Learning classifier systems use genetic algorithms to facilitate rule-discovery, where rule fitness has traditionally been payoff prediction-based. Current research has shifted to the use of accuracy-based fitness. This paper presents a simple Markov model of the algorithm in such systems, allowing comparison between the two forms of rule utility measure. Using a single-step task the previously discussed benefits of accuracy over prediction are clearly shown with regard to overgeneral rules. The effects of a niche-based algorithm (maximal generality) are also briefly examined, as are the effects of mutation under the two fitness schemes. Finally, the behaviour of the Genetic Algorithm during the solution of multi-step tasks is investigated.