In this guide
Key takeaway: The Kelly Criterion calculates the optimal proportion of your capital to wager by accounting for your edge and the available odds. In prediction markets, it solves two critical problems: wagering excessively (and facing bankruptcy) or wagering conservatively (and forfeiting potential returns).
Determining how much to stake on each trade separates winners from those who lose everything. The Kelly Criterion — a mathematical framework created by John Kelly, a researcher at Bell Labs in 1956 — gives you the theoretically optimal stake size for achieving the highest compound growth over time. This guide shows you how to use it in 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 your capital to stake
- p = your projected likelihood of success
- q = likelihood of failure (1 - p)
- b = net odds (payout / stake). For a prediction market share trading at price c, b = (1 - c) / c
Worked example
Suppose you assess a 60% chance the outcome settles YES. The current market quote 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
According to Kelly, you should allocate 27.2% of your capital to this position. If you have $1,000 available, this translates to a $272 stake.
Why full Kelly is dangerous
The Kelly formula presumes you can pinpoint your true probability with certainty — something that never occurs in practice. Miscalculating your advantage upward results in severe overexposure. Experienced market participants consistently adopt fractional Kelly instead:
- Half Kelly (f*/2): The standard choice among professionals. Surrenders roughly 25% of theoretical gains but cuts volatility in half
- Quarter Kelly (f*/4): A safer strategy when your edge assessment carries substantial doubt
- Capped Kelly: Establish a ceiling—say 5-10% of total capital per single market—irrespective of what Kelly recommends
Applying Kelly to multi-market portfolios
Once you're holding stakes across several prediction markets at once, each individual Kelly fraction requires modification. The aggregate of all Kelly fractions must stay at or below 1.0 (your entire bankroll). Practically speaking, maintain combined positions below 50% of capital so you retain dry powder for emerging opportunities.
When Kelly does not apply
Kelly's framework depends on reliable probability estimates. Several circumstances undermine this assumption:
- Situations marked by radical uncertainty (unprecedented events with no track record)
- Linked markets (such as a presidential race and legislative control, which are not independent)
- Markets where you possess no informational advantage relative to the broader market
Use PolyGram's integrated Kelly Criterion calculator to determine position sizes ahead of each transaction. The analytics suite also features payoff visualisations and volatility metrics. Start trading on PolyGram →