Abstract We consider the problem of automatically generating sequences of structured-light patterns for active stereo triangulation of a static scene. Unlike existing approaches that use predetermined patterns and reconstruction algorithms tied to them, we generate patterns on the fly in response to generic specifications: number of patterns, projectorcamera arrangement, workspace constraints, spatial frequency content, etc. Our pattern sequences are specifically optimized to minimize the expected rate of correspondence errors under those specifications for an unknown scene, and are coupled to a sequence-independent algorithm for perpixel disparity estimation. To achieve this, we derive an objective function that is easy to optimize and follows from first principles within a maximum-likelihood framework. By minimizing it, we demonstrate automatic discovery of pattern sequences, in under three minutes on a laptop, that can outperform state-of-the-art triangulation techniques.