A wager amount from a player is received. A programmer input of information based on a specified average value, a specified minimum value, and a specified maximum value is determined. The specified average value is independently specified between the specified minimum value and specified maximum value. A portion of non-gaming revenues is allocated to the progressive prize pool. A random amount is calculated from the progressive prize pool using a function that calculates the random amount using the specified minimum value, the specified maximum value and the specified average value. The calculated random amount is generated between the specified minimum value and the specified maximum value and the function is configured to calculate random amounts that average over time substantially the specified average value. The player is eligible to win the random amount from the progressive prize pool in which the portion of non-gaming revenues was allocated.