Letting bettors combine correlated events into a single wager should be dangerous for the market maker. Parlay bets expose the operator to complex joint distributions — if someone knows that events A and B are correlated and the market doesn't, the parlay is an arbitrage. Market operators typically prohibit parlays or price them with wide spreads to compensate.
Rana, Nadkarni, Moshrefi, and Viswanath show the opposite. In ParlayMarket, parlay trades improve the market's estimate of inter-event correlations. Each parlay trade reveals information about the joint distribution that individual-event trades cannot. The market maker's pricing error at stationarity is lower with parlays than without.
The mechanism: individual trades on event A and event B update marginal probabilities but reveal nothing about the relationship between A and B. A parlay on “A and B both happen” forces a price that implicitly encodes their correlation. As parlay traders exploit mispricings in the correlation structure, they correct it. The arbitrage opportunity self-destructs through the trading that exploits it.
Losses to the market maker grow at most quadratically with the number of base markets — a controlled cost. In exchange, the market converges to more accurate joint probabilities. The historical Kalshi data confirms the theory: parlay trades measurably reduce steady-state error compared to marginal-only trading.
The counterintuitive lesson: the bets that seem most dangerous to the market operator are the ones that teach it the most. Complexity is not risk — it's information in a format that simpler instruments can't express.