In this guide
Key takeaway: The Kelly Criterion calculates the optimal proportion of your capital to stake based on your probabilistic advantage and available odds. In prediction markets, it solves two critical problems: wagering excessively (and facing bankruptcy) versus wagering conservatively (and forgoing potential gains).
Determining how much to stake on each trade separates consistent winners from those who deplete their accounts entirely. The Kelly Criterion — a mathematical framework developed by John Kelly, a researcher at Bell Labs, in 1956 — establishes the theoretically ideal stake magnitude for achieving sustained capital expansion. 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 total capital to allocate
- p = your assessed likelihood of a successful outcome
- q = likelihood of an unsuccessful outcome (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 event concludes YES. The current market valuation stands at 45 cents (reflecting a 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
According to Kelly, you should allocate 27.2% of your capital. If your total capital is $1,000, this corresponds to a $272 position in this particular trade.
Why full Kelly is dangerous
The Kelly formula presumes you possess exact knowledge of your true probability — a condition that never materialises in practice. Underestimating uncertainty and overestimating your informational edge results in severe overexposure. Experienced market participants consistently adopt fractional Kelly:
- Half Kelly (f*/2): The standard choice among professionals. Surrenders roughly 25% of theoretical maximum returns whilst cutting volatility in half
- Quarter Kelly (f*/4): A more cautious approach when your edge assessment carries substantial doubt
- Capped Kelly: Establish a ceiling — for instance, never exceed 5-10% of total capital per single market, irrespective of what Kelly prescribes
Applying Kelly to multi-market portfolios
When you maintain concurrent stakes across numerous prediction markets, individual Kelly calculations require modification. The aggregate of all Kelly fractions must remain at or below 1.0 (your entire bankroll). Practically speaking, restrict cumulative exposure to under 50% so you retain dry powder for emerging opportunities and favourable dislocations.
When Kelly does not apply
Kelly's validity rests on your capacity to reliably estimate true probabilities. Multiple circumstances undermine this assumption:
- Unprecedented events characterised by extreme ambiguity (situations lacking comparable historical data)
- Interconnected markets (such as presidential election outcomes and legislative control, which share common drivers)
- Markets where consensus pricing already incorporates all publicly available information, eliminating your analytical advantage
Leverage PolyGram's integrated Kelly Criterion calculator to determine stake sizes ahead of executing any trade. The analytics suite encompasses payoff visualisations and historical drawdown metrics. Start trading on PolyGram →