A gaming system which provides the player a plurality of playing cards to form an initial primary poker hand and also displays one or more other poker hands. The player selects one or more of the initially dealt cards in the primary poker 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 poker 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 poker game outcomes which would result in each payout amount and a table regarding which poker 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.