A system for enabling a player to use residual credits on a gaming machine to provide the player with a chance to win a prize. The system includes means for determining a range of values as a function of a jackpot pool to generate randomly an outcome in the range of values, random number generation means for generating the random outcome, means for determining a range of outcome values of the player that provides a chance of the player winning the jackpot pool, and means for determining whether the generated random outcome matches any outcome value of the player.