A gaming device that enables players to accumulate awards until there are no more awards or until one or more termination variables reaches a predetermined limit is provided. A random generation device generates awards upon a player input. One or more termination variables is used, each defined by or divisible into a plurality of units, wherein a random generation device generates an amount of units upon a player input. A game termination limit of accumulated or lost termination units is provided, wherein a player generates awards until accumulating the termination limit of units.