Kelly Criterion Calculator
Calculate your optimal stake size with the Kelly Criterion. Enter odds, your estimated true probability, and bankroll — get the mathematically optimal bet size to maximize long-term growth.
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula for sizing bets to maximize the long-term geometric growth rate of your bankroll. Developed by John Kelly Jr. at Bell Labs in 1956, it's used by professional sports bettors, hedge funds (Warren Buffett's mentor Ed Thorp pioneered its use), and quantitative traders.
The formula:
f*= optimal fraction of bankroll to betb= decimal_odds − 1 (the net odds received per unit staked)p= your true probability of winningq= 1 − p (probability of losing)
Example: bet at odds 2.10 (b = 1.10), true probability 55% (p = 0.55, q = 0.45):
f* = (1.10 × 0.55 − 0.45) / 1.10 = 14.1%.
On a $1,000 bankroll, full Kelly says bet $141. That's aggressive — most pros use Quarter Kelly (25% of that = $35).
Full Kelly vs Half Kelly vs Quarter Kelly
| Strategy | Stake (vs Full) | Growth Rate | Drawdown Risk | Best For |
|---|---|---|---|---|
| Full Kelly | 100% | 100% | Very high (50%+ drawdowns common) | Perfect models only |
| Half Kelly | 50% | ~75% | Moderate | Confident estimates |
| Quarter Kelly | 25% | ~44% | Low | Most bettors (recommended) |
| Tenth Kelly | 10% | ~19% | Very low | Beginners, uncertain edge |
Key insight: dropping from Full to Half Kelly costs only 25% of growth rate but cuts drawdown variance by ~75%. Most professional bettors use 0.25× to 0.50× Kelly because:
- Probability estimates are never perfectly accurate. Fractional Kelly is a safety margin.
- Bookmakers limit/close accounts after big drawdowns and big wins. Lower variance = less attention.
- Psychology: 50% drawdowns are unbearable. 15% drawdowns are manageable.
Worked example: $1,000 bankroll, +9.2% EV bet
You find a bet at odds 2.10 with true probability 52%. EV calculator says +9.2%. Bankroll is $1,000. How much do you stake?
b = 2.10 − 1 = 1.10p = 0.52, q = 0.48f* = (1.10 × 0.52 − 0.48) / 1.10 = 0.092 / 1.10 = 8.4%(Full Kelly)- Quarter Kelly =
8.4% × 0.25 = 2.1% - Stake =
$1,000 × 2.1% = $21
Even a juicy +9.2% EV bet with Quarter Kelly only stakes 2.1% of bankroll. That feels small — but compounded across hundreds of bets per year, it grows the bankroll exponentially while keeping drawdowns under control.
Kelly Criterion rules of thumb
- Cap stakes at 5% of bankroll. Even if Kelly says 12%, never exceed 5% per bet. Probability estimation errors are amplified at extreme stakes.
- Recalculate after every bet. Bankroll changes → stake size changes. This is the compounding mechanism.
- Never bet on negative Kelly. If
f* < 0, the bet has negative EV — skip it. - Adjust for correlated bets. Multiple bets on the same game/league are correlated. Total exposure should still follow Kelly limits.
- Use sharp probabilities. Get
pfrom devigged sharp books (Pinnacle, Betfair Exchange). Your model or recreational book probabilities are too noisy. - Track CLV. Closing line value is the best validation that your
pis accurate. Beat the close consistently → your Kelly bets are well-sized.
Common Kelly Criterion mistakes
1. Using implied probability instead of true probability
Plugging the bookmaker's implied probability into Kelly always gives f* = 0. You need your probability estimate, which must be higher than implied for any bet to be +EV.
2. Betting Full Kelly with uncertain probabilities
Full Kelly assumes perfect probability knowledge. Real-world models have ±2-5% error. If you overestimate your edge, Full Kelly can cause ruinous drawdowns. Use Quarter Kelly as default.
3. Not adjusting bankroll
Static stakes (flat $50 per bet) don't compound. Kelly's power comes from staking a fraction of current bankroll — wins grow your stake size, losses shrink it. Track bankroll weekly minimum.
4. Treating correlated bets as independent
Three +EV bets on the same NBA game's Over/Spread/ML are correlated. Total stake on the game should still follow Kelly limits — don't bet 3× by treating them separately.
5. Confusing Kelly with money management
Kelly optimizes growth assuming +EV opportunities exist. It does NOT save you from a losing strategy. Garbage in, garbage out — confirm your edge is real (track CLV) before scaling.
Frequently asked questions
Is the Kelly Criterion guaranteed to work?
Mathematically yes, given (1) positive EV is real, (2) probability estimates are accurate, (3) you can make many repeated bets. In practice, all three are approximations — so use fractional Kelly to absorb estimation error.
Does Kelly work for parlays?
Yes, but tricky. Multiply individual probabilities and odds, then apply Kelly to the combined bet. The math works — but parlays compound bookmaker margin, making +EV parlays extremely rare. Singles are easier.
Can I use Kelly for hedging or arbitrage?
Pure arbitrage doesn't need Kelly — it's risk-free, just maximize stake within bookmaker limits. For partial hedges (locking in profit on a winning bet), Kelly applies to the remaining variance position.
What if I have a small bankroll ($100)?
Quarter Kelly on a $100 bankroll often produces $1-3 stakes. Some bookmakers have $5 minimums. Solutions: (1) save up to $500+, (2) use exchanges (Betfair Exchange minimums are lower), (3) round up to bookmaker minimum but reduce frequency.
Does Warren Buffett actually use Kelly?
His mentor Ed Thorp pioneered Kelly in markets. Buffett himself uses a related concept (concentrate on highest-edge opportunities), but doesn't formally publish Kelly fractions. The principle — bet bigger when edge is bigger — is universally applied by quant funds.
Next steps
- Find positive EV bets first: EVBets live value bets
- Verify each bet's EV: EV Calculator
- Get accurate probabilities: No-Vig Calculator
- Convert odds formats: Odds Converter
- Multi-leg bets: Parlay Calculator