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Kelly Criterion Calculator: Optimal Bet Sizing
Last Updated: March 4, 2026
The Kelly Criterion calculates the mathematically optimal fraction of your bankroll to wager on any bet with positive expected value. Enter your estimated win probability and the odds into the calculator above to get the precise bet size that maximizes long-term growth without risking ruin.
How Do You Use the Kelly Calculator?
The calculator takes two primary inputs: the odds on your bet (in any format) and your estimated probability that the bet wins. It outputs the full Kelly stake as a bankroll percentage, along with half Kelly and quarter Kelly alternatives.
Inputs:
- Odds — The price you are getting. Enter American (+150, -110), decimal (2.50), or a prediction market contract price ($0.40).
- Win probability — Your honest estimate of the true probability. This is the most important input. If this number is wrong, the output is wrong.
Outputs:
- Full Kelly percentage of bankroll
- Half Kelly and quarter Kelly percentages
- Dollar amounts based on your bankroll size
If the calculator returns zero or a negative value, the bet is not positive expected value at the given odds. Kelly says do not bet.
What Does a Kelly Calculation Look Like?
The formula is f* = (bp - q) / b. Here is how the variables map to a real bet:
| Variable | Definition | Example: +150 Bet, 45% Win Prob |
|---|---|---|
| b | Net odds (profit per $1 risked) | 1.50 |
| p | Win probability | 0.45 |
| q | Loss probability (1 - p) | 0.55 |
| f* | Kelly fraction | (1.5 x 0.45 - 0.55) / 1.5 = 8.3% |
On a $5,000 bankroll, full Kelly recommends a $415 wager. Half Kelly cuts that to $208, and quarter Kelly to $104.
The critical insight: even though this bet loses more often than it wins (45%), the +150 payout provides enough edge that Kelly recommends a meaningful position. Kelly always accounts for both probability and payout size together.
How Does Full Kelly Compare to Fractional Kelly?
Full Kelly maximizes the geometric growth rate of your bankroll, but the drawdowns along the way are severe. Simulations consistently show that full Kelly produces 50%+ drawdowns with uncomfortable frequency.
| Strategy | Growth Rate | Typical Max Drawdown | Best For |
|---|---|---|---|
| Full Kelly (1.0x) | Maximum | 50-80% | Theoretical benchmark only |
| Half Kelly (0.5x) | ~75% of full | 25-40% | Most professional bettors |
| Quarter Kelly (0.25x) | ~44% of full | 10-20% | Uncertain probability estimates |
| Flat betting (fixed %) | Varies | Depends on stake size | Beginners, high uncertainty |
Most professional sports bettors and prediction market traders default to half Kelly. The reasoning is straightforward: probability estimates are never perfectly calibrated, and half Kelly provides a buffer against overestimating your edge. For a deeper discussion, see our full Kelly Criterion guide.
How Does Kelly Apply to Prediction Markets?
Prediction market contracts map directly to the Kelly inputs. A contract at $0.40 with a $1.00 payout gives b = (1.00 - 0.40) / 0.40 = 1.50. If you estimate the true probability at 55%:
- f* = (1.5 x 0.55 - 0.45) / 1.5 = 25% at full Kelly
- Half Kelly: 12.5% of bankroll
- Quarter Kelly: 6.25% of bankroll
Because prediction markets display prices as direct probabilities, comparing your estimate to the market price reveals your perceived edge immediately. If the market prices an event at 40 cents and you believe the true probability is 55%, your edge is 15 percentage points — a large claim that warrants careful scrutiny before sizing up.
Track real-time contract prices across platforms on the Odds Reference dashboard to identify where your probability estimates diverge from market consensus.
How Should You Choose Your Win Probability Estimate?
The Kelly output is only as good as your probability input. Two guidelines help:
Be conservative. If your analysis says 60% but you are not highly confident, enter 55%. Underestimating your edge produces smaller bets (opportunity cost), but overestimating produces larger bets (actual losses). The downside of overconfidence is worse than the downside of humility.
Track and calibrate. Over 200+ bets, compare your estimated win rate to your actual win rate. If you consistently estimate 55% but win 51%, your Kelly sizing has been too aggressive. Recalibrate before continuing. Sound bankroll management requires ongoing calibration, not a one-time guess.
Key Takeaways
- Kelly calculates the optimal bet size that maximizes long-term bankroll growth: f* = (bp - q) / b
- Half Kelly is the professional default — it sacrifices only ~25% of growth rate while cutting variance roughly in half
- The formula requires a positive EV bet; if Kelly outputs zero or negative, do not bet
- Probability estimation error is the primary risk — conservative estimates and fractional Kelly together provide a margin of safety
- The same formula applies to prediction market position sizing, with contract price and payout mapping directly to the Kelly variables