Probability matching—where subjects given probabilistic in-put respond in a way that is proportional to those inputprobabilities—has long been thought to be characteristic ofprimate performance in probability learning tasks in a vari-ety of contexts, from decision making to the learning of lin-guistic variation in humans. However, such behaviour is puz-zling because it is not optimal in a decision theoretic sense;the optimal strategy is to always select the alternative with thehighest positive-outcome probability, known as maximising(in decision making) or regularising (in linguistic tasks). Whilethe tendency to probability match seems to depend somewhaton the participants and the task (i.e., infants are less likelyto probability match than adults, monkeys probability matchless than humans, and probability matching is less likely inlinguistic tasks), existing studies suffer from a range of defi-ciencies which make it difficult to robustly assess these dif-ferences. In this paper we present three experiments whichsystematically test the development of probability matchingbehaviour over time in simple decision making tasks, acrossspecies (humans and Guinea baboons), task complexity, andtask domain (linguistic vs non-linguistic). In Experiments 1and 2 we show that adult humans and Guinea baboons exhibitsimilar behaviour in a non-linguistic decision-making task and,contrary to the prevailing view, a tendency to maximise (ba-boons) or significantly over-match (humans) rather than prob-ability match, which strengthens over time and more so withgreater task complexity; our non-human sample size (N = 20baboons) is unprecedented in the probability-matching litera-ture. Experiment 3 provides evidence against domain-specificprobability learning mechanisms, showing that human subjectsover-match high positive-outcome probabilities to a similar de-gree across linguistic and non-linguistic tasks. Our results sug-gest that previous studies may simply have insufficient trials toshow maximising, or be too short to show maximising strate-gies which unfold over time. We thus provide evidence ofshared probability learning mechanisms not only across lin-guistic and non-linguistic tasks but also across primate species.