Nyora kupfuurira kweiyi ndima - Kukunda kwake mumakwikwi kunosanganisira kubatanidza nzvimbo yekutanga (+ 6−0 = 9) naBoris Spassky paChigorin Memorial muSochi 1965, yekutanga kuMaribor 1967 pamberi paSamuel Reshevsky, yekutanga kuKrems, uye yekutanga kuAmsterdam 1980 yakabatana naHans Ree. Muna 1950, Unzicker akagovana mubairo wepamusoro-wepamusoro bhodhi (+ 9−1 = 4) naMiguel Najdorf nekuda kwekuita kwake pabhodhi rekutanga rechikwata cheWest Germany kuDubrovnik Chess Olympiad
. PaTel Aviv 1964 Chess Olympiad Unzicker akawana 13.5 mapoinzi achitamba bhodhi rekutanga rechikwata cheWest Germany icho chakahwina menduru yebronze pasimba rekukunda 3: 1 kwechikwata pamusoro peSoviet Union. Unzicker akagovanawo nzvimbo yechina (+2−1=14) naLajos Portisch mu1966 Piatigorsky Cup muSanta Monica, California. Boris Spassky, Bobby Fischer, naBent Larsen ndivo chete vakapedza mberi kwaUnzicker. Unzicker akaiswa pamberi pemakwikwi enyika Tigran Petrosian, Samuel Reshevsky, Miguel Najdorf, Borislav Ivkov, naHein Donner. PaHastings 1969<unk>70, Unzicker akapedza ari wechipiri (+4−0=5) mushure meLajos Portisch uye pamberi paSvetozar Gligorić uye aimbova shasha yenyika Vasily Smyslov. Unzicker akapedza wechipiri (+3−2=7) kuna Viktor Korchnoi muSouth Africa 1979. Mutongi akarega basa, akanga achiri kutamba chess sebhodhi rokutanga pachikwata chechikwata "Tarrasch Munich".