Kammala jumla mai zuwa: Regedziński ya kasance memba na ƙungiyar Poland a wasannin Chess Olympiads guda huɗu (1928, 1933, 1937, 1939) da kuma na 3 na Olympiad na Chess ba bisa ƙa'ida ba a Munich 1936. A gasar wasannin Chess Olympiad ta 2 a Hague a 1928, ya ci 10/13 (+8 <unk>1 = 4) yana karɓar kyauta ta uku don mafi kyawun sakamako na mutum (ba a san umarnin hukumar ba a waɗannan kwanakin). A cikin 1933, ya buga wasa a tebur na uku (+ 2 <unk> 1 = 4) a
Gasar wasannin Chess ta 5 a Folkestone. A gasar Olympics da ba a hukuma ba a Munich 1936, inda kungiyar Poland ta dauki lambar azurfa, ya taka leda a tebur na uku (+ 9 <unk> 2 = 7). A cikin 1937, ya kai kololuwar sa ta kowane lokaci 11/13 (+10 <unk>1 =2) don cin nasarar lambar yabo ta biyu don kyakkyawan sakamako a cikin kwamitin ajiya da kuma sakamako mafi kyau na uku a duka a 7th Chess Olympiad a Stockholm. A cikin 1939, ya buga wasa a tebur na huɗu, ya lashe lambar tagulla ta mutum (+ 6 <unk> 3 = 4) a gasar Olympics ta Chess ta 8 a Buenos Aires.