Learning classifier systems traditionally use genetic algorithms to facilitate rule discovery, where rule fitness is payoff based. Current research has shifted to the use of accuracy-based fitness. This paper re-examines the use of a particular payoff-based learning classifier system—ZCS. By using simple difference equation models of ZCS, we show that this system is capable of optimal performance subject to appropriate parameter settings. This is demonstrated for both single- and multistep tasks. Optimal performance of ZCS in well-known, multistep maze tasks is then presented to support the findings from the models.