Kammala jumla mai zuwa: Nasara a gasar ya hada da na farko da ya yi daidai (+ 6−0 = 9) tare da Boris Spassky a Chigorin Memorial a Sochi 1965, na farko a Maribor 1967 a gaban Samuel Reshevsky, na farko a Krems, da na farko a Amsterdam 1980 da aka yi daidai da Hans Ree. A cikin 1950, Unzicker ya raba kyautar don mafi kyawun ƙimar saman (+ 9−1 = 4) tare da Miguel Najdorf don aikinsa a kan jirgi na farko don ƙungiyar Jamus ta Yamma a gasar cin kofin duniya ta 1950.
Gasar wasannin Chess ta Dubrovnik. A Wasannin Chess Olympiad na 1964 na Tel Aviv Unzicker ya sami maki 13.5 yana wasa a tebur na farko don ƙungiyar Jamus ta Yamma wacce ta sami lambar tagulla bisa ƙarfin nasarar ƙungiyar 3: 1 a kan Tarayyar Soviet. Unzicker kuma ya raba matsayi na huɗu (+ 2−1 = 14) tare da Lajos Portisch a gasar cin kofin Piatigorsky ta 1966 a Santa Monica, California. Sai kawai Boris Spassky, Bobby Fischer, da kuma Bent Larsen sun gama gaba da Unzicker. Unzicker ya sanya gaba da zakaran duniya Tigran Petrosian, Samuel Reshevsky, Miguel Najdorf, Borislav Ivkov, da kuma Hein Donner. A Hastings 1969<unk>70, Unzicker ya gama na biyu (+4−0=5) bayan Lajos Portisch kuma a gaban Svetozar Gligorić da tsohon zakaran duniya Vasily Smyslov. Unzicker ya gama na biyu (+ 3−2 = 7) zuwa Viktor Korchnoi a Afirka ta Kudu 1979. Wani alkali mai ritaya, har yanzu yana wasan chess a matsayin kwamitin farko a kungiyar kungiyar "Tarrasch Munich".