Kelly Criterion Calculator
Calculate optimal bet size using the Kelly Criterion formula. Determine how much of your bankroll to wager based on win probability and odds for maximum long-term growth while managing risk of ruin.
= +100 American
Expected Value per $100
+10.00
Risk Assessment
Recommended: Use half Kelly (5.00%) to capture 75% of the growth rate while significantly reducing variance. Full Kelly has brutal drawdowns - expect to halve your bankroll before doubling it about 50% of the time.
Kelly Criterion Formula
f* = (bp - q) / bWhere:
- f* = Fraction of bankroll to bet
- b = Decimal odds - 1 (net odds)
- p = Your probability of winning
- q = Probability of losing (1 - p)
Example: 55% win probability at +100 odds (b=1): f* = (1 Ć 0.55 - 0.45) / 1 = 10% of bankroll
Why Use Fractional Kelly?
Full Kelly maximizes long-term growth but assumes perfect knowledge of your edge. In reality, your edge estimates are imprecise.
| Fraction | Growth Rate | Volatility | Best For |
|---|---|---|---|
| Full (100%) | Maximum | Very High | Theoretical only |
| Half (50%) | 75% of max | Moderate | Most professionals |
| Quarter (25%) | 50% of max | Low | Conservative/beginners |
| Tenth (10%) | 20% of max | Minimal | Uncertain edges |
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About This Calculator
"How much should I bet?" It's the question that separates professional bettors from recreational gamblers who eventually go broke. You might find a +EV bet with a clear edge, but bet too much and a losing streak wipes you out. Bet too little and your bankroll grows at a snail's pace. The Kelly Criterion, developed by Bell Labs scientist John Kelly in 1956, provides the mathematically optimal answer.
The Kelly Criterion tells you exactly what percentage of your bankroll to wager based on your edge and the odds offered. It maximizes your long-term growth rate while minimizing your risk of ruin - but here's what most articles won't tell you: full Kelly is almost never used by professionals. The formula assumes you know your true edge perfectly, which you never do. That's why sharp bettors use fractional Kelly (half or quarter) to account for uncertainty while still capturing most of the growth benefits.
Our Kelly Criterion Calculator takes your win probability, the odds offered, and your bankroll to compute optimal bet sizes at full, half, and quarter Kelly. It also calculates your edge, expected value per bet, and estimated risk of ruin - everything you need for professional-grade bankroll management.
How to Use the Kelly Criterion Calculator
- 1**Enter your win probability**: This is your estimated true probability of winning the bet, not the implied probability from the odds. Be honest - overestimating your edge is the #1 mistake.
- 2**Enter the odds offered**: Input the decimal odds (e.g., 2.50) or American odds (+150). The calculator converts between formats automatically.
- 3**Enter your bankroll**: Your total betting bankroll - money specifically set aside for wagering that you can afford to lose.
- 4**Review the Kelly percentages**: See full Kelly, half Kelly, and quarter Kelly recommendations with actual dollar amounts.
- 5**Check your edge and EV**: The calculator shows your edge (your probability minus implied probability) and expected value per $100 wagered.
- 6**Consider risk of ruin**: Review the estimated probability of losing your entire bankroll at different Kelly fractions.
- 7**Choose your Kelly fraction**: Most professionals use half or quarter Kelly. Full Kelly maximizes growth but with significant variance.
- 8**Adjust for uncertainty**: If you're less confident in your edge estimate, use a smaller Kelly fraction (quarter Kelly is safest).
Formula
f* = (bp - q) / bThe Kelly Criterion formula calculates the optimal fraction (f*) of your bankroll to wager. The variables are: b = decimal odds minus 1 (the "odds to 1"), p = probability of winning, and q = probability of losing (which equals 1 - p). For example, if you have a 55% win probability at +100 odds (b = 1): f* = (1 Ć 0.55 - 0.45) / 1 = 0.10, meaning bet 10% of your bankroll. A negative Kelly value means you have no edge - don't bet at all.
Understanding the Kelly Criterion Formula
The Core Formula:
The Kelly Criterion determines what fraction of your bankroll to bet:
f = (bp - q) / b*
Where:
- f* = fraction of bankroll to wager
- b = decimal odds - 1 (the "net odds" or "odds to 1")
- p = probability of winning (as decimal, e.g., 55% = 0.55)
- q = probability of losing (1 - p)
Step-by-Step Calculation:
Let's say you estimate a team has a 55% chance of winning at +120 odds (2.20 decimal).
