In this effect, any card and any position in the deck are chosen. When the deck is counted down to the selected number, the chosen card is found at that position. This is an outgrowth of the Card at Any Number effect with tighter conditions, in which ideally any card and any number can be selected. Edme-Gilles Guyot published a version of this effect using an incomplete deck in Nouvelles Récréations Mathématiques et Physiques, 1769, p. 46 of the unpublished Hugard translation. While the card in this method is only thought of, the procedure isn't invisible as it uses the modus operandi of the Twenty-one Card Trick. But unlike its predecessor, the thought-of card can be brought to any position in the pack thanks to variations in procedure for which order the magician reassembles the piles. In the following methods, the deck in which the card appears at the demanded number is apparently not tampered with.
Jean-Eugene Robert-Houdin proved that even when the choices are restricted, the effect can be dressed up to give the impression of a thought-of card appearing at any number: “The Thoughts of Two Persons Anticipated” in Les Secrets de la Magie et de la Prestidigitation, 1868, p. 256 of the Hoffmann translation.
A method allowing two truly free choices using a full deck of cards was published by James Elliott as “The New Cigar Trick” in Mahatma, Vol. 1 No. 9, Mar. 1898, p. 96. Elliott brings the card to the top in an ungaffed deck and then second deals to the number. Both card and number are additionally predicted on a piece of paper.
Another method without false deals is Charles Shepherd's “The 'ACME' Card Trick”, The Sphinx, Vol. 7 No. 1, Mar. 1908, p. 6, using a memorized deck and a secret cut. While Shepherd used a gaffed deck to facilitate the location of the required key card, an ungaffed approach was later included in The Nikola Card System, 1927, p. 31, “Thought Anticipated”.
One method for the plot is to have one memorized deck in the possession of the spectator. After having a number named, the corresponding card is forced from a second deck. This method can be found in the French magazine L'Illusionniste, No. 73, Jan. 1908, p. 2. It was published by Edouard-Joseph Raynaly, who was mostly active during the 1870s. So he might well have been using the effect decades earlier. Jean Hugard published a translation of Raynaly's method as “Coincidence?” in Hugard's Magic Monthly, Vol. 13 No. 5, Oct. 1955, p. 346. The method was later also published by Louis Gombert (Le Prestidigitateur, Feb./Mar. 1928) and Al Baker (“A Card and a Number” in Al Baker's Book One, 1933, p. 11).
See also: Any Card and Any Number.