This study presents a strong solution for the two-player, perfect-information, zero-sum board game PYLOS under three different rule sets: the rule set for children, the standard rule set, and the rule set for mature players. Using a zero-suppressed binary decision diagram, we systematically index all pseudo-reachable positions, that is, those that satisfy necessary structural constraints but may not be reachable during actual gameplay. Retrograde analysis is then executed on each rule set to assign game-theoretic values to all positions. A total of over 12 billion pseudo-reachable positions are considered. We also develop a method to extract truly reachable positions from this superset and verify the consistency of both indexing and value assignments. Experiments show that in all three rule sets, the first player is forced to lose, from the initial position, within 36, 40, and 46 moves, respectively. Furthermore, our analysis reveals that PYLOS has a higher proportion of zugzwang positions compared to previously solved games, emphasizing the strategic importance of conserving spheres. The mature players’ rule set generated the greatest number of legal moves. This study demonstrates the feasibility of computing strong solutions to PYLOS, and highlights structural differences among the three rule sets in terms of reachability and strategy.
Sanno et al. (Thu,) studied this question.