In various embodiments, the present disclosure relates generally to gaming systems and methods that provide a first game sequence including an accumulation of designated symbols during a plurality of sequential plays of one or more of a plurality of different games of the first game sequence. In various embodiments, the gaming system determines which of the plurality of different games are employed for each play of a game of the first game sequence based on the quantity of accumulated symbols for that first game sequence prior to the start of that game play.