The recently developed two-step behavioural task promises to differentiate model-based from model-free reinforcement learning, while generating neurophysiologically-friendly decision datasets with parametric variation of decision variables. These desirable features have prompted its widespread adoption. Here, we analyse the interactions between a range of different strategies and the structure of transitions and outcomes in order to examine constraints on what can be learned from behavioural performance. The task involves a trade-off between the need for stochasticity, to allow strategies to be discriminated, and a need for determinism, so that it is worth subjects investment of effort to exploit the contingencies optimally. We show through simulation that under certain conditions model-free strategies can masquerade as being model-based. We first show that seemingly innocuous modifications to the task structure can induce correlations between action values at the start of the trial and the subsequent trial events in such a way that analysis based on comparing successive trials can lead to erroneous conclusions. We confirm the power of a suggested correction to the analysis that can alleviate this problem. We then consider model-free reinforcement learning strategies that exploit correlations between where rewards are obtained and which actions have high expected value. These generate behaviour that appears model-based under these, and also more sophisticated, analyses. Exploiting the full potential of the two-step task as a tool for behavioural neuroscience requires an understanding of these issues. 