Studies of human exploration frequently cast people as serendipitously stumbling upon good options. Yet these studies may not capture the richness of exploration strategies that people exhibit in more complex environments. Here we study behaviour in a large dataset of 29,493 players of the richly structured online game 'Little Alchemy 2'. In this game, players start with four elements, which they can combine to create up to 720 complex objects. We find that players are driven not only by external reward signals, such as an attempt to produce successful outcomes, but also by an intrinsic motivation to create objects that empower them to create even more objects. We find that this drive for empowerment is eliminated when playing a game variant that lacks recognizable semantics, indicating that people use their knowledge about the world and its possibilities to guide their exploration. Our results suggest that the drive for empowerment may be a potent source of intrinsic motivation in richly structured domains, particularly those that lack explicit reward signals.