Free Kelly Criterion Calculator – Optimal Bet Sizing Formula
This free Kelly calculator determines your mathematically optimal bet size based on your edge and odds. Enter your win probability and payout odds to see exactly what percentage of your bankroll to wager. The formula maximizes long-term growth while managing risk.
This is an educational and research tool only. All content is for learning and simulation purposes; we do not provide gambling advice or real-money recommendations.
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What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula that calculates the optimal bet size to maximize long-term bankroll growth. Developed by John Kelly at Bell Labs in 1956, it's used by professional gamblers, stock traders, and hedge funds.
The formula: Kelly % = (bp - q) / b. Where b = decimal odds - 1, p = win probability, q = loss probability (1 - p).
Unlike fixed betting systems, Kelly adjusts bet size based on your actual edge. Bigger edge = bigger bet. No edge = no bet.
The Kelly Formula Explained
Example Calculation
You estimate 55% win probability on an even-money bet (+100 odds, decimal 2.0).
b = 2.0 - 1 = 1. p = 0.55. q = 0.45.
Kelly % = (1 × 0.55 - 0.45) / 1 = 0.10 = 10%
Optimal bet: 10% of your bankroll. With $1,000 bankroll, bet $100.
When Kelly Says Don't Bet
If the formula returns zero or negative, you have no edge. Don't bet. Example: 45% win probability on even money. Kelly % = (1 × 0.45 - 0.55) / 1 = -0.10. Negative means the house has the edge.
Kelly Criterion Results Table
| Win Probability | Even Money (+100) | 2:1 Odds (+200) | 3:1 Odds (+300) |
|---|---|---|---|
| 50% | 0% (no edge) | 0% | 0% |
| 52% | 4% | 2% | 1.3% |
| 55% | 10% | 5% | 3.3% |
| 60% | 20% | 10% | 6.7% |
| 65% | 30% | 15% | 10% |
Higher odds require less certainty, but also recommend smaller bets relative to your edge.
Full Kelly vs Fractional Kelly
Full Kelly
Betting the exact calculated percentage. Maximizes growth rate but creates high volatility. Bankroll can swing wildly.
Half Kelly (Recommended)
Bet 50% of the Kelly recommendation. Reduces growth rate by 25% but cuts variance by 50%. Most professionals use half or quarter Kelly.
Quarter Kelly
Very conservative. Growth is slower but drawdowns are minimal. Good for uncertain edge estimates.
| Kelly Fraction | Growth Rate | Risk of Ruin | Best For |
|---|---|---|---|
| Full (100%) | Maximum | High volatility | Certain edge |
| Half (50%) | 75% of max | Moderate | Most bettors |
| Quarter (25%) | 50% of max | Low | Uncertain edge |
Why Kelly Works
Kelly balances two extremes. Bet too small and you waste your edge. Bet too large and one loss destroys your bankroll. Kelly finds the mathematical sweet spot.
Over thousands of bets, Kelly-sized wagers grow your bankroll faster than any other consistent strategy – assuming your edge estimate is accurate.
Common Mistakes
Overestimating Edge
If you think you have 60% win rate but actually have 52%, you'll over-bet dramatically. Be conservative with estimates.
Using Full Kelly
Full Kelly is theoretically optimal but practically brutal. A few losses can cut your bankroll in half. Use fractional Kelly.
Ignoring Kelly's Zero
When Kelly returns 0% or negative, the math says don't bet. Many gamblers ignore this and bet anyway. That's how edges disappear.
Frequently Asked Questions
Does Kelly work for casino games?
Only if you have an edge (card counting, promotional offers, etc.). For standard casino games with house edge, Kelly says don't bet.
How do I estimate my win probability?
Track your historical results. 100+ bets minimum for meaningful data. Your actual win rate is your best probability estimate.
Can I use Kelly for sports betting?
Yes – Kelly is most commonly used for sports betting. You need to estimate win probability better than the implied odds suggest.
What if my edge changes?
Recalculate Kelly for each bet. Different matchups have different edges. This calculator handles variable inputs.