1. A gaming device comprising: a game; a display device adapted to display the game; a plurality of selections in the game; a plurality of awards in the game, wherein said plurality of awards are associated with said plurality of selections; and a processor operable with said display device to control the play of the game by: (a) displaying said plurality of selections; (b) enabling a player to pick a plurality of said selections; (c) forming and displaying an offer based on the awards associated with at least one of said picked selections without revealing which picked selections said offer is based on; (d) enabling the player to accept or reject the offer; (e) providing the offer to the player if the player accepts said offer; (f) if the player rejects said offer: (i) enabling the player to deselect at least one of said picked selections; and (ii) enabling the player to pick one of the plurality of unpicked selections for each deselected selection; and (g) repeating steps (c) to (f) unless the player accepts said offer or said offer is a final offer.