1. A gaming system comprising: a housing; at least one display device supported by the housing; a plurality of input devices supported by the housing, said plurality of input devices including: (i) an acceptor, and (ii) a cashout device; and at least one memory device which stores a plurality of instructions which when executed by at least one processor cause the at least one processor to operate with the plurality of input devices and the at least one display device to: (a) if a physical item is received via the acceptor, establish a credit balance based, at least in part, on a monetary value associated with the received physical item, wherein said physical item is selected from the group consisting of: a ticket associated with the monetary value and a unit of currency, (b) accumulate at least one outcome enhancing unit for a play of a game, (c) if a quantity of accumulated outcome enhancing units is at least a designated quantity: (i) enable a player to elect to enhance at least one outcome for a play of a next game, (ii) if the player elects to enhance at least one outcome, for the play of the next game: (A) randomly select an enhanced outcome from a set of enhanced outcomes, said set of enhanced outcomes being associated with a first average expected award, (B) display the randomly selected enhanced outcome, (C) determine any award associated with the randomly selected enhanced outcome, and (D) display any determined award associated with the randomly selected enhanced outcome, and (iii) if the player elects not to enhance at least one outcome, for the play of the next game: (A) randomly select an unenhanced outcome from a set of unenhanced outcomes, said set of unenhanced outcomes being associated with a second average expected award, said second average expected award being less than the first average expected award, (B) display the randomly selected unenhanced outcome, (C) determine any award associated with the randomly selected unenhanced outcome, and (D) display any determined award associated with the randomly selected unenhanced outcome, and (d) if a cashout input is received via the cashout device, cause an initiation of any award associated with the credit balance.