A bonus game that operates in combination with a slot machine base game is provided. The bonus game includes a series of free spins or free evaluations in which symbols of a set of symbols are generated. The free spins also generate executor symbols that alone or in accumulation cause one of the symbols of the set to be eliminated or replaced. In either case the symbols remaining in the set have a higher probability of being generated and a higher probability exists that a larger award paying combination of the remaining symbols will be generated. The elimination sequence can be repeated a number of times further increasing the probability of generating a higher paying award for the player. The present invention is operable with different types of base games such as slot and poker.