A gaming system whereby the gaming system receives a wager to initiate a first play of a game, the first play of the game having a first average expected payout and including a plurality of symbols, wherein at least two of the symbols are different. In one embodiment, for the first play of the game the gaming system randomly generates a plurality of the symbols, displays the randomly generated symbols, determines any awards associated with the displayed symbols, and displays any determined awards. If the displayed symbols include a designated symbol, the gaming system of this embodiment accumulates the designated symbol. When a designated quantity of the designated symbol is accumulated, for a subsequent play of the game, the gaming system automatically causes the subsequent play of the game to have a second different average expected payout.