Kelly Criterion Calculator – Optimal Bet Sizing When You Have an Edge
Calculate the mathematically optimal bet size using the Kelly Criterion. Unlike other betting systems, Kelly only works when you have a genuine edge. No edge? Kelly says don’t bet. This is the formula professional gamblers and investors actually use.
For educational purposes only. Kelly requires accurate edge estimation — overestimate and you’ll overbid.
How This Kelly Criterion Calculator Works
Enter your win probability and odds. The calculator shows optimal bet percentage, expected growth rate, and risk of ruin at different Kelly fractions. You’ll see why professionals use half-Kelly or quarter-Kelly.
| R | Bet | Loss | Profit |
|---|
| # | Bet | Result | P/L |
|---|
Why Kelly Is Different From Every Other System
Martingale, Fibonacci, Paroli — all try to beat negative expectation games. They can’t. Kelly doesn’t try. It assumes you already have an edge and tells you how much to bet to maximize long-term growth without going broke.
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Kelly Criterion: The Only "System" That Actually Works
Every other betting system on this site tries to beat games where you have no edge. They all fail eventually. Kelly Criterion is different — it doesn't try to create an edge. It assumes you already have one and tells you exactly how much to bet.
The formula was developed by John Kelly at Bell Labs in 1956 for signal noise problems. Gamblers and investors quickly adopted it. Today, everyone from poker pros to hedge fund managers uses Kelly. Why? Because it mathematically maximizes long-term growth while minimizing risk of ruin. See the mathematical proof for details.
| Other Systems | Kelly Criterion |
|---|---|
| Try to overcome house edge | Requires existing edge |
| Eventually go broke | Maximizes survival |
| Arbitrary bet sizing | Mathematically optimal sizing |
| Work short-term (maybe) | Works long-term (proven) |
If you're playing roulette or baccarat, close this page — you have no edge. If you're a poker player, sports bettor with sharp lines, or card counter, keep reading.
The Kelly Formula Explained
The basic Kelly formula:
Kelly % = (bp - q) / b
Where:
| Variable | Meaning | Example |
|---|---|---|
| b | Decimal odds - 1 (net odds) | 2.0 odds → b = 1 |
| p | Probability of winning | 55% → p = 0.55 |
| q | Probability of losing (1 - p) | 45% → q = 0.45 |
Example Calculation
You find a bet at 2.0 odds where you estimate 55% win probability:
Kelly % = (1 × 0.55 - 0.45) / 1 = 0.10 = 10% of bankroll
With a $1,000 bankroll, Kelly says bet $100.
When Kelly Says "Don't Bet"
If Kelly returns zero or negative, you have no edge — or negative edge. Don't bet.
| Odds | Win Probability | Kelly % | Verdict |
|---|---|---|---|
| 2.0 | 50% | 0% | No edge — don't bet |
| 2.0 | 48% | -4% | Negative edge — never bet |
| 2.0 | 55% | 10% | Edge exists — bet 10% |
| 1.5 | 70% | 10% | Edge exists — bet 10% |
This is why Kelly doesn't work for casino games. Roulette at 48.6% win probability on even bets? Kelly says bet $0.
The Danger of Full Kelly
Full Kelly maximizes long-term growth — but the ride is brutal. Variance is extreme. You'll see 50%+ drawdowns regularly.
| Kelly Fraction | Growth Rate | Volatility | Max Drawdown (typical) |
|---|---|---|---|
| Full Kelly (100%) | Maximum | Extreme | 50-70% |
| Half Kelly (50%) | 75% of max | High | 30-40% |
| Quarter Kelly (25%) | 50% of max | Moderate | 15-25% |
Most professionals use half-Kelly or less. You sacrifice some growth for much smoother equity curves.
Why Professionals Use Fractional Kelly
1. Edge Estimation Is Imperfect
You think you have 55% edge. What if it's actually 52%? Full Kelly on overestimated edge = disaster. Half-Kelly provides a buffer.
