The present invention is a gaming device that provides a player with an opportunity to maximize a gaming device award. The game presents the player with a display having a plurality of groups of masked awards and enables the player to choose a masked award from each of the groups. The game does not reveal the selected award and preferably provides an indication of which masked awards the player selected. The game then provides the player with one or more opportunities to upgrade the total award. In one optimization embodiment, the player upgrades the total award having only a total award indicator to guide the player. In another optimization embodiment, the game additionally provides an indication of the possible awards. In a further optimization embodiment, the game provides an indication of the possible awards and additionally the number of each that the player has selected.