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