2. Psychological Tolerance
Can you stomach a 60% drawdown without tilting? Most can't. Fractional Kelly keeps drawdowns manageable.
3. Simultaneous Bets
Kelly assumes one bet at a time. If you're betting multiple events, full Kelly on each = massive overexposure.
| Scenario | Recommended Kelly Fraction |
|---|---|
| Very confident in edge estimate | Half Kelly (50%) |
| Moderate confidence | Quarter Kelly (25%) |
| Low confidence / learning | Tenth Kelly (10%) |
| Multiple simultaneous bets | Divide Kelly by number of bets |
Kelly for Sports Betting
Sports bettors can have an edge if they're sharper than the market. But most aren't. Be honest with yourself.
Where Sports Bettors Find Edge
| Source | Edge Size (typical) | Difficulty |
|---|---|---|
| Soft book arbitrage | 1-3% | Medium (accounts get limited) |
| Closing line value | 2-5% | High (need sharp analysis) |
| Promotions/bonuses | Variable | Low (but limited) |
| Niche markets | 3-7% | Very high (deep expertise needed) |
If you can't articulate exactly where your edge comes from, you probably don't have one. Kelly with imaginary edge = Martingale with extra steps.
Kelly for Poker Players
Poker is the most legitimate Kelly use case. You can genuinely have 55%+ equity against the field.
Bankroll Guidelines (Tournament)
| ROI | Suggested Buy-ins in Bankroll | Kelly Equivalent |
|---|---|---|
| 10% | 100+ buy-ins | ~1% Kelly |
| 30% | 50-75 buy-ins | ~2% Kelly |
| 50%+ | 30-50 buy-ins | ~3% Kelly |
Even with massive edge, poker pros use tiny Kelly fractions because variance is enormous.
Kelly for Card Counters
Blackjack card counters have measurable edge (0.5-1.5% typically). Kelly tells them exactly how to bet.
| True Count | Estimated Edge | Full Kelly Bet (1000 unit BR) | Half Kelly |
|---|---|---|---|
| +1 | 0% | 0 (minimum) | 0 (minimum) |
| +2 | 0.5% | 5 units | 2.5 units |
| +3 | 1.0% | 10 units | 5 units |
| +4 | 1.5% | 15 units | 7.5 units |
This is why counters spread bets dramatically — Kelly demands it.
Kelly vs Other "Systems"
| System | Requires Edge? | Long-term Result | Used By Pros? |
|---|---|---|---|
| Kelly Criterion | Yes | Profit (if edge is real) | Yes |
| Martingale | No | Ruin | No |
| Fibonacci | No | Ruin | No |
| 1-3-2-6 | No | Slow ruin | No |
Kelly is the only system in this list that professionals actually use. The others are entertainment.
Share Your Kelly Results
Using Kelly for real edge bets? Post your results in the community forum. Compare growth rates, drawdowns, and discuss fractional Kelly strategies — based on real data.
Frequently Asked Questions
Can I use Kelly Criterion for casino games?
No. Kelly requires a positive edge. Casino games like roulette and baccarat have negative expectation — Kelly would tell you to bet $0. Only use Kelly when you have a genuine, quantifiable edge.
Is this Kelly Criterion calculator free?
Yes. This Kelly Criterion calculator is 100% free with no signup required.
Why do professionals use half-Kelly instead of full Kelly?
Full Kelly maximizes growth but creates extreme variance — 50-70% drawdowns are common. Half-Kelly provides 75% of the growth with much smoother equity curves. It also protects against edge estimation errors.
How do I know if I have an edge?
Track your bets. If you can't show positive expected value over 1,000+ bets with statistical significance, you probably don't have an edge. Feeling lucky isn't edge. Consistent closing line value is edge.
What happens if I overestimate my edge?
Disaster. If you think you have 10% edge but actually have 2%, full Kelly will massively overbet. This leads to faster ruin than no system at all. Always be conservative with edge estimates and use fractional Kelly.