A gaming machine is described wherein a player first plays a primary game, such as the spinning and stopping of mechanical or video reels displaying symbols. A plurality of progressive jackpots is displayed to the player. Upon a jackpot-winning outcome of the primary game, the number of different progressive jackpots paid to the player depends on the number of credits bet by the player. In one embodiment, the jackpot above each column of symbols gets incremented upon a special symbol, such as a credit value, being displayed in that column. As the jackpots are won, other jackpots are shifted over the columns to replace the won jackpots. In another embodiment, the determination of which jackpot is won depends on the outcome of the primary game.