“experience weighted attraction” [@Gal13]. Here, actions that have proved successful in the past are played more frequently. In the context of cyclic competition, this can give rise to a wide range of competitive and cooperative behaviours, including quasiperiodicity, limit cycles, intermittency and chaos [@Sat03]. If agents learn by sampling a finite number of their opponents’ moves between strategy updates, the noise inherent in these samples has been shown [@Gal09] to lead to noise-sustained cycling or removal of periodic orbits present in the limit of infinite sample size. The processes of sampling in between strategy updates is referred to as “batch learning”.

In this paper we introduce learning dynamics in which agents possess a simple form of finite memory for their previous interactions. They use this to predict the current best pure strategy, adjusting their probabilistic strategy after each new interaction. Each agent’s memory acts as a sample used for “online learning” as opposed to batch learning, and this distinction is central to the effects we uncover. We use our learning rule to investigate the children’s game of rock-scissors-paper where rock blunts scissors, scissors cut paper, and paper wraps rock. The three strategies cyclically dominate each other [@Sza07], a situation which 