Various embodiments of the present disclosure provide a gaming system and method providing a selection game associated with a plurality of different sets of pickable selections. For a play of the game, the gaming system displays a first set of selections and a second set of selections, and initiates a selection round. If a designated selection of the first set remains unpicked, the gaming system enables the player to pick a selection of the first set. If a designated selection of the second set remains unpicked, the gaming system enables the player to pick a selection of the second set. If the designated ones of the first and second sets of selections have both been picked, the gaming system determines an award based on a total quantity of initiated selection rounds. If not, the gaming system ends the selection round, initiates a subsequent selection round, and repeats the above process.