Star-formation efficiency (SFE ≡ SFR/M_H2) as a function of molecular gas fraction f_gas ≡ M_H2/(M_H2 + M_⋆) of PKS 0529-549 and other galaxies at z = 1.3−4.1. High-redshift radio galaxies are plotted as magenta circles, individually labeled as (1) PKS 0529-549, the subject of this work; (2) 4C 41.17; (3) MRC 0152-209, the Dragonfly; (4) MRC 1138-262, the Spiderweb; (5) 4C 60.07; and (6) MRC 0943-242. Submillimeter galaxies are plotted as pink squares. Star-forming galaxies are plotted as blue squares, with different shades referring to the respective samples. Compact star-forming galaxies are plotted as yellow diamonds. Cluster galaxies are plotted as green circles. Full references are provided in Sect. 5.1. The symbol size denotes the stellar mass of each galaxy split in three bins of M_⋆ ⩾ 3 × 10¹¹ M_⊙, 1−3 × 10¹¹ M_⊙, and <10¹¹ M_⊙, where larger symbols represent more massive galaxies. The edge colours of each symbol indicate the M_H2 tracer: black for [C I], grey for CO, and brown for dust continuum. The grey dashed lines mark the corner for the efficiently star-forming and gas-poor galaxies.