The present invention is a gaming machine having a player time-selectable bonus award scheme whereby the player may redeem, at a time of the player's choosing winning outcomes accrued during base game play. Redemption of each of the accrued winning outcomes is accomplished when a player selects an option to display a winning symbol combination associated with the winning outcome. Selection of the option to display the winning symbol combination associated with the winning outcome always yields an award and sometimes yields another winning outcome, again redeemable at a time of the player's choosing. A counter display on the gaming machine increments a number as each winning outcome is accrued, and decrements the number as each winning outcome is redeemed.