The amount of information conveyed by linguistic conventions depends on their precision, yet the codes that humans and other animals use to communicate are quite ambiguous: they may map several vague meanings to the same symbol. How does semantic precision evolve, and what are the constraints that limit it? We address this question using a multiplayer gaming app, where individuals communicate with one another in a scaled-up referential game. Here, the goal is for a sender to use black and white (...) symbols to communicate colors. We expected that the players’ mappings between symbols and colors would grow more specific over time, through a selection process whereby precise mappings are preferentially copied. We found that players become increasingly more precise in their use of symbols over the course of their interactions. This trend did not, however, result from selective copying of precise mappings. We explore the implications of this result for the study of lexical ambiguity, Zipf's Law of Meaning, and disagreements over semantic conventions. (shrink)