Szabados was born in Budapest on 7 March 1912. He first started playing table tennis when he was thirteen, and defeated Victor Barna in a tournament in 1927.
From 1928 to 1935, Szabados won the world doubles title six times (1929–32 and 1934–35). He won mixed doubles three times (1930, 1931, and 1934), and was a member of the Swaythling Cup team five times (1929–31, 1934, and 1935). He won four world events in 1931: singles, doubles, mixed doubles, and the Swaythling Cup.
As his mother had been born Jewish, Szabados left his studies at the University of Berlin in 1933 and fled to Paris. He moved to Britain in 1936.
Szabados toured the Far East, South America, and Australia on an exhibition tour with István Kelen starting in 1937. At the Australian championships in Sydney, they won the doubles tournament, and Szabados won over Kelen for the singles title.
Szabados emigrated to Sydney after the tour and opened a table tennis club. He married Marie Alice Bracher in 1941, and they had one son. They were divorced in 1954. While serving with the Allied Works Council during World War II, Szabados he was stationed at Alice Springs, Northern Territory, in 1943–44. During this period he used his time to play and teach table tennis to his fellow colleagues at the Works Council and play bridge with the Northern Territory's administrator's wife. As a result he played more bridge than anything else as he was already an NSW Bridge champion.
He won the singles title at the Australian Table Tennis Championship in 1950 and 1952, and won doubles in 1950) and mixed doubles in 1955. He continued to run table tennis academies and coach. His students Cliff McDonald and Michael Wilcox both won the Australian singles championships.
Szabados was born a Catholic in 1912. His mother, Rosa Schwarz, changed from being Jewish to Catholic at her marriage. In spite of having never practiced the Jewish faith, he was inducted into the International Jewish Sports Hall of Fame in 1987.
Szabados was inducted into the International Table Tennis Foundation Hall of Fame in 1993.