A gaming system which provides the player a plurality of playing cards to form an initial primary card hand and also displays one or more other card hands. The player selects one or more of the initially dealt cards in the primary card hand to hold or to discard. The held cards are also held in one, more or each of the other simultaneously displayed hands. The gaming device evaluates the held cards and determines which card game outcomes are possible based on the held cards and the remaining cards in the deck. The gaming device utilizes a stored table of different distributions of card game outcomes which would result in each payout amount and a table regarding which card game outcomes are possible based on the player's held cards to determine a distribution of outcomes that provides a total payout equal to the payout of the predetermined game outcome.