1. A card shuffling apparatus configured to shuffle a stack of playing cards, the apparatus comprising: a card receiver configured to receive a stack of playing cards therein; card storage compartments; an input card moving mechanism configured to sequentially move playing cards from a stack of playing cards in the card receiver into at least some of the card storage compartments, the input card moving mechanism including: at least one pick-off roller located and configured to rotate and commence movement of a playing card from the stack of playing cards toward one of the card receiving compartments; and at least one speed-up roller located and configured to drive the playing card moving responsive to the rotation of the at least one pick-off roller into the card storage compartment; a card output tray; an output mechanism configured to transfer the playing cards from the at least some card storage compartments of the plurality to the card output tray; and a control unit configured to control movement of the input card moving mechanism and the output mechanism, the control unit configured under control of a computer program to randomly assign each playing card in the stack of playing cards in the card receiver to one of the at least some card storage compartments, to individually move each playing card to its assigned card storage compartment until all cards in the stack of playing cards in the card receiver have been moved into the at least some card storage compartments, and to then transfer the playing cards from the at least some card storage compartments to the card output tray.