A video slot machine has M reels, each displaying N symbols when stopped. Above the display of the reels is a set of generally valuable replacement symbols that have been independently selected at random independent from the reel display. Each reel is associated with a particular replacement symbol in the set. If a special symbol is displayed on a reel, the replacement symbol associated with that reel substitutes for the special symbol when determining the award. Examples of the replacement symbols include wild symbols, bonus symbols, and multiplier symbols. After each game, the replacement symbols are shifted, and used replacement symbols are randomly replaced to vary the possibilities for each game. The player is incentivized to play longer due to the possibility of using valuable replacement symbols in the symbol array and the possibility of very high awards being granted by multiple special symbols being displayed.