From birth, human infants engage in intrinsically motivated, open-ended learning, mainly by deciding what to attend to and for how long. Yet, existing formal models of the drivers of looking are very limited in scope. To address this, we present a new version of the Rational Action, Noisy Choice for Habituation (RANCH) model. This version of RANCH is a stimulus-computable, rational learning model that decides how long to look at sequences of stimuli based on expected information gain (EIG). The model captures key patterns of looking time documented in the literature, habituation and dishabituation. We evaluate RANCH quantitatively using large datasets from adult and infant looking time experiments. We argue that looking time in our experiments is well described by RANCH, and that RANCH is a general, interpretable and modifiable framework for the rational analyses of intrinsically motivated learning by looking.