- Convert to "odds to 1": b = 2.20 - 1 = 1.20
- Win probability: p = 0.55
- Loss probability: q = 1 - 0.55 = 0.45
- Kelly formula: f* = (1.20 Ć 0.55 - 0.45) / 1.20
- Calculate: f* = (0.66 - 0.45) / 1.20 = 0.21 / 1.20 = 0.175
Result: Bet 17.5% of your bankroll
Understanding the Output:
| Kelly Value | Meaning |
|---|---|
| f* > 0 | You have an edge - bet this fraction |
| f* = 0 | No edge - don't bet |
| f* < 0 | Negative edge - the other side has value |
| f* > 0.25 | Large edge - but verify your probability estimate |
Alternative Formula (American Odds):
For American odds, you can use:
Positive odds (+150):
- b = American Odds / 100 = 1.50
Negative odds (-150):
- b = 100 / |American Odds| = 0.667
Then apply the standard Kelly formula with these values.
Why Professional Bettors Use Fractional Kelly
The Problem with Full Kelly:
Full Kelly maximizes long-term growth rate, but it comes with brutal volatility. Mathematical simulations show that betting full Kelly:
- Has roughly a 50% chance of halving your bankroll before doubling it
- Can experience 85% drawdowns as part of normal variance
- Assumes you know your exact edge (you don't)
The Fractional Kelly Solution:
| Fraction | Growth Rate | Max Drawdown | Risk of Ruin |
|---|---|---|---|
| Full Kelly (100%) | Maximum | Very High (85%+) | Low but painful |
| Half Kelly (50%) | 75% of max | Moderate (50-60%) | Very Low |
| Quarter Kelly (25%) | 50% of max | Low (25-35%) | Negligible |
| One-Tenth Kelly (10%) | 20% of max | Minimal (10-15%) | Essentially Zero |
Why Half Kelly is the Sweet Spot:
Half Kelly is the most popular choice among professionals because:
- 75% of the growth rate - You capture most of the compounding benefit
- Half the variance - Your swings are dramatically reduced
- Margin for error - If you overestimate your edge by 2x, you're still only at full Kelly
- Psychological sustainability - You can actually stick to the strategy through losing streaks
When to Use Different Fractions:
| Situation | Recommended Kelly |
|---|---|
| High confidence in edge estimate | Half Kelly (50%) |
| Moderate confidence | Quarter Kelly (25%) |
| New to a market/sport | Tenth Kelly (10%) |
| Using someone else's picks | Quarter Kelly or less |
| Correlated bets in a day | Reduce total exposure |
| High-vig markets (props, futures) | Quarter Kelly |
The Overconfidence Trap:
Studies show bettors consistently overestimate their edges. If your true edge is half what you think:
- Full Kelly becomes 2x Kelly ā bankroll destruction
- Half Kelly becomes full Kelly ā still optimal
- Quarter Kelly becomes half Kelly ā conservative but profitable
This asymmetry is why fractional Kelly is essential, not optional.
Edge Calculation and Expected Value
What is Your "Edge"?
Your edge is the difference between your estimated win probability and the implied probability from the odds:
Edge = Your Probability - Implied Probability
The implied probability from odds is what you'd need to win to break even:
- At +150 (2.50 decimal): Implied = 1/2.50 = 40%
- At -150 (1.67 decimal): Implied = 1/1.67 = 60%
Example Edge Calculation:
You think a team has a 50% chance of winning at +150 odds.
- Implied probability: 40% (from the +150)
- Your estimate: 50%
- Your edge: 50% - 40% = 10%
This is a significant edge. At these odds with this edge:
- Full Kelly suggests betting 20% of bankroll
- Half Kelly: 10% of bankroll
- Quarter Kelly: 5% of bankroll
Expected Value per Bet:
Expected Value (EV) tells you how much you expect to profit per dollar wagered:
EV = (Probability Ć Win Amount) - (Loss Probability Ć Stake)
Example at +150 with 50% true probability:
- EV = (0.50 Ć $150) - (0.50 Ć $100)
- EV = $75 - $50 = +$25 per $100 bet
Edge vs EV Relationship:
| Your Edge | Typical EV per $100 |
|---|---|
| 2% | +$2 to +$4 |
| 5% | +$5 to +$10 |
| 10% | +$10 to +$20 |
| 15% | +$15 to +$30 |
| 20%+ | Extremely rare |
Most professional sports bettors operate with 2-5% edges. Edges above 10% are rare and should make you question whether your probability estimate is accurate.
Red Flags for Edge Estimates:
- Kelly suggests >25% of bankroll ā Recheck your math
- Your edge seems >15% ā You may be overconfident
- You "feel" like it's a lock ā Emotions, not analysis
- The line hasn't moved ā Market disagrees with you
Risk of Ruin: Protecting Your Bankroll
What is Risk of Ruin?
Risk of ruin is the probability of losing your entire bankroll before reaching your profit goal (or "forever" in the long run). Even with a positive edge, aggressive betting can lead to bankruptcy.
