Fizzbin
Kirk's explanation of the game included a claim that it is played by inhabitants of the planet Beta Antares IV, Spock replied that he is familiar with the inhabitants; Kirk quickly cut him off to prevent his science officer from professing ignorance of the game.
The rules of Fizzbin were intentionally very complex. Each player gets six cards, except for the player on the dealer's right, who gets seven. The second card is turned up, except on Tuesdays. Kirk dealt the henchman two jacks, which are a "half-fizzbin." When the henchman said he needs another jack, Kirk warned that a third jack is a "shralk" and is grounds for disqualification. With two jacks, one wants a king and a deuce, except at night, when one wants a queen and a four.
At this point, Kirk dealt a third jack, but to keep the ruse going, he ignored the disqualification rule he had just made up. He explained that, had a king been dealt instead of a jack, the player would get another card, except when it is dark, in which case he would have to give it back. The top hand is a "royal fizzbin," but the odds of getting one are "astronomical:" when Kirk asked Spock what the odds are, Spock truthfully replied that he had never computed them.
Kirk called the last card a "kronk" and then purposely dealt a card such that it fell on the floor. As the henchman being taught reached down, Spock nerve-pinched him while Kirk and McCoy attacked the other guards, allowing the three to escape.
Read more about this topic: A Piece Of The Action (Star Trek: The Original Series)