When do prophets profit in prediction markets?

2026-07-07

AI Summary

This study addresses the long-standing theoretical and empirical paradox in prediction markets wherein accurate forecasters often incur losses while seemingly irrational strategies yield profits. By establishing a rigorous equivalence between predictive accuracy and profitability, the authors introduce a "proper betting" strategy that relies solely on one’s own forecast and the prevailing market price: under sufficient liquidity, any forecast superior to the market price guarantees positive expected returns. The work provides the first general conditions under which accuracy translates into profit within a limit order book framework, characterizes the unique class of strategies with robust profitability guarantees, and elucidates how strategies lacking accuracy advantages can still profit. Empirical validation—through proper scoring rule–based game analysis, a novel return decomposition framework, AI model experiments, and real-world deployment on Kalshi (achieving 80.33% monthly returns and a Sharpe ratio of 3.35)—confirms this strategy as the sole effective pathway for reliably monetizing predictive skill.

Abstract

Prediction markets aggregate dispersed beliefs into prices that act as probabilistic forecasts of uncertain events. Classical theory establishes a clean equivalence between forecasting accuracy and trading profit, but only for the specific automated market maker (AMM) design. However, the largest exchanges today are based on central limit order books in which informed forecasters routinely lose money while uninformed strategies can profit on simple heuristics. We resolve this discrepancy by establishing a formal equivalence between predictive accuracy and profitability. For any strictly proper scoring rule $S$, we exhibit a "proper" betting strategy that depends only on the forecaster's prediction $\mathbf{p}$ and the market price $\mathbf{q}$, and earns positive expected profit whenever $\mathbf{p}$ outperforms $\mathbf{q}$ under $S$ and the market has sufficient liquidity. Moreover, this proper betting is essentially the only strategy with such robust profitability guarantee. The proof rests on a decomposition of expected profit that strictly generalizes the classical AMM guarantee and also explains how strategies can profit without an accuracy edge. Empirically, across thousands of forecasts by AI models, proper betting is the only strategy that reliably converts accuracy into profit, and we further identify systematic forecasting personas and show how the optimal proper strategy varies across them. A month-long live deployment on Kalshi achieves $+80.33\%$ return on investment with a Sharpe ratio of $3.35$.

Problem

• prediction markets
• forecasting accuracy
• profitability
• central limit order books
• proper scoring rules

Innovation

• proper betting strategy
• prediction markets
• strictly proper scoring rule
• profitability-accuracy equivalence
• market liquidity