GRU Learning of Asymmetric Sequence Structure in Penney’s Game

Alternation preference in random-sequence judgments has been linked to objective differences in pattern waiting times. The present study asks whether recurrent networks can learn such temporal asymmetries beyond single-pattern regularities and capture the more complex competitive structure of Penney’s game. To address this question, we adopt Penney’s game as a mathematically tractable testbed, in which competitive advantage is determined not by marginal sequence frequency but by the joint effect of self-overlap and cross-overlap structure. Based on Conway’s formula, we formulate two complementary tasks for gated recurrent units (GRUs): optimal counterstrategy prediction and win-probability estimation. Experimental results show that the GRU achieves strong performance on both tasks, recovering optimal or near-optimal second player responses and accurately estimating theoretical winning probabilities with good ranking consistency. These findings suggest that recurrent networks can learn structural regularities underlying asymmetric sequence competition, extending from single-pattern waiting-time effects to more complex competitive sequence settings.