In classifier languages, a sequence consisting of a noun (N), a numeral (Num), and a numeral classifier (CL) could in principle occur in one of six possible word orders. However, the cross-linguistic distribution of these word orders is highly uneven. Specifically, classifier languages tend to use Num-CL orders and, furthermore, N-medial orders are completely unattested in the world’s languages. We use an artificial language learning paradigm (Experiment 1) and a silent gesture paradigm (Experiment 2) to test the hypothesis that typological patterns arise from cognitive biases at the level of individual speakers. In contrast to studies that examined coarser grained ordering effects, our results do not align with typological preferences. We consider the possibility that cognitive biases might not play a role in “finer grained” ordering phenomena involving units such as classifiers, whose role in an utterance is more about grammatical well-formedness than a strong contribution to meaning.