Participants in most binary-choice tasks with multiple trialstend to probability-match (Vulkan, 2000) — i.e., provide re-sponses that match the probability distribution of the presentedpopulation. Given a single trial, however, participants usuallychoose the majority option (James & Koehler, 2011). By us-ing a method that visually presents the probabilities of the twocompeting options, we examine responses when participantsare 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, wefind robust sequence effects in participants’ initial responses,including robust maximizing behavior on the first response.This suggests that both maximizing in single-trial experimentsand aggregate probability-matching in multiple-trial ones canbe explained by a single, underlying mechanism; one thatseeks to provide a representative sample at each point duringsequence generation.