Controlling the cascade following a riffle shuffle 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 the two packets misaligned with each other. This results in a shuffled deck but with each original packet separately jogged. The cascade doesn't affect the jog. This idea is used for false shuffles and allows the magician to strip the packets apart and to return the deck to its previous order. The concept seems to have been originated by Gus Southall for use with Howard De Courcy's one-handed shuffle. See Hugard's Magic Monthly, Vol. 3 No. 7, Dec. 1945, p. 175, for the De Courcy shuffle and Hugard’s Magic Monthly, Vol. 4 No. 10, March 1947, p. 304, for Southall's false-shuffle variant, mentioned in Fred Braue's column.
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 was mentioned there.
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 jogged position as in the Katz shuffle. This approach 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.