In this guide
Key takeaway: The Kelly Criterion calculates the optimal proportion of your capital to allocate to each bet, derived from your expected advantage and available odds. In prediction markets, it solves two critical problems: wagering excessively (which threatens total loss) and wagering insufficiently (which sacrifices potential returns).
How much you stake on each position separates winning traders from those facing insolvency. The Kelly Criterion — a mathematical framework developed by John Kelly, a researcher at Bell Labs in 1956 — determines the theoretically ideal stake size for compounding wealth over time. This guide demonstrates its practical use in prediction markets.
The Kelly formula
For a two-sided prediction market (YES/NO), the Kelly fraction is calculated as:
f* = (p * b - q) / b
Where:
- f* = proportion of your total capital to stake
- p = your assessed likelihood of success
- q = likelihood of failure (1 - p)
- b = net odds (return / investment). For a market share trading at price c, b = (1 - c) / c
Worked example
Suppose you assess a 60% probability that an outcome resolves YES. The current market valuation is 45 cents (reflecting 45% implied probability).
- p = 0.60, q = 0.40
- b = (1 - 0.45) / 0.45 = 1.222
- f* = (0.60 * 1.222 - 0.40) / 1.222 = (0.733 - 0.40) / 1.222 = 0.272
The Kelly formula recommends deploying 27.2% of your capital. If your account holds $1,000, this translates to a $272 position in this opportunity.
Why full Kelly is dangerous
The Kelly formula presupposes you can determine your true probability with certainty — a condition that never materialises in practice. Miscalculating your advantage upward results in severe overexposure. Experienced traders across the industry favour fractional Kelly approaches:
- Half Kelly (f*/2): The industry standard. Surrenders roughly 25% of theoretical growth but cuts volatility in half
- Quarter Kelly (f*/4): Prudent method when your edge assessment carries significant uncertainty
- Capped Kelly: Enforce a ceiling of 5-10% per market position, overriding Kelly calculations if necessary
Applying Kelly to multi-market portfolios
Operating across numerous prediction markets at once requires modifying individual Kelly allocations. The aggregate of all Kelly fractions must remain at or below 1.0 (your full bankroll). Practically speaking, restrict cumulative exposure to 50% or less, preserving dry powder for emerging opportunities.
When Kelly does not apply
Kelly assumes you can reliably quantify your true probability. Several contexts invalidate this assumption:
- Unprecedented events lacking comparable historical data or reference points
- Interconnected markets (such as a presidential outcome and legislative control, which move together)
- Markets where you possess no analytical advantage relative to prevailing pricing
PolyGram includes a built-in Kelly Criterion calculator to optimise your stake before each trade. The advanced toolkit features payoff visualisations and maximum drawdown metrics. Start trading on PolyGram →