Rhesus macaques, trained for several hundred trials on adjacent items in an ordered list (e.g. A>B, B>C, C>D, etc.), are able to make accurate transitive inferences (TI) about previously untrained pairs (e.g. A>C, B>D, etc.). How that learning unfolds during training, however, is not well understood. We sought to measure the relationship between the amount of training and the resulting response accuracy in four rhesus macaques, including the absolute minimal case of seeing each of the six adjacent pairs only once prior to testing. We also ran conditions with 24 and 114 trials. In general, learning effects were small, but they varied in proportion to the square root of the amount of training. These results suggest that subjects learned serial order in an incremental fashion. Thus, rather than performing transitive inference by a logical process, serial learning in rhesus macaques proceeds in a manner more akin to a statistical inference, with an initial uncertainty about list position that becomes gradually more accurate as evidence accumulates.