What Is the Kelly Criterion?
The Kelly Criterion is a mathematical formula that tells you exactly how much of your bankroll to wager on a given trade. Developed by John Kelly at Bell Labs in 1956, it was originally designed for information theory — but it turns out to be one of the most powerful tools for anyone trading on prediction markets.
The core idea is simple: bet more when you have a bigger edge, and less when your edge is slim. Over time, this approach maximizes the growth rate of your bankroll while minimizing the risk of ruin.
The Kelly Formula
For prediction markets, the Kelly formula is:
f = (p × b - q) / b
Where:
- f = fraction of your bankroll to wager
- p = your estimated probability of winning
- b = the odds received (payout divided by stake, minus 1)
- q = probability of losing (1 - p)
In prediction markets, the odds are straightforward. If you buy a YES share at $0.40, you stand to gain $0.60 if you win. So b = 0.60 / 0.40 = 1.5.
Worked Example
A market prices YES at $0.40 (implied probability: 40%). After researching, you believe the true probability is 55%.
- p = 0.55
- q = 0.45
- b = 0.60 / 0.40 = 1.5
f = (0.55 × 1.5 - 0.45) / 1.5 = (0.825 - 0.45) / 1.5 = 0.375 / 1.5 = 0.25
Kelly says you should wager 25% of your bankroll on this trade. That is a substantial position, reflecting the significant edge you believe you have.
Why Full Kelly Is Dangerous
In theory, full Kelly maximizes long-term growth. In practice, it produces wild swings that most traders cannot stomach. A bad streak can cut your bankroll in half before the math works in your favor.
The problem is that the Kelly formula assumes you know the true probability with certainty. In prediction markets, your probability estimates are exactly that — estimates. If you are even slightly wrong, full Kelly can lead to massive overexposure.
The Solution: Fractional Kelly
Most experienced traders use half Kelly or quarter Kelly — meaning they wager 50% or 25% of what the full formula recommends.
Using the example above, half Kelly would mean wagering 12.5% instead of 25%. Quarter Kelly would mean 6.25%.
| Kelly Fraction | Bet Size | Growth Rate | Volatility | |---|---|---|---| | Full Kelly | 25% | Maximum | Very high | | Half Kelly | 12.5% | ~75% of max | Moderate | | Quarter Kelly | 6.25% | ~50% of max | Low |
Half Kelly sacrifices about 25% of maximum growth rate but dramatically reduces the risk of drawdowns. For most prediction market traders, this is the optimal balance.
When Kelly Says Do Not Bet
One of the most valuable outputs of the Kelly formula is when it returns zero or a negative number. This means you have no edge — or you are on the wrong side of the trade.
If you estimate a 35% probability on an event priced at $0.40:
- f = (0.35 × 1.5 - 0.65) / 1.5 = (0.525 - 0.65) / 1.5 = -0.083
A negative Kelly means you should not take this trade. In fact, it suggests you should consider betting the other side. This discipline — walking away from trades without an edge — is what separates profitable traders from gamblers.
Applying Kelly Across Multiple Markets
When you are trading multiple markets simultaneously, you need to account for your total exposure. The Kelly fractions should be calculated independently for each market, but your total allocation across all open positions should not exceed your comfort level.
A practical approach:
- Calculate the Kelly fraction for each market individually.
- Use half Kelly or quarter Kelly for each position.
- Cap your total open exposure at 50-60% of your bankroll.
- Keep the remaining 40-50% as a reserve for new opportunities.
This approach works well alongside a broader bankroll management strategy.
Common Kelly Mistakes
Overestimating your edge. If you think a 40-cent market should be at 60 cents, ask yourself: what do you know that thousands of other traders do not? Be honest and conservative with your probability estimates.
Ignoring correlation. If you have positions in five political markets that all depend on the same candidate winning, your risk is concentrated — not diversified. Treat correlated bets as a single position for Kelly purposes.
Using Kelly on low-liquidity markets. The Kelly Criterion assumes you can enter and exit at the stated price. In thin markets, slippage can destroy your edge. Stick to markets with healthy volume, like the ones featured in our best markets guide.
Recalculating too infrequently. As market prices move and new information emerges, your edge changes. Reassess your Kelly fraction regularly, especially as events approach resolution.
Kelly Criterion vs. Fixed Betting
Many beginners use a fixed bet size — say, $50 per trade regardless of the edge. While simple, this approach is suboptimal because it treats every trade equally.
Kelly dynamically adjusts your position size based on two factors: how confident you are and how mispriced the market is. This means you bet big when the opportunity is best and small when it is marginal. Over hundreds of trades, this compounding effect creates a significant performance gap.
Putting It Into Practice
Here is a practical workflow for using Kelly on Polymarket:
- Identify a market where your analysis disagrees with the current price.
- Estimate your true probability based on research, data, and reasoning.
- Calculate the Kelly fraction using the formula above.
- Apply half Kelly to get your actual position size.
- Check total exposure — make sure all open positions combined are within your risk tolerance.
- Place the trade and record your reasoning for later review.
The Kelly Criterion is not a guarantee of profit — no formula is. But combined with sound analysis, disciplined expected value calculations, and emotional control, it is the most mathematically rigorous way to size your prediction market positions.
