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Surprisingly, the earliest known Rub-a-Dub Vanish was performed with a face-up deck. Harry Louine (the stage name of Louis N. Miller) described his vanish technique in The Sphinx, Vol. 8 No. 5, July 1909, p. 94. The card was pushed off the deck beneath the right hand, but under this cover the card was pulled back beneath the deck with the left fingertips. Unlike modern-day variants, in Louine's handling the card wasn't pushed onto a surface for the vanish, but rather pushed off the deck to apparently become palmed under the right hand.
The now-common face-down Rub-A-Dub Vanish was described by Paul Stadleman (under the pen name “Thor”) in The Magical Bulletin, Vol. 12 No. 7, May 1925, p. 106. Like Louine, Stadleman would seemingly push the card into the right palm rather than onto a surface as is now commonly done. This idea of pushing the card onto a surface for the vanish was introduced by William H. McCaffrey in his “Card in the Pocket II” in John Northern Hilliard's Greater Magic, 1938, p. 256, as a method to penetrate a card through the magician's trouser pocket.
The technique gained its now-common title from its inclusion in Jean Hugard and Frederick Braue's Expert Card Technique, 1940, p. 301. The sleight was described within a trick called “Rub-A-Dub-Dub”, a title that migrated to the vanish itself.
Ed Marlo is often erroneously cited as the creator due to his inclusion of the technique in Off the Top, 1945, p. 14 & 16, as “Rub Away” and “Rub-Away-Mag”, respectively.
During his lecture on Charlie Miller at the 2007 MAGIC Live! convention in Las Vegas, Johnny Thompson made the claim that Miller was the originator of the vanish. This claim appears doubtful in light of the evidence above, because Miller was only fifteen years old when Stadleman published the sleight.
While the face-up vanish was the original, it never gained traction. The face-down handling became “the” Rub-a-Dub Vanish. Since then, several magicians have inadvertently gone full circle to develop face-up handlings of their own: these variants include Arthur Buckley's in Card Control, 1946, p. 127 (which Steve Beam reinvented in The Trapdoor, No. 9, 1985, p. 152), Jay Sankey's in Spectacle, 1990, p. 31, Allan Ackerman's in Wednesday Nights, 1994, p. 5 (utilizing the one-handed top change), and Tyler Wilson's in MAGIC, Vol. 14 No. 2, Oct. 2004, p. 86. While most of these face-up handlings are novel, Sankey's ended up being a direct reinvention of Louine's original technique.