Kelly Criterion Calculator
Calculate the optimal bet size based on your estimated fair probability, the book's odds, and your bankroll.
Kelly Criterion
Bet $206.35
20.6% of bankroll · Full Kelly
What Is the Kelly Criterion?
The Kelly Criterion is a formula developed by John Kelly at Bell Labs in 1956. It tells you the mathematically optimal fraction of your bankroll to bet when you have an edge. Bet too little and you leave money on the table. Bet too much and you risk ruin. Kelly finds the sweet spot that maximizes long-term bankroll growth.
The Formula
f* = (bp - q) / b where b is the net payout per $1 bet (decimal odds minus 1), p is your estimated true win probability, and q is 1 - p. The result f* is the fraction of your bankroll to wager.
Why Use Fractional Kelly?
Full Kelly assumes your probability estimate is perfectly accurate. In practice, it's not — you're always estimating. Full Kelly can also produce wild swings in bankroll size. Most professional bettors use 1/4 or 1/2 Kelly to account for estimation error and reduce variance. You sacrifice some theoretical growth rate but gain much smoother results.
How to Use This Calculator
- Enter your estimated fair odds — what you believe the true probability is
- Enter the book's odds — what the sportsbook is offering
- Enter your total bankroll
- The calculator shows the optimal bet size and fractional Kelly amounts
Worked Example
You've de-vigged Pinnacle's line and found the true probability of the Eagles winning is 55%. DraftKings is offering Eagles at +105 (decimal 2.05). Your bankroll is $5,000.
Using the formula: b = 2.05 - 1 = 1.05. p = 0.55. q = 0.45. Kelly fraction = (1.05 × 0.55 - 0.45) / 1.05 = (0.5775 - 0.45) / 1.05 = 0.1275 / 1.05 = 12.1%. Full Kelly says bet 12.1% of your bankroll = $607. Half Kelly = $303. Quarter Kelly = $152. Most pros would go with quarter or half Kelly here — $150 to $300 on a $5,000 bankroll.
Full Kelly vs. Fractional Kelly
| Strategy | Growth Rate | Variance | Best For |
|---|---|---|---|
| Full Kelly | Maximum | Very high | Theoretical only |
| 1/2 Kelly | ~75% of full | ~50% of full | Confident estimates |
| 1/4 Kelly | ~56% of full | ~25% of full | Most bettors (recommended) |
| 1/8 Kelly | ~36% of full | ~12% of full | Uncertain estimates |
The tradeoff is clear: fractional Kelly sacrifices some growth rate for dramatically reduced variance. Since your probability estimates are never perfect, fractional Kelly also protects you from the cost of overestimating your edge — which is far more damaging than underestimating it. To get fair probability estimates for Kelly sizing, use our De-Vig Calculator or check if a bet is worth taking at all with the EV Calculator.
Common Questions
What if Kelly says don't bet?
If the Kelly fraction is zero, it means you don't have an edge at the offered odds. The book's implied probability is equal to or higher than your fair probability — there's no positive expected value.
Why is the 'aggressive' warning at 25%?
Betting more than 25% of your bankroll on a single wager is extremely risky. Even with a genuine edge, a few losses in a row could devastate your bankroll. The 25% threshold is a widely-used guideline in professional betting circles.
How do I estimate fair probability?
You can use our De-Vig Calculator or EV Calculator to derive fair probabilities from sharp book lines. Or use your own model. The key is having a probability estimate that's better than the book's implied odds.
Does Kelly work for parlays?
The basic Kelly formula is for single bets. There are extensions for simultaneous bets (simultaneous Kelly) and correlated bets, but they're more complex. This calculator handles single-bet Kelly.
Should I use full Kelly or half Kelly?
Almost always fractional Kelly — typically 1/4 or 1/2 Kelly. Full Kelly maximizes long-term growth rate in theory, but assumes your probability estimates are perfectly accurate. In practice, using 1/2 Kelly sacrifices only about 25% of the growth rate while cutting variance roughly in half. Most professional bettors and hedge fund managers use fractional Kelly.
What bankroll do I need for Kelly betting?
There's no minimum, but Kelly works best with a dedicated bankroll you can size bets against consistently. If your bankroll is $1,000 and Kelly says to bet 3%, that's $30 per bet. The key is tracking your bankroll accurately and resizing after wins and losses — Kelly is dynamic, not static.
What happens if I bet more than Kelly suggests?
Over-betting Kelly is worse than under-betting it. Betting 2x full Kelly actually has the same expected growth rate as betting zero — you're just adding pure variance with no added return. Bet more than 2x Kelly and your expected bankroll actually shrinks over time. This is why fractional Kelly is so popular — the downside of over-betting is much worse than the downside of under-betting.