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, yet game theory suggests that being unpredictable to an opponent requires true randomness. In our first experiment (50 Japanese adults), we show that when the goal shifts from being random to being unpredictable, participants do the opposite, generating sequences with a strong repetition bias. In a second experiment, we asked a new sample of 50 Japanese adults 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.