Patent ID: 7270604

Claim:
A gaming device operable under control of a processor, said gaming device comprising: at least two potential award offers adapted to be formed and displayed to a player, wherein (a) a first one of the potential award offers is formed from a first quantity of first values, wherein the first quantity is greater than one; and (b) a second one of the potential award offers formed from a second quantity of second values, wherein the first quantity is, on average, greater than the second quantity, and the second values are, on average, greater than the first values; and a display device; wherein said processor is operable with the display device and programmed to: (a) determine the greater of the first and second potential award offers; (b) cause the display device to display an initial offer to the player, wherein the initial award offer is the determined greater of the first and second potential award offers; and (c) enable the player to accept the initial award offer or reject the initial award offer to instead receive a third award offer.