Knowledge of language involves knowledge of complex linguistic systems, such as syntax and phonology. One difficulty in acquiring complex linguistic systems is that children must infer the correct system components while only ever encountering examples of the system's output in the form of the observable data native speakers generate. Recent computational modeling work has suggested that children can succeed in acquiring a parametric system of metrical phonology for English if selective learning biases on the data intake are used in tandem with probabilistic learning algorithms (Pearl, 2008; Pearl, submitted). The present modeling study supports the necessity of a learning bias by showing that unbiased probabilistic models fail on this same case study. While the unbiased models specifically examined are likely to be more cognitively plausible than other possible unbiased models, the more general result found is that all unbiased models—of whatever complexity—will fail, due to properties of English child-directed speech. This suggests that children cannot be unbiased probabilistic learners, and instead must rely on additional constraints in order to acquire complex linguistic systems.