The effect of one sequential group of cards magically resorting themselves into the order of a second packet mixed by a spectator was published by Ellis Stanyon in Magic, Vol. 14 No. 3, Dec. 1913, p. 25. This uses packets of three cards each. Stanyon comments, “I have reason to believe 'Selbit' should be credited with the invention of the trick in its original form,” although he seems to be referring to the method and prop rather than the resorting effect.
The Sympathetic Clubs—as the now-established plot using packets of thirteen cards (sometimes called “Sympathetic Cards” or “Sympathetic Thirteen”)—is the creation of Herbert R. Milton. The first report of him performing it can be found in The Magic Circular, Vol. 15 No. 169, Nov. 1920, p. 31. According to reports in the same periodical, Milton called the effect “Sympathy” at the time. While creation dates of 1913 and 1917 have been mentioned for Milton's trick, there is currently no other evidence to support them.
The first publication of the trick appeared under Leipzig's name in John Northern Hilliard's Greater Magic, 1938, p. 562, as “The Sympathetic Clubs”. A year later, Theodore Annemann published the trick under the same title but corrected the attribution to Herbert Milton in The Jinx, No. 53, Feb. 1939, p. 380. In the introduction, Annemann makes the claim that “Milton published it years ago in a British magazine”. This however seems mistaken, as no such early article describing Milton's method has been found; certainly none under his byline. Only brief mentions of his effect appeared in print. It seems that Milton never published the effect himself. This is backed up by Peter Warlock in Pentagram, Vol. 8 No. 1, Oct. 1953, p. 15:
Herbert never published or gave permission for publication of the effect. Actually when Leipzig was in England in the twenties, Herbert and Nate swapped ideas and effects, and as most Americans know Leipzig used the “Sympathetic Clubs” in the States. Somehow or another with due credit to Herbert Milton, a version somewhat like the original was described in the Jinx.
In the early 1920s, Nate Leipzig received permission from Milton to perform the trick. Peter Warlock gave the year as 1922 when discussing this event in The New Pentagram, Vol. 2 No. 8, Oct. 1970, p. 72. Leipzig liked the effect very much, but told Dr. Jacob Daley that he had never been able to get as strong an audience reaction to it as he desired. See The Phoenix, No. 218, Dec. 1950, p. 870.
As a side note, the Jinx description was rerun in The Phoenix, No. 218, and on page 872 it says the following, which is sometimes quoted when discussing the history of this plot:
Sam Horowitz remembers that Arthur Finley made up the first set of double facers for Nate Leipzig way back in 1913. Then four years later Jordan put the effect out as a single sheet mss. under the name of the “Self Arrangers.”
This seems to be incorrect. As mentioned above, there is no evidence that Milton was performing the trick as early as 1913, at which time he would have been around sixteen years old. And, while Jordan put out a trick “The Mystic Self-Arrangers” in 1923, it is not Milton's effect (see the reproduction of the advertisement in Karl Fulves's Charles T. Jordan - Collected Tricks, 1975, p. 311). No other known Jordan effect resembling Milton's has surfaced.