People successfully communicate in everyday situations using vague language. In particular, colour terms have no clear boundaries as to the ranges of colours they describe. We model people’s reasoning process in a dyadic reference game using the Rational Speech Acts (RSA) framework and probabilistic semantics, and we find that the implementation of probabilistic semantics requires a modification from pure theory to perform well on real-world data. In addition, we explore approaches to handling target disagreements in reference games, an issue that is rarely discussed in the RSA literature.