Many studies that aim to detect model-free and model-based influences on behavior employ two-stage behavioral tasks of the type pioneered by Daw and colleagues in 2011. Such studies commonly modify existing two-stage decision paradigms in order to better address a given hypothesis, which is an important means of scientific progress. It is, however, critical to fully appreciate the impact of any modified or novel experimental design features on the expected results. Here, we use two concrete examples to demonstrate that relatively small changes in the two-stage task design can substantially change the pattern of actions taken by model-free and model-based agents. In the first, we show that, under specific conditions, computer simulations of purely model-free agents will produce the reward by transition interactions typically thought to characterize model-based behavior on a two-stage task. The second example shows that model-based agents' behavior is driven by a main effect of transition-type in addition to the canonical reward by transition interaction whenever the reward probabilities of the final states do not sum to one. Together, these examples emphasize the benefits of using computer simulations to determine what pattern of results to expect from both model-free and model-based agents performing a given two-stage decision task in order to design choice paradigms and analysis strategies best suited to the current question.