An interactive game having a pre-determined outcome (e.g., a game of finite poker) that displays an initial hand of cards, receives a player-specified designation as to which cards are to held and which are to be discarded, and then displays an intermediate hand generated in accordance with the player-specified designation. Then a final hand is shown, and in those cases where the player-specified designation (Hold/Discard) is inconsistent with a transition from the intermediate hand to the final hand, an entertaining display is shown, such as a sequence of alternative playing cards. In some cases, the initial hand is a winning hand according to a predetermined payout schedule, and the final hand is a winning hand with a higher payout than the initial hand according to the same payout schedule. The disclosed methods can be used with other games, including reel-type games.