1. A gaming system comprising: at least one input device; at least one display device; at least one processor; and at least one memory device storing a plurality of instructions which, when executed by the at least one processor, cause the at least one processor to operate with the at least one display device and the at least one input device to: (a) display a non-progressive award; (b) enable a player to play a base game; (c) upon an occurrence of a designated award display changing triggering event: (i) remove the display of the non-progressive award, and (ii) display a progressive award in place of the non-progressive award; and (d) upon an occurrence of designated award providing triggering event: (i) if the non-progressive award is displayed, provide the non-progressive award to the player; and (ii) if the progressive award is displayed, provide the progressive award to the player.