The gaming device disclosed herein includes a plurality of matrices of symbol positions. At least a first reel in a first reel set or matrix is associated with or linked to at least a first reel in a second reel set or matrix and at least a second reel in the first reel set not associated with or linked to any reel in any second reel set. In a play of the game, symbols are independently generated for each reel set and the symbols displayed for each reel set are independently evaluated to provide any awards for any winning symbol combinations. After the evaluation, the gaming device removes zero, one, or more symbols from reels in the reel sets. If any empty symbol positions are formed on the first reel in the second reel set, the gaming device shifts or transfers one or more symbols from the first reel of the first reel set to the linked first reel of the second reel set to occupy the one or more empty symbol positions. The gaming device generates symbols to fill the empty symbol positions in the reel sets and the symbols displayed for each reel set are independently evaluated to provide any awards for any winning symbol combinations.