The Paradox of Unpredictability: Trying to Be Unpredictable Makes Sequences More Predictable

Human intuition about randomness is systematically biased. When asked to generate random sequences, people systematically generate too many alternations. At the same time, game-theoretic analyses of competitive interactions prescribe truly random mixed strategies as the unique way to remain unpredictable to an opponent. Despite this formal equivalence between randomness and unpredictability, research on cognitive biases in sequential judgment and on strategic behavior in games has largely proceeded in parallel, leaving open how biased internal models of randomness shape behavior when the explicit goal is to be unpredictable. Here we bring these traditions together in two experiments in which one group of participants generates sequences and another predicts them. In our first experiment, we show that when the goal shifts from being random to being unpredictable, participants reverse this pattern, generating sequences with a strong repetition bias. In a second experiment, we asked new participants to predict two model-derived sequences that were empirically calibrated to the group-level statistics from the first experiment (Competitive-like vs Random-like). We found a paradox: the repetitive sequences intended to be unpredictable were in fact more predictable than the alternating sequences intended to be random. This paradox appears to stem from an asymmetric reinforcement learning mechanism, whereby success selectively strengthens beliefs in repetition but not alternation. Our findings bridge classic cognitive bias and strategic behavior, suggesting how a fundamental learning mechanism can shape paradoxical predictability.