Nyora kupfuurira kweiyi ndima - Benko akapedza ari panzvimbo yokutanga (kana kuti akaenzana panzvimbo yokutanga) muU.S. Open Chess Championships sere, chinyorwa. Mazita ake okuremekedza akanga ari aya: 1961, 1964, 1965, 1966, 1967, 1969, 1974, 1975. Akakunda 1964 Canadian Open Chess Championship. Akamirira Hungary pa1957 Student Olympiad muReykjavík pa, achiwana 71⁄2/12, uye Hungary yaive yechina sechikwata. Akanga ambotamba nechikwata chenyika yeHungary paMoscow 1956 Olympiad, pabhodhi matatu, achiwana 10/15, uye achibatsira Hungary kuhwina bronze. Akatamira kuUnited States, asi kwakanga kusati kuri kutozosvikira muna 1962 apo akaoneka muchikwata cheU.S. Aizopedzisira ava mumapoka matanhatu akatevedzana. MuVarna muna 1962
, Benko akatamba pabhodhi rechipiri, akawana 8/12 nokuda kwemenduru yesirivha pabhodhi rake, uye U.S. yakapedza yechina. MuTel Aviv 1964, akanga arizve pabhodhi rechipiri, akawana 91⁄2/14, uye U.S. yakaguma iri yechitanhatu. MuHavana 1966, Benko akanga ari mubhodhi rechitatu, akawana 8/12, uye vokuAmerica vakakunda sirivha yeboka. PaLugano 1968, akaita 6/12 ari pabhodhi rechitatu, uye U.S. yakapedza yechina. PaSiegen 1970, Benko akanga ari pabhodhi rechina, achiwana 81⁄2/12, uye vaAmerica vakapedzazve vari vechina. Olimpiki yake yokupedzisira yakanga iri muSkopje 1972, uko akatamba pabhodhi rechitatu, akaita 9 1⁄2/16, uye U.S. yakaguma yechipfumbamwe.