The idea of miming the playing of a game of cards with an imaginary deck is probably very old. Reports have been located from 1922 forward describing comic sketches in which games of cards were played with an imaginary or invisible deck. For example, in the June 25, 1922, New York Morning Telegraph: “At the same time he [Hamtree Harrington] has a quality all his own, and his graphic pantomime and eloquent facial expression as he deals out the imaginary cards at a poker game and plays his hand, are masterpieces of comedy.” And in the same paper on July 27, 1922: “In the second half the comedy incidents show [Johnnie] Weber a glorious victor in an imaginary battle with a bartender, also a generous pinochle scorekeeper in a game played with invisible cards by Scottie [Friedell] and Raymond [Paine].”
But who was the first to use the idea of an invisible deck for a card trick? Bill Mullins, who provided the two citations above, has found this mention in The Magic World, Vol. 6 No. 12, Mar. 1923, p. 179: “Leslie Henson was at his best in an impromptu speech on magic, and then, with an imaginary pack of cards, doing an imaginary trick. It was screamingly funny.” No further information concerning Henson's “imaginary trick” and its gags is given.
Most of the gags that are now standard in presentations of “The Invisible Deck” can be seen in a Laurel and Hardy film, "Oliver the Eighth", made by Hal Roach and released in February 1934. This film sketch may have been the source, if not the origin, of the gags for magicians, as tricks using the “invisible deck” premise began to appear in conjuring periodicals shortly after the release of “Oliver the Eighth”. In the film, Jack Barty, a comic actor playing a character named Jitters, goes through an entire invisible deck routine, removing the invisible deck from a real, empty card case. He shakes the case to get all the cards, shuffles them, both overhand and tabled riffle, squares them, then plays a comic game of solitaire. Stan Laurel wanders by and sees him do this. Barty gathers the invisible cards and has Laurel pick one. Barty names the seven of diamonds and is correct. He then urges Laurel to show the trick to Hardy. Hardy knocks the invisible cards from Laurel's hands in disgust, and Barty gathers them from the floor and leaves. Laurel calls him back to hand him one he missed.
A photographic retelling of the sketch with stills from the film can be seen in Bill Abbott's article “Invisible Origins Revealed” in Cocktail Card Magic, 2008, p.21.
It is possible that this routine was developed as a vaudeville sketch before it reached film.
The year after the film, the idea made its way into the magic world as an actual trick, rather than as merely a gag. Theo Annemann described the effect (without a method) of having a spectator shuffle an invisible deck, take a card, and shuffle it back in—all invisibly, of course. The performer placed the invisible deck in his pocket and asked the spectator to name her card. He reached into his pocket and pulled out a visible version of her card. He described this under the title, “WANTED - A Card Routine without cards!” in The Jinx, No. 12, Sep. 1935, p. 60. U.F. Grant later offered two methods for this in 50 Crazy Card Stunts, 1939, p. 9.
The aforementioned film was a likely inspiration–although Leslie Henson's gag trick might also have been the starting point–for “You're Crazier Than I Am!” in Roger Montandon and Logan Wait's Not Primigenial, 1942, p. 19. Montandon and Wait use it strictly as a gag, but it has relevance to the history of the Invisible Deck presentation as Bob Longe, Don Alan, and Eddie Fields later developed it.