A standard assumption in neuroscience is that low-effort model-free learning is automatic and continuously used, whereas more complex model-based strategies are only used when the rewards they generate are worth the additional effort. We present evidence refuting this assumption. First, we demonstrate flaws in previous reports of combined model-free and model-based reward prediction errors in the ventral striatum that probably led to spurious results. More appropriate analyses yield no evidence of model-free prediction errors in this region. Second, we find that task instructions generating more correct model-based behaviour reduce rather than increase mental effort. This is inconsistent with cost-benefit arbitration between model-based and model-free strategies. Together, our data indicate that model-free learning may not be automatic. Instead, humans can reduce mental effort by using a model-based strategy alone rather than arbitrating between multiple strategies. Our results call for re-evaluation of the assumptions in influential theories of learning and decision-making.