A gaming system which includes a game sequence, such as a free game sequence, which enables a player to selectively apply modifiers after viewing the results of games. For a game associated with an available modifier, following the display of the results of that game, the gaming system enables the player to either utilize the available modifier for that game or accumulate another modifier to be potentially utilized for another game. If the player selects to utilize the available modifier, the gaming system modifies one or more aspects of the play of the game to result in a modified game outcome and/or a modified game award. If the player selects to not utilize the available modifier, the gaming system accumulates another modifier for the player, wherein the other modifier may or may not be subsequently utilized by the player to modify any designated aspects of a subsequent play of the game.