Interacting with a system is key to uncovering its causal structure. A computational framework for interventional causal learning has been developed over the last decade, but how real causal learners might achieve or approximate the computations entailed by this framework is still poorly understood. Here we describe an interactive computer task in which participants were incentivized to learn the structure of probabilistic causal systems through free selection of multiple interventions. We develop models of participants’ intervention choices and online structure judgments, using expected utility gain, probability gain, and information gain and introducing plausible memory and processing constraints. We find that successful participants are best described by a model that acts to maximize information (rather than expected score or probability of being correct); that forgets much of the evidence received in earlier trials; but that mitigates this by being conservative, preferring structures consistent with earlier stated beliefs. We explore 2 heuristics that partly explain how participants might be approximating these models without explicitly representing or updating a hypothesis space.