An opportunity for higher awards for particular winning outcomes in a wagering game enhances the entertainment and enticement provided by a wagering game. In one embodiment, the opportunity is provided when the player has an initial set of indicia which contains a winning outcome. The opportunity allows a player to forgo this initial winning outcome for the chance to obtain increased awards for other winning outcomes. In this manner, the opportunity enhances a wagering game by allowing players a choice to take the award for the initial winning outcome or to risk this award in return for the chance to win increased awards for other winning outcomes. The increased awards for each winning outcome may be slight or substantial depending on the odds of the winning outcome occurring from the player's initial set of indicia.