A key goal of visual neuroscience is to explain how our brains infer object properties such as colour, curvature or gloss. Here we used machine learning to identify computations underlying human gloss judgements-traditionally considered a challenging inference. We rendered thousands of objects with varied shapes using a Ward reflectance model across lighting and viewpoints, then obtained gloss ratings for each image. Observers' judgements were consistent with one another, yet systematically deviated from reality. We compared these ratings with neural networks trained either to estimate physical reflectance ('ground-truth networks') or to reproduce human judgements ('human-like networks'). While estimating physical reflectance required deep networks, shallow networks accurately replicated human judgements. Remarkably, even a single-filter network could predict human judgements better than the best ground-truth network and generalized to known gloss illusions. These results suggest that gloss perception relies on simple general-purpose computations, and demonstrate the power of interpretable 'tiny' networks in understanding cognition.