Róbert Ruck has repeatedly represented Hungary at the European Youth Chess Championship and World Youth Chess Championships in various age groups. Róbert Ruck achieved his best result in 1992, in Rimavská Sobota, when he shared 2nd - 3rd place in European Youth Chess Championship in U16 age group, and in 1994, in Szeged when he shared 2nd - 3rd place in European Youth Chess Championship in U18 age group, and in 1994, in Chania when he shared 2nd - 4th place in World Youth Chess Championship in U18 age group.
Róbert Ruck is winner of many international chess tournaments, including Zagreb (1997), Budapest (2000), Keszeg (2000), Kladovo (2001), Lippstadt (2003).