Key takeaway: The Kelly Criterion determines the optimal proportion of your capital to wager, derived from your informational advantage and available odds. Across prediction markets—whether Polymarket, Kalshi, Betfair, or Smarkets—it guards against two pitfalls: staking excessively (risking total loss) and staking insufficiently (forgoing potential returns).
The ability to size positions correctly separates consistently profitable operators from those facing financial collapse. The Kelly Criterion — a mathematical framework created by John Kelly, a researcher at Bell Labs, in 1956 — delivers the theoretically ideal stake magnitude for achieving sustainable wealth expansion. This guide demonstrates its practical implementation in prediction markets.
The Kelly formula
For a two-sided prediction market (YES/NO), the Kelly fraction is:
f* = (p * b - q) / b
Where:
- f* = proportion of total capital to stake
- p = your assessed likelihood of success
- q = likelihood of failure (1 - p)
- b = decimal odds (return / investment). For a prediction market contract trading at price c, b = (1 - c) / c
Worked example
Suppose you assess a 60% probability that an outcome resolves affirmatively. The current market quotation stands at 45 cents (suggesting 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 formula indicates wagering 27.2% of available funds. If your account holds $1,000, this corresponds to a $272 position.
Why full Kelly is dangerous
The Kelly formula presupposes certainty regarding your genuine probability — an assumption rarely satisfied in practice. Miscalculating your informational edge produces severe overexposure. Institutional investors and experienced traders routinely employ fractional Kelly instead:
- Half Kelly (f*/2): The industry standard. Surrenders roughly 25% of theoretical returns whilst cutting volatility in half
- Quarter Kelly (f*/4): Prudent choice when edge estimates carry substantial uncertainty
- Capped Kelly: Establish a ceiling—typically 5-10% of total capital per individual market, overriding Kelly calculations
Applying Kelly to multi-market portfolios
When maintaining concurrent stakes across numerous prediction markets, individual Kelly allocations require recalibration. The aggregate of all Kelly percentages ought to remain at or below 1.0 (your entire bankroll). Practically speaking, maintain cumulative deployment beneath 50% to preserve dry powder for emerging opportunities.
When Kelly does not apply
Kelly presupposes reliable estimation of your genuine probability. Several contexts undermine this assumption:
- Unprecedented or novel events lacking sufficient historical data
- Interdependent markets (such as a legislative outcome and subsequent regulatory changes)
- Markets where consensus pricing already reflects your information set
Leverage PolyGram's integrated Kelly Criterion calculator to determine appropriate stake amounts ahead of each transaction. The analytics suite encompasses payoff visualisations and maximum drawdown metrics. Start trading on PolyGram →