History
Mathematical card stacks in which each card's value progresses by 3, 4, or 5 are detailed in magic literature as early as the 16th Century.
The system was originally published in the United States in Boston or New York around 1898 by Si Stebbins (real name William Coffrin), in a pamphlet titled Si Stebbins' Card Tricks And The Way He Performs Them and a later edition Card Tricks And The Way They Are Performed.
Despite contrary claims, Stebbins maintained that the stack was his invention:
...I am the ORIGINATOR of this system for doing these tricks, and the first Vaudeville Artist to present them in the better class theaters of the United States.In fact, the first time they were ever presented to an American vaudeville audience was by myself, at the Columbia Theater, St. Louis, Mo., during the season of 1898-9, and on the Keith and Orpheum Circuits the season of 1900.
I am printing this statement to refute the claims of a few would-be imitators.
—Si Stebbins, Card Tricks And The Way They Are Performed. p.9Howard Thurston claimed to have invented the system in his 1903 book Howard Thurstons Card Tricks referring to it as "The 'Thurston' System of Expert Card Manipulation." and thanking Stebbins "...for many valuable suggestions and ideas with regard to its conception."
The card stack is generally known as Si Stebbins today, and is referred to as such in many card magic books including The Encylopedia of Card Tricks and Expert Card Technique.
Read more about this topic: Si Stebbins
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