Buuxi weedha soo socota: Ururintu waxay bilaabmaysaa 1957, iyadoo laga reebay "Ciyaarta qarniga" ee caanka ah ee ka dhanka ah Donald Byrne 1956 (ciyaartan waxaa lagu soo daray shaqo yar, oo si fudud loo sharraxay oo la yiraahdo "Bobby Fischer's Games of Chess", oo la daabacay 1959). Saddexda guuldaro waa Tal ee Tartanka Musharixiinta 1959, Spassky ee Mar del Plata 1960, iyo Geller ee Skopje 1967. Waxaa ka mid ah ciyaarta barbaraha ah kulankiisii kaliya ee uu la yeeshay horyaalkii aduunka Mikhail Botvinnik, ciyaartii Varna 1962
Ciyaaraha Olombikada. Ciyaartan waxaa ku jira falanqaynta ugu dheer ee buugga, iyadoo Fischer uu soo gabagabeeyay inuu seegtay guul dhamaadka ciyaarta. Botvinnik ayaa markii dambe ku dooday arintan, isagoo ka soo horjeestay mid ka mid ah ardaydiisa dugsiga shaashadda, Garry Kasparov oo 13 jir ah. Tani waa mid ka mid ah tusaalooyinka tirada yar ee falanqaynta Fischer ee su'aal laga keenay. Guulahaas waxaa ka mid ah guushiisii ugu horreysay ee uu ka soo gaaray Grandmaster-ka Soviet, Paul Keres ee Zurich 1959, iyo guushiisii 21-ta ah ee uu ku guuleystay Robert Byrne ee 1963/64 US Championship. Waxaa jira toddobo ciyaarood oo ka mid ah tartankiisii ugu horreeyay ee Musharixiinta ee 1959, laakiin kaliya laba ka mid ah kii labaad ee Curaçao 1962. Ciyaaraha oo dhan waxaa lagu ciyaaray xaaladaha tartanka marka laga reebo ciyaar saaxiibtinimo oo ka dhacday guriga Reuben Fine sanadkii 1963 iyo guul ka soo gaartay safarkii bandhigga isku mar ee Fischer ee 1964 ee Mareykanka.