A method involves a video poker game in which a first set of card representations is displayed at a player station display device. The first set of card representations is organized into a number of card representation subsets comprising at least one card representation in each subset. After the player selects one of the subsets, a second set of card representations is displayed at the player station display device to combine with the selected subset. The combination is used to produce an optimum card hand that represents the player's result for the game. The player's result may be determined based on the combination of cards or may be predetermined from a lottery-type game, bingo-type game, or a result generator. In the latter cases the card representations displayed in the game are controlled so as to be consistent with the result identified for the player.