Robert Kuczyński twice won the Polish Junior Chess Championship: U-18 in 1980 (Chełmno), and U-20 in 1985 (Wrocław).

From 1985 to 2001 he played sixteen times in the Polish Chess Championship's finals.

In Polish Team Chess Championships Kuczyński won eight medals: seven gold (1989, 1993, 1994, 1995, 1999, 2000, 2001) and silver (1998).

In 1986 Kuczyński achieved great success, winning the young master's tournament in Oakham (before Viswanathan Anand).

[3] In 1991, shared second place (with Oleg Romanishin) in Rubinstein Memorial in Polanica-Zdrój.