A gaming system provides a bonus gaming session that is activated during a play of a five-card draw poker base game when a predetermined plurality of the first set of five cards dealt meets a predetermined criteria, for example at least four of the five cards dealt and held by the player share a common suit. When activated, the gaming system repeats plays of the game in the bonus gaming session until a winning draw poker outcome has been generated. In the bonus gaming session, the card that is not co-suited with the plurality of the held first set of cards is discarded and randomly replaced until a winning five-card hand is generated, upon which the gaming device provides an award. The gaming system provides a correspondingly larger award for a winning flush hand for each additional re-drawn fifth card required to achieve a winning five-card flush hand.