A new version of the game of blackjack, in which players may discard one of the two cards that they are initially dealt, if they pay a discard fee before any cards are dealt. The player who discards then draws another card to replace the card that has been discarded. The discard fee is preferably a percentage of the amount that the player has bet. The discard option is preferably limited to players who do not have an ace in their initial hand, and who have an initial hand with a point value of sixteen or less. If the dealer has a blackjack, a player who has an ace or card with a value of ten in his or her initial hand, and has paid the discard fee, may discard the other card and draw a replacement card. If the player then has a blackjack, they win the hand.