A gaming device includes a plurality of symbol groups which each include a plurality of symbols. In one embodiment, each of the symbols is associated with a probability of being generated. The gaming device includes a plurality of player selectable selections. The gaming device includes a plurality of outcome pools. Each pool includes the number of designated symbols which are generated for each selection. That is, each pool determines how many symbols will be generated for the indicated group for each selection. Each time a player picks one of the selections, the gaming device selects one of the pools. The gaming device generates the designated number of symbols associated with the picked selection which is determined by the selected pool. The gaming device provides the player an outcome or award, based at least in part, on the generated symbols.