A gaming device having a bonus scheme, wherein the player may choose when to play a bonus scheme, so long as the player is qualified to do so. The method of qualifying the player to enter the bonus round connects or links the base game operation of the gaming device with the bonus scheme. The reels of the base game contain symbols which alone or in combination with other symbols yield one or more bonus awards to a player. The bonus awards are escrowed and displayed a bonus award escrow display. Once the player obtains a single bonus award, the player becomes eligible or qualified to play the bonus round and the player may choose to do so at any time. The player can accumulate bonus awards and use multiple bonus awards at one time.

 
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> Game system and game information storage medium used for same

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