He became an International Master in 2001, since 2002 he is the Grand Master. With its highest ever Elo rating of 2706 in September 2011, he was behind Péter Lékó and Zoltán Almási in third place of the Hungarian and 41st FIDE rankings.
Berkes was Hungarian U12 and U14 Champion. He was in Heraklion U18 World Champion 2002. In the U20 Junior World Championships in Istanbul in 2005, he finished second behind Şəhriyar Məmmədyarov.
In December 2001, he won a First Saturday GM Tournament in Budapest. When the Moscow Aeroflot Open in February 2004, he was only half a point behind the winner Sergei Rubljowski. In April 2004 he won the Grand Prix Zalaegerszeg ( category 13 ), the Tenkes Kupa in Harkány and in December 2006 the 5th November 2006 Subasic Memorial in the Bosnian Zenica.
Hungarian singles champion in 2004 and 2007 he was in Budapest, Szeged, 2010, and 2013 in Gyula.
In the U18 European Championships in 2001, 2002 and 2003, which were held in Balatonlelle at Lake Balaton, he was very successful. 2001, when the Hungarian national team finished fourth, he received an individual gold medal for his score of 5.5 out of 7 on the first board. In 2002, Hungary was fourth and Berkes was awarded a bronze medal for his individual score of 4.5 out of 7 on top board. 2003 Hungary won the tournament. On the first board this time he scored 6.5 out of 7 with an Elo performance of 2892nd When Mitropa Cup 2002 in Leipzig, he received the bronze medal with the Hungarian national team and for his score of 7.5 out of 9 on the second board an individual gold medal ( Elo performance 2740 ). For the Hungarian national team, he participated in the Chess Olympiads 2004, 2006, 2008, 2010 and 2012, in part with a positive total return of 33.5 points from 51 games ( 20, = 27, -4, 65.6 %). At the Chess Olympiad 2008 he received an individual bronze medal for his score of 6.5 out of 9 on the first reserve board.
He played in the Hungarian ( for ASE Paks), Croatian, French, Greek, Spanish, Turkish, Slovenian (for the ŠK ZM Branik Maribor) and Serbia (for the SK Spartak, with whom he was 2008 team champion ) team championship, as well as in the British 4NCL. In the Bosnian Premijer league he played in 2007 and 2008 for the ŠK Bihać and since 2011 for the ŠK Bosna Sarajevo. With Sarajevo he won in 2011 in Neum, the team championship. In Austria he played for the first Wiener Neustadt SV, in the highest Austrian league, the chess Bundesliga, last in the season 2003/04. In Germany he played in the 2003/04 season on top board of Preetzer TSV in the 2nd Bundesliga Nord. Since the 2007/ 08 season he plays in the German Bundesliga chess chess club Epping. In the 2008 /09 season he had in the German Chess Bundesliga with 8.5 points over 10 games with an Elo performance of 2848, the best performance of all participating players.