1. A gaming device comprising: a display device; an input device; a processor; and a tangible memory component storing a program, which when executed by the processor, causes the processor to operate with the display device and the input device to: receive, from a player, a total wager amount for at least one play of a wagering game, in which the total wager amount is received in at least one payment; transmit an indication associated with the total wager amount to a controller; receive an indication associated with a total payout amount from the controller; receive, from the player, a selection of one of a plurality of different total quantities of wagering game events; receive a payout distribution parameter from the player; allocate, based on the payout distribution parameter, the total payout amount among the selected total quantity of wagering game events, said allocation including a determination of a distinct expected value for each of the selected total quantity of wagering game events such that a sum of each of the determined expected values equals the total payout amount; display at least a portion of the total payout amount in association with the at least one play of the wagering game; and cause the total payout amount to be provided to the player.