Tomczak won the amateur World Chess Championship twice. The first victory was in 2001 in the under-16 category, and the second was in 2005 in the under-20 category. He also achieved victory in 2006 during the Voivode of the Pomeranian Voivodeship. In 2007, he came in second place at the Polish Chess Championship. In 2010, Tomczak won the International Chess Tournament "MetLife Amplico" in Warsaw, and the same year, he earned the title of Grandmaster.
Tomczak is also known for his success in team tournaments. He participated in the Polish Team Chess Championship and contributed significantly to his teams' victories in 2010, 2012, and 2013. His team also won the Polish blitz chess championship in 2010. Internationally, Tomczak represented Poland at the European Team Chess Championship in 2011. He also played for Polish teams in the European Chess Club Cup in 2010 and 2012.