A progressive jackpot slot machine, or group of slot machines, is described herein. A plurality of progressive jackpots are accumulated as the slot machine is played. In one preferred embodiment, a first progressive jackpot is accumulated at a first rate, and a second progressive jackpot is accumulated at a rate higher than the first rate. Additional jackpots accumulate at higher rates. The betting of additional monetary amounts enables the player to win additional jackpots. This provides added incentive for the player to bet additional monetary amounts.