Invented by Tom Sellers and published in his 1935 booklet Novel Necromancy under the title “It's Only Chance.” Floyd Thayer later published his version of the Sellers effect in Genii, Vol. 1 No. 2, Oct. 1936, p. 7, under the name “Bank Night” and it is that name that has stuck.
In Tops (Vol. 10 No. 1, Jan. 1945, p. 5), Sid Lorraine recounted how Sellers was inspired to create this effect after having read of a carnival swindle in which a pitchman of lucky charms claimed a shilling was in one of three apples. Members of the crowd picked two of the apples, and a shilling was found only in the one left to the “lucky” pitchman.