Bart Whaley's "Encyclopedic Dictionary of Magic" has this listing:
Bank Night; Bank Nite [US]
n. Effect where spectators freely take all but one of several envelopes, one of which contains paper money; the remaining one-the magician's-is always found to be the one with the money; Just Chance (Brit.).
Invented by Scottish magician Tom Sellers and published by him as "It's Only Chance" in 1935 in his booklet Novel Necromancy (pp.7-8). Renamed by him as "It's Just Chance" in 1939. An instant success in depression-ridden Britain, but much less so in the US until popularized in June 1939 by Ballard with the British contingent that attended the IBM annual convention at Battle Creek, Michigan. Modifications were made in the method by Floyd Thayer (who had first marketed it in 1936 as "Bank Night"), Braun and Judah (in 1937 as "Bingo"), Sid Lorraine (in 1939 as "Dollar Day"), Joe Karson (as "Fat Chance"), and Dr. R. Beebe (in 1946).
REF: Lenier (l979); Lorraine in Jinx #61 (1939), 435; Abbott's Catalog No.6 (1940), 231; Sellers, Scot's Magic (1939), 23; Tarbell, V (1948), 183.
I hope this helps.