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 a specific automated market maker (AMM) design.
However, the largest exchanges today are based on central limit order books where informed forecasters often lose money while uninformed strategies can profit through 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 $\mathbf{q}$, earning 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 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. We further identify systematic forecasting personas and show how the optimal proper strategy varies across them.
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Blogger's Review: This article delves into the profit mechanisms within prediction markets, revealing how to achieve profitability even in information-asymmetrical environments through rational betting strategies. It provides valuable insights for traders, especially in today's complex market conditions. The right strategy relies not only on accurate predictions but also on market liquidity, offering crucial guidance for practical trading decisions.