His college education in Innsbruck and Vienna centred on business studies; it was chess, though, that captured his imagination and he had exceptional results representing Austria at the Olympiads of 1930, 1933 and 1935.

Other early successes included outright or joint first place at Budapest 1934 (the Hungarian Championship), Linz 1934, Zürich 1935, Milan 1937; and match wins against Rudolf Spielmann (in 1932, 1936 and 1937).

Documentary evidence later showed that the Nazi regime had scheduled him a 1941 match with the World Champion,[1] but had subsequently abandoned the idea.

He played under the German flag at the 1939 Buenos Aires Olympiad, during which World War II began, when Eliskases (along with many other players) decided to stay in Argentina (and for a while in Brazil) rather than return to Europe.

He was considered an expert in the endgame—at Semmering 1937, he outplayed and beat Capablanca in this phase, despite this being the forte of the Cuban ex-world champion.

Hans Ree observes that Eliskases is one of only four players (along with Keres, Reshevsky and Euwe) to beat both Capablanca and Bobby Fischer.