Based on the work by Eliaz and Spiegler (2020), we design a laboratory experiment aimed at understanding whether people, when facing competing narratives, are drawn to hopeful ones, defined depending on whether the agent’s actions do affect the probability to win in a zero-sum game against a robot. Our treatments consist of different manipulations of the instructions so to suggest, from ambiguous evidence, which rule governs the zero-sum game. We show that subjects’ ability to suppress an incorrect, intuitive answer, as measured by the Cognitive Reflection Test (CRT), mitigates their biased and inconsistent behaviour.