He has won the South African Closed Championship three times, in 1998, 2003 and 2011, and the South African Open twice, in 2004 and 2008. Kobese was awarded by FIDE the title of International Master (IM) in 1995. He played for South Africa in the Chess Olympiads of 1992, 1994, 1996, 1998, 2004, 2006, 2008, 2010, 2012, 2014, 2016 and 2018