Kammala jumla mai zuwa: Jobava ya taka leda a tawagar 'yan wasan kasar Georgia a gasar Olympics ta Chess tun 2000. Ya lashe lambar zinare a shekara ta 2004, inda ya ci maki 81⁄2/10. A cikin
2010, ya doke dan wasan duniya na daya 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.