Participants in most binary-choice tasks with multiple trials tend to probability-match (Vulkan, 2000) — i.e., provide re- sponses that match the probability distribution of the presented population. Given a single trial, however, participants usually choose the majority option (James & Koehler, 2011). By us- ing a method that visually presents the probabilities of the two competing options, we examine responses when participants are given only a single trial, and initial responses when partic- ipants are given multiple trials. While we still observe aggre- gate probability-matching in the multiple-trial condition, we find robust sequence effects in participants’ initial responses, including robust maximizing behavior on the first response. This suggests that both maximizing in single-trial experiments and aggregate probability-matching in multiple-trial ones can be explained by a single, underlying mechanism; one that seeks to provide a representative sample at each point during sequence generation.