A central challenge in cognitive science is to measure and quantify the mental representations humans develop - in other words, to 'read' subject's minds. In order to eliminate potential biases in reporting mental contents due to verbal elaboration, subjects' responses in experiments are often limited to binary decisions or discrete choices that do not require conscious reflection upon their mental contents. However, it is unclear what such impoverished data can tell us about the potential richness and dynamics of subjects' mental representations. To address this problem, we used ideal observer models that formalise choice behaviour as (quasi-)Bayes-optimal, given subjects' representations in long-term memory, acquired through prior learning, and the stimuli currently available to them. Bayesian inversion of such ideal observer models allowed us to infer subjects' mental representation from their choice behaviour in a variety of psychophysical tasks. The inferred mental representations also allowed us to predict future choices of subjects with reasonable accuracy, even in tasks that were different from those in which the representations were estimated. These results demonstrate a significant potential in standard binary decision tasks to recover detailed information about subjects' mental representations.