In this video, Magician Dai Vernon performs the cups and balls trick on Mark Wilson's Magic Circus TV show in the early 1970s. Vernon's version of the trick has become a well-known classic.
Dai Vernon (1894 - 1992) was called "The Professor" by magicians, and was a highly regarded teacher of magic who became known for magic performed close to the audience. Earlier in his career he billed himself as "The Man Who Fooled Houdini" because he stumped Houdini with a card trick. One well-known piece of advice he gave to magicians was for them to perform naturally, without excess flourishing and gestures.
(Thanks to Gregg at Astonishing Productions )