Kelly Criterion Calculator
Work out the mathematically optimal bet size for any Polymarket or Kalshi market. Enter your bankroll, your estimated probability, and the current market price. Get the exact fraction of your bankroll to risk.
The formula: f* = (bp - q) / b, where b is net odds, p is your probability, and q = 1 - p. A positive result is the fraction to bet; a negative result means skip the bet.
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Kelly Criterion FAQ
- What is the Kelly Criterion?
- The Kelly Criterion is a formula for sizing each bet so you maximize the long-run growth of your bankroll. It answers the question 'what fraction of my bankroll should I risk on this bet?' given your estimated probability of winning and the market price. It was developed by John Kelly at Bell Labs in 1956 and is used by professional traders in every speculative market.
- How do I use this Kelly Calculator for Polymarket or Kalshi?
- Enter three numbers: your bankroll (total dollars you are willing to risk across all bets), your estimated probability the market resolves YES (as a decimal between 0 and 1), and the current market price (also as a decimal). The calculator returns the Kelly fraction and the exact dollar amount to bet. If the Kelly fraction is negative, the bet has negative expected value and you should skip it.
- What is fractional Kelly and should I use it?
- Fractional Kelly means betting some fraction (commonly half or quarter) of the full Kelly amount. Most serious traders use fractional Kelly because full Kelly produces high volatility and assumes perfect knowledge of your true win probability. Half-Kelly gives you about three quarters of the growth rate with roughly half the variance. If your probability estimates are calibrated, start with half-Kelly.
- What happens if I enter a probability below the market price?
- The Kelly fraction will be zero or negative. A negative fraction means the market is pricing the event higher than your estimated probability, so buying YES would be a losing bet in expectation. The calculator will tell you to skip the bet.
- Does Kelly assume my probability estimate is accurate?
- Yes. Kelly is optimal only if your probability estimate is correctly calibrated. If you systematically overestimate your edge, full Kelly will ruin you faster than any other sizing rule. This is why calibration tracking matters and why fractional Kelly is the more robust practical choice.
Worked example
Suppose you have a $1,000 bankroll and a market is trading at 40¢ YES. You estimate the true probability at 55%.
Plugging in: b = (1 - 0.40) / 0.40 = 1.5, p = 0.55, q = 0.45.
Kelly fraction: (1.5 × 0.55 - 0.45) / 1.5 = 0.25, or 25% of bankroll.
Full Kelly bet: $250. Half-Kelly (recommended): $125.