Probabilistic forecasts are fundamental tools for making decisions under uncertainty in a wide variety of fields, including weather, energy use, and finance. I will present a scheme whereby a base probabilistic forecasting system that is poorly-calibrated may be recalibrated by incorporating past performance information to produce a new forecasting system that is demonstrably superior to the original one, in that it can consistently win wagers against the original system. The scheme utilizes Gaussian Process modeling to estimate probability measures in a manner that gives closed-form access to information entropy measures, which allows prediction of winnings in certain wagers against the base forecasting system. The recalibration scheme is formulated in a framework that exploits the deep connections between information theory, forecasting, and betting.