The present invention is directed to a gaming machine and a method of playing a wagering game having a basic set of rules for playing a wagering game. Under the basic set of rules, a player can accumulate and save assets that are associated with the wagering game. In addition to the basic set of rules, the wagering game includes modifiers to the basic set of rules that modify the assets, enhance the assets or provide new assets. These modifiers may, for example, multiply an award associated with an asset or group of assets, provide additional rolls of the dice, provide a bonus award, provide additional player selections, allow the player to continue game play after a game-terminating event has occurred, allow the player to use assets at a later gaming session, or allow a player to access new assets at a different gaming machine. The assets and modifiers can be shared by players at different gaming machines to influence the outcome of the wagering games and can be saved for use in subsequent gaming sessions.