1. A method of operating a gaming system, said method comprising: causing a processor to operate with a display device and an input device to: (a) display an amount of credits in a credit balance for a player, said displayed amount of credits beginning at an initial amount of credits greater than zero; (b) receive a wager amount for a gaming session, said gaming session including a plurality of plays of a game; (c) reducing the amount of credits in the credit balance by the wager amount; and (d) for each play of said plurality of plays of the game: (i) determine one of a plurality of different game outcomes, (ii) display the determined game outcome, (iii) if the determined game outcome is any designated winning outcome, display a first payout greater than zero credits associated with said designated winning game outcome; (iv) if the determined game outcome is a qualifying game outcome and no designated winning game outcome associated with said first payout has been displayed, utilize the initial amount of credits to determine a second payout, said second payout, when added to the credit balance, causes the amount of credits in the credit balance to at least equal the initial amount of credits; and (v) if the determined game outcome is said qualifying game outcome and at least one designated winning game outcome associated with said first payout has been displayed, utilize the initial amount of credits to determine a third payout different from said second payout, said third payout, when added to the credit balance, causes the amount of credits in the credit balance to at least equal the initial amount of credits.