The method of the present invention involves a Twenty-One game, in which, in addition to his normal wager, a player will have the option of making an additional wager that becomes part of, and makes the player eligible to win, the progressive jackpot. If the player's Twenty-One hand comprises a particular, predetermined arrangement of cards, the player will win all, or part of, the amount showing on the progressive jackpot. In a Twenty-One game using any number of decks of cards, the predetermined winning arrangements of cards preferred in the present invention are an Ace, Two, Three, Four and Five suited; a Two, Three, Four and Five suited; a Four, Five and Six suited; a Four, Five and Six unsuited and an Ace-Jack suited; and optionally additionally any Blackjack Suited and any Blackjack unsuited. In a Twenty-One game that utilizes a six deck shoe, an alternative predetermined winning arrangements of cards preferred in the present invention are Five Three's unsuited; Three Five's suited; a Four, Five and Six suited; a Four, Five and Six unsuited and an Ace-Jack suited.