Gaming systems, gaming devices and methods that provide games that control volatility. In one embodiment, the gaming system disclosed herein enables a player to select values, or cells associated with values, that are displayed in a particular arrangement. The player selected values are distributed to other values or cells according to one or more predefined rules. In one embodiment, one or more of the player selectable values are progressive award values. At some point during the game, the gaming system randomly picks one of the remaining values that have not been selected and provides an award to the player based at least in part on the selected value.