When do prophets profit in prediction markets?

Prediction markets aggregate dispersed beliefs into prices that act as probabilistic forecasts of uncertain events. Classical theory establishes how a better-than-market forecast can yield positive trading profit. However, it hinges crucially on the specific automated market maker (AMM) design, and is not applicable to popular exchanges today which are based on central limit order books. This paper fills that gap. For any prediction market and any proper scoring rule S, we exhibit a ``proper'' betting strategy that depends only on the forecaster's prediction p and the market price q, and earns positive expected profit whenever p outperforms q under S and the market has sufficient liquidity. Moreover, this proper betting is essentially the only strategy with such robust profitability guarantee. Our proof rests on a decomposition of expected profit that strictly generalizes the classical AMM guarantee and also explains how strategies can profit even 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. For feasibility demonstration, we run a monthlong live pilot test on Kalshi; the encouraging preliminary results show that proper betting can survive real-world spreads, fees, discrete fills, and limited liquidity.