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Curiosity—our desire to know—is a fundamental drive in human behaviour, but its mechanisms are poorly understood. A classical question concerns the curiosity motives. What drives individuals to become curious about some but not other sources of information?1 Here we show that curiosity about probabilistic events depends on multiple aspects of the distribution of these events. Participants (n = 257) performed a task in which they could demand advance information about only one of two randomly selected monetary prizes that contributed to their income. Individuals differed markedly in the extent to which they requested information as a function of the ex ante uncertainty or ex ante value of an individual prize. This heterogeneity was not captured by theoretical models describing curiosity as a desire to learn about the total rewards of a situation2,3. Instead, it could be explained by an extended model that allowed for attribute-specific anticipatory utility—the savouring of individual components of the eventual reward—and postulates that this utility increased nonlinearly with the certainty of receiving the reward. Parameter values fitting individual choices were consistent for information about gains or losses, suggesting that attribute-specific anticipatory utility captures fundamental heterogeneity in the determinants of curiosity.