A gaming device that provides a player with an opportunity to maximize a gaming device award. The gaming device presents the player with a display having a plurality of symbols and enables the player to choose one or more of the symbols. The game reveals the award(s) associated with the selected symbols but does not reveal which awards are associated with which symbols. The game then provides the player with one or more opportunities to upgrade the total award by deselecting one or more of the selected symbols and re-selecting another symbol for each deselected symbol.