Rubuta ci gaba don wannan sakin layi - Jobava ya taka leda a tawagar 'yan wasan Georgia a gasar Olympics ta Chess tun 2000. Ya lashe lambar zinare a shekara ta 2004, inda ya ci maki 81⁄2/10. A shekara ta 2010
, ya doke dan wasa na daya a duniya Magnus Carlsen a wasan Georgia da Norway. A cikin 2016, ya lashe lambar zinare ta mutum don mafi kyawun wasan kwaikwayon, wanda ya haɗa da nasara a kan tsoffin zakarun duniya Ruslan Ponomariov da Veselin Topalov.