short-term drawdowns are normal and expected
Simultaneous Kelly
When placing multiple bets at once:
Total Exposure = Sum of individual Kelly %
If total exceeds 100%, scale down proportionally.
Kelly with Transaction Costs
If there are fees or costs:
Adjusted Kelly = Standard Kelly - (Cost / Bet Size)
Practical Tips for Using Kelly
1. Start with Quarter Kelly
Until you’re confident in your probability estimates, be conservative.
2. Track Your Results
Compare actual win rates to estimates. Adjust your estimation process accordingly.
3. Set a Maximum Stake
Even with high edge, cap stakes at 5-10% of bankroll to handle estimation errors.
4. Use for Long-Term Planning
Kelly works over hundreds of bets. Don’t judge results on 10-20 bets.
5. Combine with Value Betting
Kelly tells you HOW MUCH to bet. Value betting tells you WHAT to bet. Use both.
Frequently Asked Questions
What is a good Kelly percentage?
Typically 1-5% for most value bets. Above 10% suggests either a very strong edge or possibly an overestimated probability. Most pros use half or quarter Kelly to reduce variance.
What if Kelly shows negative percentage?
A negative Kelly means you have negative expected value - don’t place the bet. The odds aren’t good enough for your estimated probability.
How do I estimate win probability?
Use historical data, statistical models, expert analysis, or your own research. The key is developing your own view independent of the bookmaker’s odds. Many successful bettors use regression models or Elo ratings.
Is Kelly Criterion better than flat betting?
Kelly is mathematically optimal for long-term growth if you can accurately estimate probabilities. However, flat betting is simpler and less sensitive to estimation errors. Many recreational bettors prefer flat betting.
Why use half Kelly instead of full Kelly?
Half Kelly gives 75% of the growth rate with only 25% of the variance. This dramatically reduces drawdowns and makes the betting experience more sustainable psychologically.
Can I use Kelly for accumulators?
Technically yes, but you need accurate probability estimates for the combined outcome. In practice, Kelly is most useful for single bets where probability estimation is more reliable.
Start Optimizing Your Bet Sizes
Use our free Kelly Criterion calculator above to:
- Enter odds in any format (decimal, fractional, American)
- Input your estimated win probability
- Enter your bankroll (optional)
- Choose your Kelly fraction (full, half, or quarter)
- See your optimal stake and expected value
The calculator instantly shows whether a bet has positive expected value and exactly how much to stake for optimal long-term growth.
Remember: Kelly is only as good as your probability estimates. Be honest with yourself, track your results, and adjust your approach over time.