A gaming machine displays a set of virtual center reels, creating an M×N array of symbols, and an independent set of virtual peripheral reels surrounding the M×N array. The peripheral reels are part of a secondary game, and each peripheral reel displays only one symbol position. The center reels contain at least one trigger symbol for trigging the secondary game. Each of the reels spins and randomly stops. Awards are granted for winning symbol combinations on the center reels. If the trigger symbol is displayed in the M×N array, or other trigger condition exists, a bonus award is granted for winning symbol combinations on the peripheral reels. The bonus award may be based on the number of peripheral symbols that match the displayed trigger symbol or may be based on other criteria. In one embodiment, the trigger symbols are only on one of the center reels.