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Triumph
The plot of mixing cards face up and face down, then having them right themselves (with several variations) seems to have first appeared as Theodore DeLand's “Inverto”, 1914, a marketed effect that employed a deck in which every other card was double-backed. DeLand also seems to have manufactured, at least initially, a version in which the double-backers were shortened, to allow the deck to be displayed by riffling the ends. An explanation of the trick was run in the August 1914 issue of The Sphinx (Vol. 13 No. 6, p. 16), along with an ad offering the special deck for sale. A good history of “Inverto” is given by Richard Kaufmann in his DeLand: Mystery and Madness, 2018, p. 384.
A few years later, Ellis Stanyon published a packet variation, using just ten cards in Magic, Vol. 15 No. 3, Dec. 1919, p. 18, under the title “The Self-Reversing Cards”. The Stanyon routine includes a magical reversion of the cards to a face-up, face-down condition.
Charles Jordan published an ungimmicked version, “The Alternate Reverse”, in Thirty Card Mysteries, 1919, p. 54 of the second edition.
Another early example appears in Walter B. Gibson's Twenty New Practical Card Tricks, 1925, p. 16, credited to Herbert Johnson, and includes a reverse Topsy-Turvy effect wherein an unmixed deck instantly becomes mixed with face-up cards interspersed between face down, as Stanyon had done in his ten-card version. This is also a precursor to the effect of the deck that magically shuffles itself.
In Two Dozen Effective Practical Card Tricks, 1927, p. 37, Walter B. Gibson published “The Shuffle Reverse”, which features a dovetail shuffle of an apparently face-up half into a face-down half.
In Underworld, No. 2, 1995, p. 21, Karl Fulves mentions another version of the plot that appeared in Art Altman's marketed trick “Altman's Upside Down Trick”, 1928 (see the advertisement in The Sphinx, Vol. 27 No. 9, Nov. 1928, p. 440). The original instructions are reprinted in Underworld. This version is the first known to add the revelation of a chosen card to the magical righting of the deck.
When, late 1948, U. F. Grant marketed “Inverto”, without credit to DeLand, he renamed it “Cheek to Cheek” (see The Linking Ring, Vol. 28 No. 10, Dec. 1948, p. 14), he changed DeLand's procedure of alternating face-up and face-down cards by dealing. Instead, he adopted the idea of riffle shuffling the halves of the deck together, as Walter Gibson had in his ungimmicked method, which greatly speeds the mixing process.
The name “Triumph” was established when Dai Vernon's version of this trick appeared in Stars of Magic, Series 2, No. 1, 1946, p. 23 of the 1961 compilation book. It quickly became the generic title for the effect frequently called “Topsy-Turvy” in previous times. Vernon's also seems to be the first of the riffle-shuffle variety to employ a false shuffle instead of a secretly reversed portion of the deck.
The first instance of doing Triumph with a freely named card seems to be Roy Walton's “Named-Card Shuffle” in Ibidem, Nos. 34/35, Aug. 1969, p. 827.
Also see Slop Shuffle, Traveling Triumph and Play It Straight.