Systems and methods for incrementally increasing a tiered plurality of progressive jackpots

An electronic gaming system includes a progressive system server configured to establish a tiered plurality of progressive jackpots that includes a first jackpot increasable a first cap value, a second jackpot increasable to a second cap value greater than the first cap value, and at least one intermediate jackpot increasable to at least one intermediate cap value greater than the first cap value and less than the second cap value. The progressive system server is further configured to allocate portions of player wagers to one of i) the first jackpot, ii) the at least one intermediate jackpot, and iii) the second jackpot, whereby the first jackpot is initially incrementally increased to the first cap value, the at least one intermediate jackpot is next incrementally increased to the at least one intermediate cap value, and the second jackpot is next incrementally increased to the second cap value.