A gaming device and method having a game with multiple player selectable award opportunities. In one embodiment, the gaming device displays a plurality of groups to a player. Each of the groups include related award opportunities. An indicator simultaneously indicates at least two of the award opportunities in one of the groups. In an alternative embodiment, components of an award opportunity are accumulated in an accumulated award opportunity. The accumulated award opportunity is indicated along with at least one other award opportunity. The player chooses one of the indicated award opportunities and receives the outcome which results from the indicated award opportunity picked by the player. In one embodiment, the average expected values of the outcomes which result from the indicated award opportunities in each group are approximately equal.