Prediction markets: when prophets profit, Kalshi +80.33%

When do prophets profit in prediction markets?, submitted 7 July 2026 by Anri Gu, Nicole Kagan, Alec Sun, Jibang Wu and Haifeng Xu, establishes a formal link between forecasting accuracy and trading profit and reports a month-long live deployment on Kalshi that returned +80.33% with a Sharpe ratio of 3.35. The paper proves a constructive result and backs it with empirical tests across thousands of AI model forecasts.

What did the paper prove?

The authors prove that for any strictly proper scoring rule S there exists a "proper" betting strategy that depends only on a forecaster's prediction p and the market price q, and that this strategy earns positive expected profit whenever p outperforms q under S and the market has sufficient liquidity. They also show that this proper betting strategy is essentially the only strategy that offers such a robust profitability guarantee. The proof uses a decomposition of expected profit that generalizes the classical automated market maker (AMM) guarantee.

The paper contrasts that classical result with the reality of modern exchanges, noting that the classical equivalence between forecasting accuracy and trading profit holds for the specific AMM design, while the largest exchanges today use central limit order books where informed forecasters can routinely lose money and uninformed heuristics can make money.

How does the "proper" betting strategy work?

The core idea is simple: map forecast accuracy measured by a strictly proper scoring rule into a betting rule that only needs the forecaster's prediction p and the prevailing market price q, and place bets that have positive expected value whenever the scoring-rule comparison favors p over q. The paper constructs this betting rule and proves the claim under a liquidity assumption, and it proves a uniqueness-type result showing that few other strategies can provide an equally robust accuracy-to-profit guarantee.

Methodologically the authors derive a decomposition of expected profit that both extends the AMM guarantee and explains why some trading strategies can profit even without an accuracy edge. Empirically they apply the proper betting rule to thousands of forecasts produced by AI models and find that proper betting is the only tested strategy that reliably converts improved accuracy into trading profit.

What evidence supports the claim?

The paper reports two empirical points: first, tests across thousands of forecasts by AI models show that proper betting consistently converts accuracy into profit where other strategies do not. Second, a month-long live deployment on the Kalshi exchange produced a +80.33% return on investment with a Sharpe ratio of 3.35. Those figures anchor the theoretical claim with a concrete trading outcome.

Why it matters

Prediction markets are often pitched as mechanisms that turn dispersed beliefs into useful price signals. The paper resolves a long-standing puzzle: classical AMM theory tied accuracy directly to profit, but many real-world markets use central limit order books and have produced counterintuitive results where accurate forecasters lose. By giving a betting strategy that formally converts accuracy into expected profit, the authors bridge theory and practice and explain how market design and liquidity conditions shape whether accurate forecasting pays.

This matters for market designers, institutional forecasters and AI teams producing probabilistic predictions, because it clarifies when improving forecast quality yields economic value and when it may not.

What to watch

Look for formal follow-ups that test the proper betting strategy across additional live venues and varying liquidity regimes, and for implementations by market makers or platforms. The paper's arXiv entry is arXiv:2607.06166 and the live Kalshi result — +80.33% ROI with a Sharpe ratio of 3.35 over one month — is the clearest immediate signal that the construction can work in practice.