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The pick-up dynamic of this shuffle is used in the first full-deck false shuffle method S. W. Erdnase described in the Legerdemain section of Expert at the Card Table, 1902, p. 163. This shuffle was of the haymow variety, rather than an overhand shuffle, designed to maintain the order of the entire deck and resulting in giving the cards only a simple cut.
The same year, Henri De Manche published an overhand false shuffle in C. Lang Neil's The Modern Conjurer, 1902, p. 51, that utilized the lift shuffle methodology.
Jack Merlin describes his Outjog Shuffle in Merlin's Master Manipulations, 1928, p. 5. This is a false shuffle designed to control a card to the top during a single overhand shuffle. It uses an outjog to delay the pick up action until later in the shuffle. While Merlin refers to the style of shuffling as a “haymow”, evidence suggests that the shuffle he used is what is called today an overhand shuffle. (Conjuring literature of the period sometimes used “haymow” to refer to both the haymow and overhand shuffling methods.) This detail is clarified by Jean Hugard in his revision of Merlin's trilogy ...and a Pack of Cards, 1940, p. 12.
Judson Brown contributed a control using the pick-up dynamic under the title “The Shuffle Pass” to Genii, Vol. 3 No. 4, Dec. 1938, p. 113. The pick-up is done immediately after the card is returned to the deck, during an interruption of the process of shuffling. Brown again refers to the shuffle method as a haymow. While the control could conceivably be managed with a haymow shuffle, an overhand shuffle was probably meant.
The use of a series of pick-ups, one after every shuffle movement, resulting in a complete false shuffle, was described as “An Easy False Shuffle” by Tom Munroe in The Linking Ring, Vol. 29 No. 1, Mar. 1949, p. 49.