The present invention relates to a progressive game that can be incorporated either as a bonus game or a stand-alone game in a progressive linked gaming machine environment. The game utilizes a plurality of progressive jackpot pools each associated with a particular game outcome (i.e., such as Quiniela, Exacta, Trifecta and Superfecta in the case of a horse race derby game). Each progressive jackpot pool is funded through play at the underlying linked game such as a contribution of each wager or through separate wagers. When the game of the present invention initiates, a plurality of successive game rounds are played. Each successive game round reduces the number of possible game outcomes such as by reducing the number of horses in each successive horse race. Therefore, with each successive game players have a higher probability of winning. The terminating round is reached in which the last game always results in at least one guaranteed winner through reduction of the possible game outcomes. However, a player (or players) may win in the first or any successive round which would immediately terminate the overall common game.