A gaming device including a game which displays a plurality of symbols to a player. A probability of being selected by the processor is associated with each of the symbols. Additionally, at least two picks of the symbols are provided to the player where the number of picks is less than the number of symbols. In a game, the processor randomly picks the symbols for the number of picks provided to the player. The player receives any awards associated with the symbols picked by the processor. The processor then eliminates the picked symbols from further selection in the game. Eliminating the picked symbols increases the probabilities associated with the unpicked symbols for future picks based on the probabilities associated with the picked symbols. The player continues to pick selections until there are no picks remaining in the game.