To assess ACC’s involvement in model-based and model-free control, we require that the task recruit both systems and disambiguate the contribution of each to behavior. In the original two-step task, the contribution of each systems can be assessed by examining the so-called stay probabilities of repeating the first-step choice as a function of subsequent trial events. Model-based control causes the interaction of state transition (common or rare) and outcome (rewarded or not) to determine stay probabilities (Daw et al., 2011). This is because rewards following common transitions promote repeating the same choice on the next trial, but rewards following rare transitions increase the value of the state commonly accessed via the not-chosen first-step action and hence promote switching. Model-free control by contrast causes the outcome, but not transition, to determine stay probabilities, because rewards directly reinforce actions that precede them irrespective of the transition that occurred.