Risk of Ruin Formula (Simplified):
For even-money bets with edge e and betting fraction f:
RoR ā ((1-e)/(1+e))^(B/f)
Where B is bankroll in units. This simplifies the relationship between bet sizing and survival.
Risk of Ruin by Kelly Fraction:
| Kelly Fraction | Approx. RoR (5% Edge) | Approx. RoR (2% Edge) |
|---|---|---|
| Full Kelly | ~1-5% | ~5-10% |
| Half Kelly | <0.5% | ~1-2% |
| Quarter Kelly | <0.01% | <0.1% |
| Tenth Kelly | Essentially 0% | Essentially 0% |
The Variance Reality:
Full Kelly optimizes for maximum growth but accepts brutal swings:
- 50% chance of halving before doubling
- 25% chance of reaching 25% of your starting bankroll
- 10% chance of reaching 10% of starting bankroll
These aren't "disasters" - they're normal Kelly variance. Most people can't psychologically handle watching their bankroll drop 75% even when the strategy is mathematically optimal.
Bankroll Recommendations by Strategy:
| Betting Style | Minimum Bankroll | Recommended Bankroll |
|---|---|---|
| Full Kelly | 50 units | 100+ units |
| Half Kelly | 30 units | 50+ units |
| Quarter Kelly | 20 units | 30+ units |
| Fixed 1-2% flat | 50 units | 100+ units |
A "unit" is your standard bet size. With quarter Kelly on a $10,000 bankroll, your bets might range from $100-500 depending on edge.
Practical Risk Management:
- Never bet money you can't lose - Your bankroll should be 100% discretionary
- Start smaller than you think - Use quarter Kelly until you prove your edge exists
- Track everything - You can't manage what you don't measure
- Set stop losses - Consider stopping if you hit 50% drawdown to reassess
- Separate bankrolls - Don't mix betting money with living expenses
Bankroll Management Best Practices
The Professional Approach:
Professional bettors treat betting like a business. Key principles:
- Dedicated Bankroll: Separate account only for betting
- Proper Sizing: Never risk more than Kelly suggests
- Detailed Records: Track every bet, probability estimate, and result
- Regular Review: Assess whether your edge estimates are accurate
- Emotional Discipline: Never chase losses or increase bets after wins
How Much Should Your Bankroll Be?
Base your bankroll on:
- What you can truly afford to lose (100%)
- Your expected bet volume
- Your preferred Kelly fraction
Example calculation:
- You want to bet 5 games per day
- Average edge: 3%
- Using quarter Kelly: ~2-3% of bankroll per bet
- To bet $50 per game: Need ~$2,000 bankroll
Handling Winning and Losing Streaks:
Kelly Naturally Adjusts:
One beauty of Kelly betting is automatic adjustment:
- After wins, your bankroll grows ā bets get larger
- After losses, bankroll shrinks ā bets get smaller
This protects you during losing streaks and accelerates growth during winning streaks.
Never do these:
- Increase bets to "get back to even" after losses
- Decrease bets after wins because you're "due for a loss"
- Bet more because you "feel it" about a game
Correlation and Multiple Bets:
When betting multiple games in one day:
- Independent events: Each bet can use full Kelly allocation
- Correlated events: Reduce total exposure
- Same player/team props: Highly correlated - be careful
Example: If you're betting 3 NFL games and one upset affects the other results, your total exposure should be less than 3Ć single-bet Kelly.
Withdrawing Profits:
Two schools of thought:
- Never withdraw: Let compounding work its magic
- Regular withdrawals: Take profits at milestones
A middle ground: Withdraw 50% of profits quarterly while keeping your working bankroll at a fixed target level.
Common Kelly Criterion Mistakes
Mistake #1: Overestimating Your Edge
The most dangerous mistake in Kelly betting. If you think you have a 10% edge but really have 5%:
- Full Kelly becomes 2Ć Kelly ā bankroll destruction
- Your expected growth becomes negative
Solution: Always use fractional Kelly (half or quarter) to build in margin for error.
Mistake #2: Using Kelly for Negative EV Bets
Kelly is meaningless without a real edge. Applying Kelly to casino games or betting "gut feelings" doesn't create value - it just helps you lose optimally.
Test your edge: Track 500+ bets. If you're not profitable at flat betting, Kelly won't help.
Mistake #3: Ignoring Correlation
Kelly assumes independent bets. If you bet:
- Same team across multiple markets
- Player props that are outcome-dependent
- Parlays
Your actual risk is higher than Kelly suggests. Reduce exposure accordingly.
