Acting judiciously in an environment requires capitalising on the statistical structure underlying observed stimuli. However, structure is expensive to determine and exploit, so efficient learners should focus exclusively on utility-relevant characteristics. To assess this, we administered a pair of related tasks, the first ('learning') required subjects to determine and exploit relevant, and ignore irrelevant, structure to maximize reward; the second ('read-out') quantified their resulting sensitivity to different structure components. Statistical relationships were realised in sampled three-dimensional scenes rendered using a graphics engine to achieve greater ecological validity. In the learning task, participants learned a binary categorisation of stimuli from partial feedback, where only part of the higher-order structure in stimulus statistics was helpful for determining the optimal action. The read-out task involved a two-alternative forced choice familiarity judgement, where one of each pair of displayed images was sampled from the distribution used in the learning task, with the other being drawn from an ablated version of the distribution. Different conditions used ablations that kept either the reward-relevant or the reward-irrelevant part of the higher-order structure intact, or removed it all. The participants’ ability to identify which image came from the true distribution was indicative of them having learned the part of the higher-order structure absent in the ablated distribution. We collected data via Prolific using three variants of the design, and found that participants somewhat consistently exhibited statistical learning. In block designs, statistical learning was specific to the reward structure in the learning task for the participants performing well during learning, while it was unspecific for low performers. This result is consistent with cognitive resources for statistical learning being allocated taking usefulness in tasks into account. However, perplexing aspects of the behavioural patterns in our paradigm motivate further empirical assessment of task-based statistical learning in humans.