We study the potential value to stakeholders of probabilistic long-term forecasts, as quantified by the mean information gain of the forecast compared to climatology. We use as a case study the USA Climate Prediction Center (CPC) forecasts of 3-month temperature and precipitation anomalies made at 0.5-month lead time since 1995. Mean information gain was positive but low (about 2% and 0.5% of the maximum possible for temperature and precipitation forecasts, resp.) and has not increased over time. Information-based skill scores showed similar patterns to other, non-information-based, skill scores commonly used for evaluating seasonal forecasts but tended to be smaller, suggesting that information gain is a particularly stringent measure of forecast quality. We also present a new decomposition of forecast information gain into Confidence, Forecast Miscalibration, and Climatology Miscalibration components. Based on this decomposition, the CPC forecasts for temperature are on average underconfident while the precipitation forecasts are overconfident. We apply a probabilistic trend extrapolation method to provide an improved reference seasonal forecast, compared to the current CPC procedure which uses climatology from a recent 30-year period. We show that combining the CPC forecast with the probabilistic trend extrapolation more than doubles the mean information gain, providing one simple avenue for increasing forecast skill.