Mistake #4: Using One Bankroll Number
Your "bankroll" should be your total betting capital, not what's in one sportsbook. If you have $2,000 across DraftKings, FanDuel, and BetMGM:
- Bankroll = $6,000 total
- Kelly calculations use $6,000
- Individual book balances don't matter
Mistake #5: Rounding Up Kelly Bets
Kelly often gives numbers like 2.7% or 4.3%. Don't round up:
| Kelly Says | Wrong | Right |
|---|---|---|
| 2.7% | Bet 3% | Bet 2.5% or 2.7% |
| 4.3% | Bet 5% | Bet 4% or 4.3% |
| 8.6% | Bet 10% | Bet 8.5% or lower |
Consistently rounding up accumulates to significant overbetting.
Mistake #6: Not Adjusting for Uncertainty
Your 55% probability estimate isn't 55.000%. It might be anywhere from 50-60%. Factor this in:
- High confidence (strong model): Half Kelly
- Medium confidence: Quarter Kelly
- Low confidence (subjective): Tenth Kelly or skip
Mistake #7: Emotional Kelly Adjustments
"I feel great about this one, so I'll bet more" "I've lost 5 in a row, better bet smaller"
Kelly already accounts for probability. Making emotional adjustments destroys the mathematical edge the formula provides.
Kelly Criterion for Different Bet Types
Standard Single Bets:
Use the basic Kelly formula directly:
- f* = (bp - q) / b
- Apply your chosen Kelly fraction (typically 50% or 25%)
Parlays and Accumulators:
Parlays amplify both edge AND variance. For Kelly on parlays:
- Calculate combined probability: pā Ć pā Ć pā...
- Calculate combined odds: dā Ć dā Ć dā...
- Apply Kelly to combined values
- Use even smaller Kelly fraction (quarter or less)
Warning: The Kelly percentage for parlays is often smaller than you'd expect. A 3-leg parlay might suggest only 1% of bankroll even with edges on each leg.
Futures and Outrights:
Long-term bets tie up capital. Adjust Kelly for:
- Capital lock-up: Money isn't available for other bets
- Time value: Opportunity cost of waiting
- Higher uncertainty: Probability estimates are less reliable
Rule of thumb: Use quarter Kelly or less for futures, and count the bet against your daily exposure limit even though it won't settle for months.
In-Play / Live Betting:
Rapid-fire betting during games is dangerous for Kelly:
- Less time to estimate probabilities
- Lines move quickly
- Easy to overtrade
If live betting, use tenth Kelly or have strict daily limits regardless of Kelly suggestions.
Arbitrage Bets:
For true arbitrage (guaranteed profit), Kelly doesn't apply - you're not risking anything. But for "soft" arbitrage with slight timing risk, extremely small Kelly fractions (or flat 1% bets) are appropriate.
Betting Exchanges:
When trading on exchanges (back and lay), Kelly applies to each position separately. Be aware of:
- Lay bets have liability > stake
- Adjust Kelly for your actual liability, not stake
- Account for commission on winnings
Pro Tips
- š”Never use full Kelly - even professionals rarely go above half Kelly because overestimating your edge is devastating.
- š”Your bankroll is your TOTAL betting capital across all sportsbooks, not just one account balance.
- š”Track every bet with your probability estimate. After 500+ bets, compare estimates to actual results to calibrate.
- š”If Kelly suggests more than 15% of your bankroll, double-check your probability estimate - you may be overconfident.
- š”Start with quarter Kelly until you've proven your edge over at least 500 bets, then consider moving to half Kelly.
- š”Never round up Kelly recommendations. If Kelly says 2.7%, bet 2.5% or 2.7%, not 3%.
- š”Account for correlation when betting multiple games - your total exposure should be less than the sum of individual Kelly amounts.
- š”A negative Kelly value means the bet has negative expected value - don't bet at all.
- š”Kelly already handles losing streaks automatically by reducing bet sizes - never manually increase bets to chase losses.
- š”Consider stopping and reassessing if you experience a 50% drawdown - this is unusual even at half Kelly and may indicate edge estimation problems.
- š”For futures and long-term bets, use quarter Kelly or less due to capital lock-up and higher uncertainty.
- š”Your edge likely ranges from 1-5%. Edges above 10% are extremely rare and should make you question your analysis.
Frequently Asked Questions
The Kelly Criterion is a mathematical formula developed by John Kelly in 1956 that determines the optimal size of a series of bets to maximize long-term wealth growth. The formula is f* = (bp - q) / b, where f* is the fraction of your bankroll to bet, b is the decimal odds minus 1 (the net odds), p is your probability of winning, and q is your probability of losing (1 - p). It works by finding the bet size that maximizes the expected logarithm of wealth - which corresponds to maximum geometric growth rate. When you have an edge (your estimated probability exceeds the implied probability from odds), Kelly tells you exactly how much to bet to grow your bankroll fastest while avoiding ruin.
