Kelly Criterion for Prediction Markets: Size Your Bets
Key takeaway: The Kelly Criterion tells you what fraction of your bankroll to bet based on your edge and the odds. In prediction markets, it prevents the two most common mistakes: betting too much (risking ruin) and betting too little (leaving profits on the table).
Position sizing is the difference between a profitable trader and a broke one. The Kelly Criterion — a formula developed by Bell Labs researcher John Kelly in 1956 — provides the mathematically optimal bet size for maximising long-term growth. Here is how to apply it to prediction markets.
The Kelly formula
For a binary prediction market (YES/NO), the Kelly fraction is:
f* = (p * b - q) / b
Where:
- f* = fraction of bankroll to bet
- p = your estimated probability of winning
- q = probability of losing (1 - p)
- b = net odds (payout / stake). For a prediction market share at price c, b = (1 - c) / c
Worked example
You believe there is a 60% chance an event resolves YES. The market price is 45 cents (implying 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
Kelly says bet 27.2% of your bankroll. With a $1,000 bankroll, that is $272 on this trade.
Why full Kelly is dangerous
The Kelly formula assumes you know your true probability exactly — which you never do. Overestimating your edge leads to catastrophic overbetting. Professional traders universally use fractional Kelly:
- Half Kelly (f*/2): The most common recommendation. Sacrifices ~25% of optimal growth but reduces volatility by 50%
- Quarter Kelly (f*/4): Conservative approach for uncertain edge estimates
- Capped Kelly: Never bet more than 5-10% of bankroll on a single market, regardless of Kelly output
Applying Kelly to multi-market portfolios
When you have positions in multiple prediction markets simultaneously, the individual Kelly fractions need adjustment. The sum of all Kelly fractions should not exceed 1.0 (100% of bankroll). In practice, keep total exposure under 50% to maintain reserves for new opportunities.
When Kelly does not apply
Kelly assumes you can estimate your true probability accurately. In several situations this breaks down:
- Events with deep uncertainty (novel situations with no historical precedent)
- Correlated markets (election outcome + party control are not independent bets)
- Markets where you have no informational edge over the consensus
Use PolyGram's built-in Kelly Criterion calculator to size your bets before every trade. The risk toolkit also includes payoff diagrams and drawdown analysis. Start trading on PolyGram →