KL-Divergence Arb Detector

What is KL Divergence?

Kullback–Leibler divergence is an information-theoretic measure of how different two probability distributions are. In prediction markets, each platform's YES/NO price defines a binary probability distribution. When two platforms price the same event differently, KL divergence quantifies the gap — not just in raw cents, but in terms of how inconsistent the two belief systems are.

Why use KL instead of just taking the price difference? A 10¢ gap at 50¢ vs. 40¢ is very different from a 10¢ gap at 90¢ vs. 80¢. KL divergence is sensitive to where in the probability space the gap occurs — extreme probabilities create larger divergence for the same raw price difference, which is exactly what you want when hunting for exploitable mispricings.

The ARB threshold

A symmetric KL above 0.15 is our flag for a potentially exploitable divergence. At that level, the two distributions are meaningfully inconsistent — one price is significantly wrong relative to the other. That doesn't guarantee a riskless arb (resolution terms, liquidity, and timing matter), but it tells you one of these prices deserves scrutiny. The bigger the symmetric KL, the more one-sided the story.

How to act on it

When the tool flags ARB, the next step is verifying that both markets resolve on the same event, on the same date, with compatible terms. If they do, you buy YES on the cheap platform and NO on the expensive one (or YES on both if the combined cost is below $1.00). Then check bid-ask spreads and order book depth — a flagged arb with thin books may not be executable at the displayed price.