A gaming system including a central server linked to a plurality of gaming machines. The gaming system includes at least one and preferably a plurality of progressive awards wherein upon a suitable initiating event, a wager amount or value is randomly generated from at least one predetermined range of wager amounts or values. Upon a suitable triggering event, such as an accumulated wager pool incrementing to the randomly generated wager amount or value, a designated award, such as a progressive award, is provided to a player. In one such embodiment, upon the occurrence of the triggering event, an independent determination occurs regarding which one of the plurality of progressive awards will be provided to a player.