Periodic prize draws are conducted by a jackpot controller (13) in a gaming system having one or more electronic gaming devices (10). The probability of each electronic gaming device winning a particular prize draw is dependent upon the amount wagered on that gaming machine during a period preceding that prize draw. The prize may be a progressive jackpot which comprises an initial starting value and a contribution from the amounts wagered on the electronic gaming devices. If an electronic gaming device wins a prize draw, its player may be granted a feature game to determine the actual prize. Jackpots are suspended pending the completion of the feature game. The probability that a gaming device will win the prize draw, or the relative win probabilities of the gaming devices, may be displayed graphically.