1. A system for handling and verifying sets of playing cards, the system comprising: an automatic card shuffler, comprising: a card-shuffling mechanism configured to shuffle a set of playing cards; and a printing device for applying a same set symbol to each card in the set of playing cards to uniquely identify the set of playing cards prior to removal of the set of playing cards from the automatic card shuffler; a card output tray comprising: a receptacle for receiving playing cards from the set of playing cards in the automatic card shuffler; and a set symbol reader for reading each card of the set of playing cards for a presence and identity of a set symbol; and at least one processor programmed to randomly select the set symbol for application to each card in the set of playing cards by the printing device and configured to verify, using data from the set symbol reader, that each playing card of the set of playing cards includes a set symbol matching the randomly selected set symbol.