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The sandwich effect can be found in Richard Neve's The merry companion: or, delights for the ingenious, 1716, p. 121; see “To make any one blow a Card in between two Cards.” An early modern example of this effect (perhaps the earliest) is Louis F. Christianer's “Obedient Card” in The Magic Wand, Jan. 1917, p. 78.
There was also a variant in which the two reversed sandwich cards appear by surprise, surrounding the selection. William Larsen and T. Page Wright had one of these in their L. W. Card Mysteries, n.d. (c. 1928), p. 10. Jack McMillen and Judson Brown published another method for the L. W. effect, titled “A New Reverse Location” in Take a Card, 1929, p. 8.