The Stroop effect suggests that humans arbitrate between automatic and controlled processing. Previous work argues that this arbitration reflects a cost-benefit analysis, weighing cognitive effort against performance. However, it is unclear how these costs and benefits can be quantified and how the trade-off between them can be performed. We present a Bayesian network model of the Stroop effect in which actions are selected by minimizing variational free energy. Based on this approach, we derive information-theoretic measures of the costs and benefits of both automatic and controlled processing and show that minimizing free energy optimizes the trade-off between them. Furthermore, we demonstrate that the so-called congruency and proportion congruency effects in the Stroop task are the result of this optimization, in an environment that contains specific statistical regularities. Thereby, we provide an explicit account of when and how much automatic and controlled processing should be expected under a rational trade-off.