Regularity detection, or statistical learning, is regarded as a fundamental component of our cognitive system. To test the ability of human participants to detect regularity in a more ecological situation (i.e., mixed with random information), we used a simple letter-naming paradigm in which participants were instructed to name single letters presented one at a time on a computer screen. The regularity consisted of a triplet of letters that were systematically presented in that order. Participants were not told about the presence of this regularity. A variable number of random letters were presented between two repetitions of the regular triplet, making this paradigm similar to a Hebb repetition task. Hence, in this Hebb-naming task, we predicted that if any learning of the triplet occurred, naming times for the predictable letters in the triplet would decrease as the number of triplet repetitions increased. Surprisingly, across four experiments, detection of the regularity only occurred under very specific experimental conditions and was far from a trivial task. Our study provides new evidence regarding the limits of statistical learning and the critical role of contextual information in the detection (or not) of repeated patterns.