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Correcting a Mistake / Magician Makes Good / Matching the Cards
The usual seminal reference for this plot is “Correcting a Mistake” in Hatton and Plate's Magicians' Tricks: How They Are Done, 1910, p. 93. An early record of Dai Vernon's experimenting with the plot (later called “Matching the Cards” in Dai Vernon's Inner Secrets of Card Magic, 1959, p. 22) appeared in The Sphinx, Vol. 24 No. 11, Jan. 1926, p. 425, in Max Holden's “Trouping Around in Magic” column.
Jean Hugard put a gambling spin on the plot in his “Magician vs. Gambler” in Hugard's Annual of Magic 1937, 1937, p. 43. Karl Fulves has written that this trick “is sometimes credited to Braue”; see The Pallbearers Review: Close-up Folio #9, 1977, p. 1021. However, Fulves gives no source for the attribution, and Fred Braue himself gives credit to Hugard for the trick in two instances, in his “Roundabout with Fred Braue” column in the March 1947 issue of Hugard's Magic Monthly, Vol. 4, No. 10, p. 305, when reporting on nominations for the best five card tricks poll.
In the same year Hugard published his trick, Joe Berg published his handling of “The Magician Makes Good” in Here's New Magic, 1937, p. 8.