Rubuta ci gaba don wannan sakin layi - Héðinn ya yi gasa a Gasar Iceland a 1991, amma bai sake yin wasa ba har zuwa 2006, inda ya gama na biyu. Hakanan bai buga wasan Chess Olympiads ba a wannan lokacin, ya dawo a 2008
don samun maki 4/7. A shekara ta 2009, ya lashe gasar Reykjavik Open a kan Yuriy Kryvoruchko da Hannes Stefánsson. Ya sake bugawa Iceland wasa a gasar Olympiad ta Chess ta 39, inda ya ci 6/10. Tun daga wannan lokacin ya lashe Gasar Iceland sau biyu: a cikin 2011 da 2015.