An evolutionary multi-agent system is described that develops a rule-based approach to playing the game Dots and Boxes, under a probabilistic reinforcement learning paradigm. The process and behaviour using probabilistic action selection with a Boltzmann distribution is compared with an alternative technique using an Artificial Economy. The probabilistic system developed was played against a rule-based software opponent, and able to produce behaviour under a self-organising process able to perform better than the software opponent it was trained against.