The role of intuitive monitoring and control of analytic calculations in the bat-and-ball problem

We explore intuitive monitoring and control within a Brunswikian framework where intuition refers to probabilistic processes rooted in perception and inductive experience, while analysis involves deterministic processing of facts and symbols, in turn implying operational criteria in terms of different response distributions. In the context of the bat-and-ball problem, we test the claim that intuition uses contextual cues to monitor the analytic calculations. Across two experiments, we show that participants' responses fall into three categories: (i) the normative algorithm, (ii) a simple response bias, and (iii) responses where contextual cues are taken into consideration by switching the cost of the bat and the ball when such a shift is intuitively plausible. The results suggest that, although it may be difficult to elicit intuitive control in a maths quiz like the bat-and-ball problem, the choice of analytical calculation is affected by the intuitive plausibility of the output in the predicted direction.