Kammala wannan jumla: Gygli ya wakilci Switzerland a gasar Olympics ta Chess a Hague 1928, Warsaw 1935, da kuma a
3rd ba bisa hukuma ba Chess Olympiad, Munich 1936. Ya kuma taka leda a wasannin sada zumunta na Switzerland da Faransa (1946), Yugoslavia (1949), da Jamus ta Yamma (1952).