Economic research on entertainment is scant despite its large share of time use. We test economic theories of belief-based utility in the context of video-game engagement. Using data on 2.8 million matches from League of Legends, we find evidence supporting reference-dependent preferences, loss aversion, preferences for surprise and suspense, preferences for clumped surprise, and flow theory from psychology. We then leverage our estimated model and an evolutionary algorithm to find the information-revealing process that maximizes player engagement. We find that the optimal version of the game has increased game play equivalent to 43% of the winner-loser gap.