Humans build models of their environments and act according to what they have learnt. In simple experimental environments, such model-based behaviour is often well accounted for as if subjects are ideal Bayesian observers. However, more complex probabilistic tasks require more sophisticated forms of inference that are sufficiently computationally and statistically taxing as to demand approximation. Here, we study properties of two approximation schemes in the context of a serial reaction time task in which stimuli were generated from a hierarchical Markov chain. One, pre-existing, scheme was a generically powerful variational method for hierarchical inference which has recently become popular as an account of psychological and neural data across a wide swathe of probabilistic tasks. A second, novel, scheme was more specifically tailored to the task at hand. We show that the latter model fit significantly better than the former. This suggests that our subjects were sensitive to many of the particular constraints of a complex behavioural task. Further, the tailored model provided a different perspective on the effects of cholinergic manipulations in the task. Neither model fit the behaviour on more complex contingencies that competently. These results illustrate the benefits and challenges that come with the general and special purpose modelling approaches and raise important questions of how they can advance our current understanding of learning mechanisms in the brain.