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Controlling a riffle shuffle's cascade can prevent the two packets from fully coalescing, providing an advantageous position for the magician to manipulate further. The origins of the concept stem from shuffling the deck with each packet jogged from each other. This results in a shuffled deck, but with each original packet still jogged. The cascade doesn't affect the jog. It was used for false shuffles, allowing the magician to strip the packets apart and return the deck to its previous order. The idea seems to have originated for the one-handed shuffle, with the two-handed variant close on its heels. Guy Southall's false one-handed shuffle appeared in Hugard’s Magic Monthly, Vol. 4 No. 10, March 1947, p. 304.
The two-handed variant is commonly referred to as the Henry Hay False Shuffle due to its appearance in Henry Hay's The Amateur Magician's Handbook, 1950, p. 58, but Max Katz described nearly the same shuffle two years prior in Hugard’s Magic Monthly, Vol. 5 No. 2, July 1947, p. 333, just a few months after Southall's shuffle.
A later improvement eliminated the open sidejog during the riffle. This was done by keeping the riffle square, but then applying pressure to opposite corners of the cards during the cascade to allow the packets to end in the same position as the Katz shuffle. This was created by Steve Beam and published in The Trapdoor, No. 4, 1984, p. 59. Both Eric Anderson and Guy Hollingworth are often cited as the creators of this concept, but they were over a decade late to the party, publishing their handlings in Ah-Ha, 1997, p. 37, and Drawing Room Deceptions, 1999, p. 169, respectively.
Instead of using the concept for a false shuffle, Joshua Jay used the sidejogged position for an application of the ribbon spread hideout, allowing half the deck to be hidden during a spread. Jay included the application in The Magic Atlas, 1999, p. 61.