1. A gaming system comprising: a housing; at least one processor; a plurality of input devices supported by the housing, said plurality of input devices including: (i) an acceptor, (ii) a validator, and (iii) a cashout device; at least one display device supported by the housing; and at least one memory device which stores a plurality of instructions, which when executed by the at least one processor, cause the at least one processor to operate with the at least one display device and the plurality of input devices to: (a) if a physical item is received via the acceptor: (i) identify, via the validator, the received physical item, and (ii) establish a credit balance based, at least in part, on a monetary value associated with the received and identified physical item; (b) receive an input associated with a placement of a wager on a play of a primary game, (c) associate one of a plurality of different virtual competitors with a player, (d) for the play of the primary game: (i) determine a primary game outcome, (ii) display the determined primary game outcome, (iii) determine any primary game award associated with the determined primary game outcome, and (iv) display any determined primary game award associated with the determined primary game outcome, (e) for each competitor point accumulation event which occurs, accumulate a quantity of competitor points for the associated competitor, (f) if a competition sequence triggering event occurs and the associated competitor is eligible to participate in a competition sequence: (i) enable the associated competitor and at least one additional competitor to participate in the competition sequence, said at least one additional competitor being associated with a quantity of competitor points, and (ii) for each participating competitor, determine a competition sequence outcome based, at least in part, on a relative probability of the competitor achieving a designated outcome in the competition sequence, said relative probability being based, at least in part, on the quantity of competitor points accumulated for the competitor relative to the quantity of competitor points accumulated for each of the participating competitors, and (g) if a cashout input is received via the cashout device, cause an initiation of any payout associated with the credit balance.