Kelly Criterion Position Sizer
Calculate the optimal position size for your Polymarket trades using the Kelly Criterion. Adjust the Kelly fraction to balance growth against variance, and see how different sizing affects your expected long-run growth rate.
Full Kelly Stake
$200.00
Your Kelly Stake
$50.00
Number of Shares
100.00
Bankroll at Risk
5.00%
Expected Growth Rate (per bet): 0.8757%
Kelly Growth Rate Comparison
| Kelly Fraction | Stake | Growth Rate |
|---|---|---|
| 0.125x | $25.00 | 0.4688% |
| 0.25x(Quarter Kelly)← | $50.00 | 0.8757% |
| 0.5x(Half Kelly) | $100.00 | 1.5042% |
| 0.75x | $150.00 | 1.8850% |
| 1x(Full Kelly) | $200.00 | 2.0136% |
| 1.5x | $300.00 | 1.4749% |
Kelly Criterion for binary markets: f* = (p - price) / (1 - price) for Buy Yes, f* = (price - p) / price for Buy No. Fractional Kelly multiplies f* by your chosen fraction to reduce variance at the cost of slightly lower expected growth.
How the Kelly Criterion Works
The Kelly Criterion answers a fundamental question in trading: given a favorable bet, how much should I risk? Bet too little and you leave growth on the table. Bet too much and a bad streak can devastate your bankroll. The Kelly formula finds the exact fraction that maximizes your long-run compound growth rate.
For Polymarket, the formula simplifies to: f* = (p - price) / (1 - price) for Buy Yes, where p is your estimated true probability and price is the market price. The result is the fraction of your bankroll to bet. For example, if the market prices an outcome at $0.50 and you believe the true probability is 60%, Kelly suggests betting 20% of your bankroll.
Why Fractional Kelly?
Full Kelly maximizes theoretical growth but assumes perfect probability estimates — which nobody has. Even small errors in your estimate can lead to over-betting. Quarter Kelly (0.25x) is the most common professional choice: it captures roughly 75% of the growth rate at a fraction of the variance. Half Kelly is a moderate approach. Full Kelly is aggressive and only appropriate if you have high confidence in your probability estimate.
Frequently Asked Questions
What is the Kelly Criterion?
The Kelly Criterion is a formula for optimal bet sizing that maximizes long-run wealth growth. It was developed by John Kelly at Bell Labs in 1956. For Polymarket applications, it tells you how many shares to buy based on your edge (the gap between your estimated probability and the market price) and your bankroll.
Why use fractional Kelly instead of full Kelly?
Full Kelly creates extreme swings. A string of losses — which will happen — can draw down your bankroll significantly. Fractional Kelly sacrifices a small amount of theoretical growth for dramatically smoother returns. Most professionals in finance and prediction markets use 0.25x to 0.5x Kelly.
What happens if I bet more than Kelly suggests?
Over-Kelly betting is counterproductive. At 2x Kelly, expected growth drops to zero. Beyond that, it turns negative — you expect to lose money over time even with an edge. The growth rate table in the calculator visualises this: watch how growth peaks at 1x Kelly and declines beyond it.
Calculate your edge first with the EV calculator, check exact fees with the fee calculator, and model your P&L with the profit calculator. For strategy context, see our guides on fundamental analysis and quantitative analysis.