A method of providing a game for a gaming device using random payout from a prize pool, the game including a plurality of possible game outcomes, is provided. The method comprises: receiving, at the gaming device, a wager amount; receiving an input to initiate game play; and qualifying the wager amount to win a random award from the prize pool for each of at least two game outcomes from the plurality of game outcomes. A predetermined average pool size for the progressive prize pool is stored. A random payout is calculated using a function that calculates the random payout using a specified minimum amount, a specified maximum amount, and a specified average value. The specified average value is independently specified between the specified minimum value and specified maximum value. The random payout calculated by the function is included within the specified minimum amount and the specified maximum amount, wherein the function is configured to calculate random payouts that average over time substantially the specified average value. The random payout is provided where when the specified average value is set at an average contribution to the progressive prize pool, an average random payout over time is substantially equal to the average contribution to the progressive prize pool in order to maintain the progressive prize pool at the predetermined average pool size.