Every symmetric 3×3 global game of strategic complementarities has noise-independent selection

► We prove that all 3×3 symmetric supermodular global games are noise independent. ► Our proof applies to 3×3 games that do not admit an MP maximiser. ► This generalises previous results that all rely on the existence of an MP maximiser. ► It implies that noise independence is not equivalent to the existence of an MP maximiser, nor to the existence of a robust equilibrium robust to incomplete information.