Kelly Criterion Calculator for Prediction Markets
Calculate optimal position sizing for Kalshi, Polymarket, and other prediction markets. The Kelly Criterion maximizes long-term bankroll growth when you have an edge.
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View Live Edges →What is the Kelly Criterion?
The Kelly Criterion is a formula developed by John L. Kelly Jr. at Bell Labs in 1956 for determining the optimal size of a series of bets. Unlike fixed-percentage betting, Kelly dynamically adjusts your position size based on your edge — bet more when you have a bigger advantage, less when your edge is slim.
The mathematical insight is that Kelly maximizes the expected logarithm of wealth, which translates to the highest long-term geometric growth rate. This makes it particularly valuable for prediction market traders who make many bets over time.
The Kelly Formula for Prediction Markets
In prediction markets like Kalshi and Polymarket, contracts trade at prices representing implied probabilities. The Kelly formula adapts to this structure:
Edge = Your Probability - Market Price
Decimal Odds = 1 / Market Price
Net Odds (b) = Decimal Odds - 1
Kelly % = (b x p - q) / b
Where p is your probability estimate and q is 1 - p. The result tells you what fraction of your bankroll to wager on a single contract.
Why Use Half Kelly or Quarter Kelly?
Full Kelly betting is mathematically optimal only if your probability estimates are perfectly calibrated — which they never are. In practice, most traders use fractional Kelly for several reasons:
Estimation error: If you overestimate your edge by even a small amount, Full Kelly leads to systematic overbetting and can result in significant drawdowns. Half Kelly provides nearly 75% of the growth rate with substantially less variance.
Psychological comfort: Full Kelly swings can be emotionally difficult. A 40% drawdown is mathematically fine under Kelly, but psychologically devastating for most traders. Fractional Kelly smooths the equity curve.
Correlated bets: Kelly assumes independent bets. In prediction markets, many positions may be correlated (e.g., multiple political markets). Fractional Kelly provides a margin of safety.
Kelly Criterion vs. Expected Value
Expected Value (EV) tells you whether a bet is profitable on average. Kelly tells you how much to bet once you've found a positive EV opportunity. A bet can have high EV but still warrant a small Kelly allocation if the odds are long (high variance).
For example, a 5% edge on a 10% probability event has great EV (+50% of stake), but Kelly would recommend a smaller position than a 5% edge on a 50% probability event because the former has much higher variance.
Common Mistakes with Kelly Betting
Overconfidence in edge estimates: The biggest mistake is assuming your probability estimate is more accurate than it is. Always be conservative — if you think you have a 10% edge, assume it's 5% for sizing purposes.
Ignoring bankroll updates: Kelly should be recalculated after each bet based on your current bankroll, not your starting bankroll. Wins mean larger absolute bets; losses mean smaller ones.
Applying Kelly to correlated positions: If you have five positions that all depend on the same underlying event, you can't size each at full Kelly independently. Consider your total exposure to correlated outcomes.