In this guide
Key takeaway: The Kelly Criterion determines the optimal proportion of your bankroll to allocate to each bet, accounting for your edge and available odds. In prediction markets, it guards against two critical pitfalls: wagering excessively (and facing bankruptcy) or wagering conservatively (and forgoing potential gains).
Proper bet sizing separates successful market participants from those who deplete their capital. 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 maximum sustainable returns. This guide explains its application within prediction markets.
The Kelly formula
For a binary prediction market (YES/NO), the Kelly fraction is:
f* = (p * b - q) / b
Where:
- f* = proportion of bankroll to wager
- p = your projected likelihood of success
- q = likelihood of failure (1 - p)
- b = net odds (payout / stake). For a prediction market share at price c, b = (1 - c) / c
Worked example
Suppose you assess a 60% probability that an outcome settles YES. The current market quotation stands at 45 cents (reflecting an implied 45% 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
According to Kelly, allocate 27.2% of your bankroll. If your capital totals $1,000, you would deploy $272 on this position.
Why full Kelly is dangerous
The Kelly formula presumes you possess perfect knowledge of your true probability — a condition that never materialises in practice. Miscalculating your advantage results in severe overexposure. Seasoned market operators consistently adopt fractional Kelly:
- Half Kelly (f*/2): The industry standard. Surrenders roughly 25% of theoretical gains but halves volatility exposure
- Quarter Kelly (f*/4): Prudent method when confidence in your edge remains limited
- Capped Kelly: Establish a ceiling of 5-10% of total capital per individual market, overriding any Kelly calculation that exceeds this threshold
Applying Kelly to multi-market portfolios
When you maintain concurrent stakes across numerous prediction markets, individual Kelly percentages require recalibration. The aggregate of all Kelly percentages must remain at or below 1.0 (your complete bankroll). Realistically, maintain cumulative risk beneath 50% to preserve dry powder for emerging opportunities.
When Kelly does not apply
Kelly presupposes reliable estimation of your true probability. Multiple contexts undermine this assumption:
- Situations involving extreme ambiguity (unprecedented circumstances lacking historical reference points)
- Interdependent markets (a presidential election and legislative composition exhibit statistical dependence)
- Markets where your analysis offers no advantage relative to prevailing market consensus
Leverage PolyGram's integrated Kelly Criterion calculator to determine appropriate stake amounts prior to executing each transaction. The risk management toolkit incorporates payoff visualisations and maximum drawdown metrics. Start trading on PolyGram →