A winning progressive jackpot ticket is selected from deals of instant tickets that are dispensed from a network of gaming machines by randomly selecting, upon initiation of a progressive jackpot, a progressive jackpot value that falls within a predetermined range of progressive jackpot values, detecting in the server when the progressive jackpot value is reached as a result of a purchase of an instant ticket at one of the gaming machines, randomly selecting the winning progressive jackpot ticket from all of the currently unplayed instant tickets, or from the next n number of currently unplayed instant tickets, when the progressive jackpot value is detected as reaching the progressive jackpot value that was randomly selected, and awarding the current progressive jackpot amount to the player who subsequently purchases the winning progressive jackpot ticket.