The present invention includes an improved 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 another 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.