In this guide
Key takeaway: The Kelly Criterion determines the optimal percentage of your capital to allocate to each wager, accounting for your informational advantage and available odds. In prediction markets, it guards against two critical pitfalls: excessive wagering (which threatens total capital loss) and insufficient wagering (which forgoes achievable returns).
Stake allocation separates consistently profitable market participants from those who deplete their capital. The Kelly Criterion — a mathematical framework derived by John Kelly, a researcher at Bell Labs, in 1956 — calculates the theoretically optimal allocation size for achieving sustainable capital expansion. This guide explains its implementation 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 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
The Kelly formula recommends committing 27.2% of your capital. If your total capital is $1,000, this translates to a $272 position in this particular trade.
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 informational advantage produces severe overallocation. Institutional traders and sophisticated participants routinely employ fractional Kelly:
- Half Kelly (f*/2): The predominant choice among professionals. Surrenders roughly 25% of theoretical maximum growth whilst cutting volatility in half
- Quarter Kelly (f*/4): A more cautious approach suited to situations where edge confidence remains limited
- Capped Kelly: Establish an absolute ceiling — typically 5-10% of capital per individual market — irrespective of Kelly's recommendation
Applying Kelly to multi-market portfolios
When you maintain concurrent stakes across several prediction markets, the individual Kelly allocations require recalibration. The aggregate of all Kelly percentages must remain at or below 1.0 (100% of capital). Practically speaking, restrict cumulative deployment to 50% or lower to preserve dry powder for emerging opportunities.
When Kelly does not apply
The Kelly framework depends on reliable probability assessment. Several circumstances undermine this assumption:
- Situations characterised by extreme unpredictability (unprecedented events lacking historical data)
- Markets exhibiting statistical dependence (such as presidential election outcome and legislative control, which are not autonomous events)
- Markets where your analysis yields no advantage relative to the aggregate market view
PolyGram provides an integrated Kelly Criterion calculator to optimise your allocation prior to execution. The analytical suite encompasses payoff visualisation and maximum drawdown measurement. Start trading on PolyGram →