Réti was born to a Jewish family in Bazin, Austria-Hungary (now Pezinok, Slovakia), where his father worked as a physician in the service of the Austrian military.

His older brother Rudolph Reti (who did not use the acute accent) was a noted pianist, musical theorist, and composer.

He had his greatest early successes in the period 1918 through 1921, in tournaments in Kaschau (Košice; 1918), Rotterdam (1919), Amsterdam (1920), Vienna (1920), and Gothenburg (1921).

This tournament was also the only occasion in which Réti beat future world champion Alexander Alekhine, accomplishing this feat in the same number of moves.

The idea of the solution is to move the king to advance on both pawns at the same time using specific properties of the chess geometry.