A gaming system displays a plurality of independent reels, wherein each independent reel generates a symbol from a plurality of symbol positions of that independent reel in accordance with a plurality of probabilities. At least two adjacent independent reels generate symbols according to relatively high probabilities of generating a designated symbol. For a play of the game, the gaming system generates and displays a symbol for each independent reel and provides an award for any displayed winning symbol combinations. In one embodiment, for at least one symbol position of at least one winning symbol combination, the gaming system re-generates a symbol for one or more independent, such as by displaying a symbol from an adjacent symbol position of that independent reel. The gaming system provides an award for any winning symbol combinations and repeats until no winning symbol combinations are displayed.