An offer acceptance game for a gaming or wagering device. One embodiment comprises: (i) an offer provided to a player; (ii) an input device by which the player accepts the offer; (ii) an input device by which the player rejects the offer; (iii) an advance threshold communicated to the player; and (iv) an advance provided to said player if the offer exceeds the advance threshold. The gaming device preferably includes at least one additional offer that is provided upon rejection of the first offer, wherein the game provides the advance if the final provided offer exceeds the advance threshold. The advance preferably includes second bonus game. The gaming device also preferably includes a limit communicated to said player, wherein the player does not obtain the advance if the second offer exceeds the limit.