An early (perhaps the first) printed description of a full card-palm in which the card is gripped between the sides of the thumb and fourth finger appears in Robert-Houdin's Tricheries des Grecs dévoilèes, 1861; in Joseph Forester's 1891 English translation, Card-Sharpers, see p. 179. In introducing the sleight, the eminent conjurer states: “There is another kind of withdrawal [palming], but this is less practised by Greeks [card cheats] than by conjurers, who employ it in circumstances where the first would not be suitable.”
Not withstanding Robert-Houdin's informed assessment, this form of palming, in the twentieth century, became widely known to magicians as the Gambler's (or Gamblers') Flat Palm (not to be confused with the palming grip given that name by Hugard and Braue in Expert Card Technique, 1940, p. 56) and the name has stuck. Hugard and Braue called it the Gamblers' Squaring Palm (p. 55).