A method for providing bonus jackpot payoffs during a bonus mode time period in a system of linked gaming machines interconnected to a controller. Eligible gaming machines are determined at the time the bonus time period starts. Once the bonus mode time period starts, a portion of the eligible gaming machines are randomly selected for multiple jackpot bonus payoff opportunities. The random selection determines the rate the opportunities are issued and the average length of the bonus mode time period. Once gaming machines are selected they are allowed to complete the game they are currently involved in and should the play result in a winning combination, then the game payoff is multiplied by a bonus multiplier. The underlying gaming machine is responsible, in a conventional fashion, for paying the game payoff and the controller then authorizes a further jackpot bonus payoff of the bonus multiplier less one times the game payoff. The bonus pool value is then decremented by the amount paid by the controller. This process repeats until the bonus mode multiplier opportunities for each bonus multiplier in each bonus round is completed or until the bonus pool value drops below zero.