Current theories propose that our sense of curiosity is determined by the learning progress or information gain that our cognitive system expects to make. However, few studies have explicitly tried to quantify subjective information gain and link it to measures of curiosity. Here, we asked people to report their curiosity about the intrinsically engaging perceptual ‘puzzles’ known as Mooney images, and to report on the strength of their aha experience upon revealing the solution image (curiosity relief). We also asked our participants (279) to make a guess concerning the solution of the image, and used the distribution of these guesses to compute the crowdsourced semantic entropy (or ambiguity) of the images, as a measure of the potential for information gain. Our results confirm that curiosity and, even more so, aha experience is substantially associated with this semantic information gain measure. These findings support the expected information gain theory of curiosity and suggest that the aha experience or intrinsic reward is driven by the actual information gain. In an unannounced memory part, we also established that the often reported influence of curiosity on memory is fully mediated by the aha experience or curiosity relief. We discuss the implications of our results for the burgeoning fields of curiosity and psychoaesthetics.