Kelly Criterion: The Optimal Bet Sizing Formula for Prediction Markets

The Kelly Criterion is a mathematical formula for determining the optimal size of a bet. Developed by John L. Kelly Jr. at Bell Labs in 1956, it's become the gold standard for bankroll management among professional bettors, traders, and investors.

Unlike fixed-percentage betting or gut-feel sizing, Kelly dynamically adjusts your position based on your edge. Bigger edge? Bet more. Smaller edge? Bet less. The result is mathematically optimal long-term growth.

How the Kelly Criterion Works

The Kelly formula answers one question: what fraction of my bankroll should I bet on this opportunity?

For prediction markets, the formula adapts to binary contracts that trade at prices representing implied probabilities:

Edge = Your Probability − Market Price
Net Odds = (1 / Market Price) − 1  
Kelly % = (Net Odds × Your Probability − Loss Probability) / Net Odds

Let's break this down with an example.

Say Kalshi prices a contract at 40% (you pay $0.40 to win$1.00). You believe the true probability is 55%. Here's the math:

Variable	Calculation
Your Edge	55% − 40% = 15%
Net Odds	(1 / 0.40) − 1 = 1.5
Kelly %	(1.5 × 0.55 − 0.45) / 1.5 = 25%

Kelly says to bet 25% of your bankroll on this opportunity.

Why Fractional Kelly Is Standard Practice

Here's the thing about full Kelly: it's aggressive. A 25% allocation to a single position means wild swings in your bankroll. Win, and you're up big. Lose, and you've taken a significant hit.

Professional traders almost universally use fractional Kelly—typically half Kelly or quarter Kelly.

Strategy	% of Full Kelly	Growth Rate	Volatility
Full Kelly	100%	Maximum	Very High
Half Kelly	50%	~75% of max	Moderate
Quarter Kelly	25%	~50% of max	Low

Half Kelly is the sweet spot for most traders. You capture roughly 75% of the theoretical maximum growth rate while cutting volatility nearly in half. The math works out elegantly: you're trading a small amount of expected growth for a large reduction in variance.

The Edge Estimation Problem

Kelly assumes you know your true edge with certainty. You don't.

If you believe you have a 15% edge but you actually have a 5% edge, full Kelly will systematically overbet. Over time, this leads to ruin. It's the single biggest mistake amateur bettors make with Kelly.

The solution is conservative edge estimation:

If you think you have a 15% edge, assume it's 7.5% for sizing purposes.

This effectively creates a built-in margin of safety. Combined with half Kelly, you're unlikely to blow up even when your probability estimates are off.

Kelly in Prediction Markets vs Traditional Sports Betting

Prediction markets like Kalshi and Polymarket have a unique property that matters for Kelly: the prices are the implied probabilities.

On a traditional sportsbook, you have to convert American odds (-110, +150) into implied probabilities, then back out the vig to estimate fair odds. It's messy.

On prediction markets:

• A 40-cent contract implies 40% probability
• The market's estimate is transparent
• Your job is to decide if your estimate is different

This makes Kelly calculations more straightforward. Your edge is simply the difference between your probability and the market price. No vig adjustment required.

When Not to Use Kelly

Kelly has limitations. Here are situations where it breaks down:

Correlated bets. If you have five positions that all depend on the same underlying outcome (say, multiple markets that all hinge on who wins an election), you can't size each independently at full Kelly. Your actual exposure is much higher than it appears.

Low liquidity markets. Kelly assumes you can execute at your desired price. In thin prediction markets, slippage can destroy your edge. Size down accordingly.

Unknown unknowns. Kelly works when you can estimate probabilities. For true uncertainty—events with no historical precedent—even sophisticated probability estimates are guesses.

Calculating Your Kelly Size

Our Kelly Criterion Calculator handles the math for you. Enter three numbers:

1. The market price (what the contract costs)
2. Your probability estimate (what you believe the true odds are)
3. Your bankroll (your total trading capital)

The calculator outputs full Kelly, half Kelly, and quarter Kelly allocations, along with your expected value and effective edge.

It's free, no sign-up required.

The Bottom Line

Kelly is a powerful framework, but it's not magic. The formula is only as good as your probability estimates. Overconfident estimates lead to overbetting. Overbetting leads to ruin.

Use fractional Kelly. Be conservative with edge estimates. And remember that the goal isn't to win any single bet—it's to grow your bankroll over hundreds or thousands of bets.

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Related resources:

• Kelly Criterion Calculator — Calculate your optimal position size
• Dutching Calculator — Spread stakes across multiple outcomes
• Live Edge Dashboard — Find mispricings in real-time

All trading involves risk. This is a research tool, not financial advice.