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Kelly Criterion Guide
The math behind optimal bet sizing. Bet too much, you go broke. Bet too little, you leave money on the table.
What Is the Kelly Criterion?
The Kelly Criterion is a formula that tells you exactly how much to bet to maximize long-term bankroll growth. It was developed by John Larry Kelly Jr. in 1956 at Bell Labs — originally for information theory, not sports betting.
Professional bettors and hedge fund managers use it. The math is proven. The hard part isn't the formula — it's estimating your edge accurately.
The Formula
Kelly % = (bp - q) / b
Where:
b = decimal odds - 1 (your profit per $1 bet)
p = probability of winning
q = probability of losing (1 - p)
Here's a worked example. You estimate a 55% chance of winning a -110 bet:
- b = 0.909 (decimal odds 1.909 - 1)
- p = 0.55
- q = 0.45
- Kelly % = (0.909 × 0.55 - 0.45) / 0.909 = 10.1%
With a $10,000 bankroll, you'd bet $1,010. That's a big bet — and that's the point. Kelly bets aggressively when you have an edge.
Why Kelly Works
Three reasons the math is solid:
- Maximizes geometric growth. Kelly optimizes for the long run, not any single bet.
- Prevents over-betting. Bet too much and you go broke even with an edge. Kelly prevents that.
- Adjusts based on edge size. Bigger edge = bigger bet. Smaller edge = smaller bet. It's adaptive.
Fractional Kelly: The Smart Approach
Here's the thing — full Kelly is aggressive. Really aggressive. Most professionals use fractional Kelly, betting a fraction (usually 1/4 to 1/2) of the full Kelly amount.
| Kelly Fraction | Growth Rate | Volatility |
|---|
| Full Kelly (1/1) | 100% | Maximum |
| Half Kelly (1/2) | 75% | 50% |
| Quarter Kelly (1/4) | 50% | 25% |
Half Kelly gives you 75% of the growth rate with 50% of the volatility. That's a trade-off most professionals happily make.
Why not full Kelly? Because your edge estimate is never perfect. If you think your edge is 5% but it's really 3%, full Kelly will over-bet and increase your risk of ruin. Fractional Kelly gives you a safety margin.
When to Use Kelly
- When you have a genuine edge. Kelly is useless — even harmful — if you're guessing at probabilities.
- For bankroll management. It tells you exactly how much to risk on each bet.
- To prevent emotional betting. The formula removes ego from the equation.
- For long-term wealth building. This is how professional bettors compound their edge over time.
When NOT to Use Kelly
- Recreational betting. If you're betting for fun, Kelly takes the fun out of it.
- When you don't have an edge. Kelly on a coin flip at -110 tells you to bet zero. That's correct.
- When your estimates are rough. If you're not confident in your probability estimates, use quarter Kelly or skip it entirely.
Pro Tips
- Your edge estimate must be accurate. Garbage in, garbage out. Kelly is only as good as your probability estimates.
- Start with quarter Kelly. It's safer. You can always increase later.
- Track your results to calibrate. If Kelly says bet 5% but you're going broke, your edge estimates are too high.
- Kelly works best with many small bets. The more bets you make, the closer you get to the theoretical growth rate.
- Never bet more than Kelly suggests. Even if you "feel" confident. The math doesn't care about your feelings.
Try Our Kelly Criterion Calculator →
Frequently Asked Questions
What if Kelly says to bet zero?
That means you don't have an edge. Don't bet. It's the most valuable output Kelly gives you — telling you when to stay on the sidelines.
Can I use Kelly for parlays?
Technically yes, but the probability estimates for parlays are much harder to make accurately. Stick to single bets for Kelly.
How often should I recalculate?
Every time your bankroll changes significantly (10%+), or when you get new information that changes your edge estimate. Most people recalculate weekly.
For informational purposes only. Not legal gambling advice. Must be 21+ in your jurisdiction. Gamble responsibly.