FIDE Grandmaster (1993). From 1985 to 2001 he played sixteen times in the Polish Chess Championship"s finals. He was awarded the International Master title in 1986 and Grandmaster title in 1993.
In 1991, shared second place (with Oleg Romanishin) in Rubinstein Memorial in Polanica-Zdrój.
Robert Kuczyński played for Poland in Chess Olympiads:
In 1988, at third board in the 28th Chess Olympiad in Thessaloniki (+4, =2, -3),
In 1990, at third board in the 29th Chess Olympiad in Novi Sad (+2, =5, -1),
In 1992, at second board in the 30th Chess Olympiad in Manila (+3, =7, -2),
In 1994, at first board in the 31st Chess Olympiad in Moscow (+1, =5, -4),
In 1996, at fourth board in the 32nd Chess Olympiad in Yerevan (+1, =6, -0). Robert Kuczyński played for Poland in European Team Chess Championship:
In 1989, at third board in the 9th European Team Chess Championship in Haifa (+2, =1, -4).