A gaming device having a plurality of start values. The player selects one of the start values, as part of a game sequence. During the game sequence, the gaming device increments the start value to an apparent award. The gaming device in one embodiment enables the player to keep the apparent award or trade it for another apparent award. The other apparent award in one embodiment is derived from one of the other start values. After one or more keep or trade sequences, the player achieves one of the apparent awards. The gaming device then performs a sequence in which the apparent award changes into an actual award. The gaming device provides the actual award to the player.