Hromádka played in the 1st unofficial Chess Olympiad, Paris 1924, and scored 6.5/8 for first place in the Consolation Cup. In Qualification Group 1 he finished in third place. Hromádka played in the 1st Chess Olympiad, London 1927, and scored +4 =3 -5. Notably, he also had a plus score against Siegbert Tarrasch (+2 -0 =0).