The gaming system disclosed herein accounts for game play over a gaming session in determining a bonus game attribute for a triggered bonus game. The gaming system maintains a plurality of different bonus game attributes. Each different bonus game attribute is associated with a different bonus game attribute modification event and an initial probability of that bonus game attribute being selected for a play of a bonus game. For each bonus game attribute modification event that occurs, the gaming system modifies the probability that the associated bonus game attribute will be selected for a play of a bonus game. Upon an occurrence of a bonus game triggering event, the gaming system randomly selects one of the maintained bonus game attributes. The gaming system then displays a bonus game and determines a bonus game award utilizing the selected bonus game attribute.