Blackjack, "also known as 21, a number which defines the object of the game," is a Human recreational gambling game.
The rules are as follow: "10s and picture cards are worth 10, ace -- 1 or 11 -- the other cards face value. The dealer must hit 17 -- five cards under pays double." (TNG: "The Royale")
On Theta VIII, blackjack was one of the games emulated in the physical representation of the novel The Hotel Royale. When the USS Enterprise-D investigated the planet, Data proved to be a skilled Blackjack player. He beat the odds to get a "five card Charlie." (TNG: "The Royale")
Blackjack was also the code name of the ground controller for Captain John Christopher's mission to intercept the USS Enterprise during its inadvertent voyage to 1969. (TOS: "Tomorrow is Yesterday")
Ben suggested to play blackjack after Taurik, Sito Jaxa, and Alyssa Ogawa left the poker round and only he and Sam Lavelle were left, but Lavelle decided to get more sleep. (TNG: "Lower Decks")
In the Bashir 62 holoprogram, Vic Fontaine, Frank Sinatra and Dean Martin lost fifteen thousand dollars in a blackjack game in 1958. (DS9: "His Way")
In early 2375, to avoid having to sing All the Way, Vic suggested to Worf that they should play "a little blackjack to get the blood pumping". (DS9: "Image in the Sand")
Kira Nerys and Frankie Eyes played blackjack later that year. (DS9: "Badda-Bing, Badda-Bang")