A gaming device that selects one or more offer components and forms an initial offer based on the selected offer components. The gaming device enables the player to accept or reject the initial offer. If the player rejects the initial offer (and the player has at least one offer remaining), then a component number modifier generator selects one of a plurality of component number modifiers. The selected component number modifier alters or changes the number of selected offer components by either adding or subtracting at least one offer component to or from the previously selected offer components. If the selected component number modifier is associated with a negative number or value, then the gaming device deselects at least one of the previously selected offer components. The remaining selected offer components form a subsequent offer which the gaming device enables the player to accept or reject. If the selected component number modifier is associated with a positive value or number, then at least one of the offer components from the provided plurality of offer components is selected. The value or award associated with each of the additionally selected offer components is added or otherwise combined with the values of the previously selected offer components to form a subsequent offer which the gaming device enables the player to accept or reject.