Factorial typologies derived from ranked constraints are familiar to most phonologists; the Jakobson syllable typology is a classic example. Probabilistic typologies that arrange syllables by their relative well-formedness can be similarly derived from probabilistic grammars. Evidence from Dagaare and Finnish shows that the same probabilistic universals hold true in two unrelated languages. Surprisingly, these universals only arise under some theories but not others. In particular, Maximum Entropy (ME) typologies are so unrestrictive that no syllable is predicted to be universally worse than any other syllable. Descriptively, ME models often fit the data closely, but these descriptive gains can be offset by explanatory losses. The fact that ME predicts many unnatural and hence unattested probabilistic relations among syllable types suggests that in this respect it is not a satisfactory basis for a theory of natural language phonology.