A gaming device that enables a player to pick one or more of a plurality of selections. A selection group associated with each of the picked selections is revealed and the picked selections are moved or positioned at the lowest ranking available or unoccupied position in the associated selection group. An offer based on the occupied positions is offered to the player. If the player keeps the offer, the offer is provided to the player and the selection game ends. If the player rejects the offer and the player has at least one remaining offer, then the position of at least one of the picked selections is modified or moved to another position wherein even after the picked selections are modified or moved, the lowest ranking available or unoccupied position of each selection group must be occupied before any other position of that selection group may be occupied. Another offer based on the awards or values associated with the modified positions of the picked selections is offered to the player for acceptance or rejection. If the offer is accepted or the player does not have at least one new offer remaining, the offer is provided to the player and the selection game ends. If the offer is rejected and the player has at least one new offer remaining, then the gaming device again modifies or moves the positions of the picked selections as described above.