Decision-making algorithms face a basic tradeoff between accuracy and effort (i.e., computational demands). It is widely agreed that humans can choose between multiple decision-making processes that embody different solutions to this tradeoff: Some are computationally cheap but inaccurate, whereas others are computationally expensive but accurate. Recent progress in understanding this tradeoff has been catalyzed by formalizing it in terms of model-free (i.e., habitual) versus model-based (i.e., planning) approaches to reinforcement learning. Intuitively, if two tasks offer the same rewards for accuracy but one of them is much more demanding, we might expect people to rely on habit more in the difficult task: Devoting significant computation to achieve slight marginal accuracy gains would not be “worth it.” We test and verify this prediction in a sequential reinforcement learning task. Because our paradigm is amenable to formal analysis, it contributes to the development of a computational model of how people balance the costs and benefits of different decision-making processes in a task-specific manner; in other words, how we decide when hard thinking is worth it.

To support reward-based decision-making, the brain must encode potential outcomes both in terms of their incentive value and their probability of occurrence. Recent research has made it clear that the brain bears multiple representations of reward magnitude, meaning that a single choice option may be represented differently—and even inconsistently—in different brain areas. There are some hints that the same may be true for reward probability. Preliminary evidence hints that, even as systematic distortions of probability are expressed in behavior, these may not always be uniformly reflected at the neural level: Some neural representations of probability may be immune from such distortions. This study provides new evidence consistent with this possibility. Participants in a behavioral experiment displayed a classic “illusion of control,” providing higher estimates of reward probability for gambles they had chosen than for identical gambles that were imposed on them. However, an fMRI study of the same task revealed that neural prediction error signals, arising when gamble outcomes were revealed, were unaffected by the illusion of control. The resulting behavioral–neural dissociation reinforces the case for multiple, inconsistent internal representations of reward probability, while also prompting a reinterpretation of the illusion of control effect itself.