One embodiment of the invention is a method of playing computerized card games against real players at a table. The cards games are usually variations of poker, where the quality of the players' hands is due to skill and strategy rather than the luck of the draw. Players request desired cards from an actual or computerized dealer without knowledge of which cards other players have requested. A null card, which has no value in determining the outcome of the game, is delivered to players who request the same card as another player has requested regardless of whether the card was requested previously or during the current round. In another embodiment, a null card is delivered only when two or more players request the same card during the current round or if a player requests a card that has already been distributed. Each player has a display screen showing that player's hand. The players may make card selections using a touchscreen.