The present invention provides a gaming device (10a, 10b) that has an award modification function for player selectable awards that may be implemented with a primary or bonus game. More specifically, the present invention provides a processor controlled gaming device that randomly generates a plurality of positions or digits of an award and enables the player to pick which position or digit receives a first randomly generated number, which digit receives a second randomly generated number, etc., until each of the positions has a number, whereby the gaming device determines the player's ultimate award. The present invention further provides a plurality of modification methods for modifying the digits of the award.