Central determination gaming system and method for providing a persistence game with predetermined game outcomes

A gaming system which provides a persistence game which utilizes predetermined game outcomes. One or more predetermined game outcomes include a persistence game award value. If a predetermined game outcome including such a persistence game award value is selected to be provided to the player in association with a current play of a primary game, the gaming system determines whether to provide this persistence game award value to a player in association with the current play of the primary game, or to store this persistence game award value to be subsequently provided to a player in association with a subsequent play of the primary game. The determination of whether to provide or store the persistence game award value is based on the then current progress of the persistence game (i.e., the current state of an accumulation meter).