A gaming device having an improved offer and acceptance bonus scheme wherein the gaming device provides a plurality of masked selections and briefly reveals to the player one or more of the offers which will be associated with one or more of the masked selections. In one embodiment, one offer is revealed and that revealed offer is the maximum potential offer the player may obtain. In one embodiment, if the player selects the revealed offer, the game ends. In one embodiment, if the maximum offer is not selected, the player simply obtains the selected offer and the game ends. In another embodiment, the player may select the offer, or reject the offer and select another masked selection wherein the player may again obtain the previously selected offer.