A method of presenting and playing a game provides the opportunity for enhanced awards. In one embodiment, if a winning game outcome is a predetermined winning outcome, an enhanced paytable or award is activated. The enhanced paytable or award offers the player a chance for enhanced winnings in one or more subsequent games. The enhanced award may be activated when a particular winning outcome is received in a game and may then be won by repeating that winning outcome in one or more subsequent games. The award might also be won by designating the outcome before a game and then receiving that outcome during the play of the game. The enhanced award or paytable may remain in effect for a period of time or for a certain number of games, and may be triggered, be selected by a player or be selected by a casino.