Mezue ahịrịokwu na-esonụ: Iturrizaga meriri n'asọmpi mba anọ n'usoro site na 2005 ruo 2008, ma na-egwuri egwu maka Venezuela na Chess Olympiad kemgbe 2004. Ihe ngosi ya kachasị mma bịara na
37th Chess Olympiad (2006), mgbe o nwetara akara 8.5/11 na-egwu bọọdụ nke abụọ. Nsonaazụ ahụ mere ka o nweta ihe nrite ọla nchara n'otu n'otu. Ọ tozuru oke maka World Chess Cup 2007 mgbe ọ kesara ebe mbụ na American Continental Championship. A na-eme ya ka ọ na-eche ihu Peter Svidler na agba nke mbụ, mana ọ kwụsịrị egwuregwu mbụ n'ihi ịla n'iyi n'etiti ọdụ ụgbọ elu Russia. Ọ tụfuru egwuregwu nke abụọ. N'afọ 2008, Iturrizaga meriri asọmpi ịntanetị maka C-group na 2009 Corus Chess Tournament, na-emeri GM Alexandr Fier 3-1 na ngwụcha. Ọ kwụsịrị na ebe asatọ n'ime iri na anọ na asọmpi isi, na-enweta 5.5/13. Iturrizaga gbara onye nke abụọ na 2008 Ibero-American Championship na Linares, Spain, na-efunahụ Julio Granda na njedebe. Iturrizaga bụ onye ikpeazụ bịarutere asọmpi ahụ, ọ ga-egwu otu egwuregwu n'abalị, ọ fọrọ nke nta ka ọ bịarute n'oge maka otu n'ime egwuregwu.