The overarching methodological approach of this plot is that the performer confidently improvises his way through the procedural portion of a magic trick — without the audience recognizing this fact — to arrive at a desired outcome. There have been many approaches to this concept.
Conard B. Rheiner created “The Touch of Mephistopheles”, which he claimed was a new idea. He published it in The Sphinx, Vol. 19 No. 4, June 1920, p. 110. In it, he would force a card and then draw random cards from a face-down tabled spread, which he would add or subtract from each other until he arrived at the value of the selection, also using the suits of the drawn cards to improvise a revelation of the suit of the selection.
An approach to arriving at the location of a force card through on-the-spot finagling was published by (but not specifically claimed by) Theodore Annemann in 202 Methods of Forcing, 1933, p. 14. It relied entirely on mathematics. Annemann didn't describe the method in 101 Methods of Forcing, 1932, which suggests he may have learned it in the intervening year.
Milt Kort recalls that Stewart James described an improvisational card effect and its procedures in a letter. A discussion of James's approach, which he called “The Face-Up Prediction,” can be found in The James File, Volume 1, 2000, p. 1000. James claims to have created the trick in 1939.
Dai Vernon's name is often attached to the plot due to his popular approach and methods, described in Dai Vernon's More Inner Secrets of Card Magic, Ganson, 1960, p. 76.