You’ve found a +EV bet. You know you have an edge. But how much should you wager? Too little and you’re leaving money on the table. Too much and a losing streak wipes you out. The Kelly Criterion gives you the mathematically optimal answer.
What is the Kelly Criterion?
The Kelly Criterion is a formula that calculates the optimal bet size to maximize long-term bankroll growth. It was developed by John Kelly at Bell Labs in 1956 and has since become the gold standard for bet sizing in finance, gambling, and investing.
Kelly tells you the exact percentage of your bankroll to wager based on your edge and the odds.
The Formula
Kelly % = (bp - q) / b
Where:
b = decimal odds - 1 (the net profit per $1 wagered)
p = your estimated probability of winning
q = probability of losing (1 - p)
Example
You find a bet at +150 odds and estimate the true win probability is 45%:
b = 1.50 (decimal odds 2.50 - 1)
p = 0.45
q = 0.55
Kelly % = (1.50 × 0.45 - 0.55) / 1.50 = (0.675 - 0.55) / 1.50 = 0.0833 = 8.33%
On a $1,000 bankroll, Kelly says to bet $83.30.
Try the kelly-criterion-calculator→
Why Kelly Works
Kelly maximizes the geometric growth rate of your bankroll. In simple terms, it grows your bankroll as fast as mathematically possible without risking ruin.
Bet more than Kelly: You risk overbetting and potential ruin
Bet exactly Kelly: Maximum long-term growth rate
Bet less than Kelly: Slower growth but less volatility
The key insight is that Kelly balances aggression (betting more on bigger edges) with survival (never risking so much that a loss is catastrophic).
Full Kelly vs. Fractional Kelly
Full Kelly is mathematically optimal but comes with wild swings. Most professional bettors use fractional Kelly — betting a fraction of what the formula recommends.
| Approach | Bet Size | Growth Rate | Volatility |
|---|---|---|---|
| Full Kelly | 100% of Kelly | Maximum | High |
| Half Kelly | 50% of Kelly | 75% of max | Much lower |
| Quarter Kelly | 25% of Kelly | ~56% of max | Low |
Half Kelly is the most common recommendation. You sacrifice 25% of the theoretical growth rate but cut volatility dramatically. For most bettors, the smoother ride is worth it.
When Kelly Says “Don’t Bet”
If the Kelly formula returns a negative number, the bet is -EV. Don’t place it. The formula naturally tells you to wager 0% on bad bets.
If the formula returns 0%, the bet is break-even. You have no edge and there’s no reason to bet.
Common Mistakes with Kelly
Overestimating Your Edge
Kelly is only as good as your probability estimate. If you think you have a 60% edge but you really have 50%, Kelly will have you massively overbetting. This is the most dangerous mistake. When in doubt, be conservative with your probability estimates and use fractional Kelly.
Ignoring Correlation
If you have multiple bets that are correlated (like two players on the same team), Kelly for each bet individually will overestimate the safe bet size. The bets aren’t independent.
Using Full Kelly
In theory, full Kelly is optimal. In practice, the variance is brutal. A few bad losses at full Kelly can crater your bankroll. Half or quarter Kelly is almost always the smarter move.
Not Recalculating
Your bankroll changes after every bet. Kelly should be recalculated based on your current bankroll, not your starting bankroll. As you win, your bet sizes increase. As you lose, they decrease. This is built-in risk management.
Kelly for Sports Betting: Practical Tips
Start with quarter Kelly until you’ve verified your edge over a few hundred bets
Be conservative with win probability estimates — if you think 55%, use 52-53%
Recalculate after every session based on current bankroll
Cap maximum bet size at 3-5% of bankroll regardless of what Kelly says
Track your results to validate that your probability estimates are accurate
Key Takeaways
Kelly Criterion gives the mathematically optimal bet size based on your edge
Use fractional Kelly (half or quarter) in practice to reduce volatility
The formula requires accurate probability estimates — garbage in, garbage out
Kelly naturally protects your bankroll: big edges get bigger bets, no edge means no bet
