Abstract: A gaming system and method that provides an extra award feature in a gaming environment, wherein the extra award feature provides an easier way than known methods for providing non-linear adjustments to the average expected return for the player for a play of a game without changing or reconstructing the underlying components of the game or any related game. The extra award feature provides for these non-linear adjustments to the average expected return to the player that can be based in part on wager level increases by the player. The extra award feature can include a determination of whether to provide the player a first extra award, and in certain instances, a determination of whether to provide the player a second extra award based in part on an escrow pool.