Someone has you at their mercy. They could snuff you out without breaking a sweat, and there's nothing you can do to save yourself. Or isn't there?
If you can convince them that you're more entertaining alive than dead, then turn the tables and use your entertainment talents to defeat them, you are pulling the Scheherezade Gambit. Named for the legendary Persian queen and origin of One Thousand and One Nights, who beguiled her captor into hearing a thousand Cliffhangers in order to buy time.
Compare Holding the Floor, Talking Your Way Out. Contrast Get It Over With.
Black Lagoon: After Rock asks Balalaika not to destroy the Washamine group, Balalaika holds him at gunpoint and threatens to kill him saying that this trope is the only way he's going to get out of this alive. He manages to pull it off and walks away relatively unharmed.
This is precisely how Cell turns the tables on Vegeta in Dragon Ball Z just as the latter is about to pound the former, still in Imperfect form, into oblivion.
You'd think Cell would have learned his lesson; instead, he gives Our Heroes the perfect opening to turn this gambit around on HIM when he gives them time to prepare for the Cell Games.
Snow White uses the tactic in the Fables graphic novel 1001 Nights of Snowfall. The title is a clear allusion to One Thousand and One Nights.
Used by Cyclops in Astonishing X-Men. Knowing that the Breakworld has his ship bugged, he deliberately makes some vague reference to a mysterious superweapon, and then throws himself into suicidal danger, banking that the Breakworlders will value intelligence on the superweapon more than his death. He's right.
He ALSO lied about not having his powers back...
A Star Wars Expanded Universe comic called Vader's Quest, the Emperor offers to reward a bounty hunter whose efforts had been impressive. He offers her the chance to join him and get a new, non-derelict body with a better name. She thanks him, but she has all the reward she needs, she likes her name, and she prefers to win with the hand she was dealt, not a stacked deck.
Palpatine: "I see. You do realize where you are and whose word your life depends on, do you? Why should I let your insolence go unpunished?" Mala Mala: "Because it amuses you to do so?" Palpatine: "Quite. Well played, little one!"
In Boba Fett: Bounty on Bar-Kooda, the travelling magician Wim Magwit was once captured, along with several other entertainers, by the carnivorous space pirate Bar-Kooda. After Bar-Kooda got bored with each entertainer, he would kill them them and have them served as his next meal. Magwit refused to explain the secret behind his "magic" teleportation hoop to Bar-Kooda, realizing that once the act would bore the pirate after losing its mystery. Bar-Kooda kept him alive in the hopes to learn its trick, buying Magwit enough time to escape. Boba Fett uses a combination of Magwit's hoop and Bar-Kooda's unsatisfied curiosity to lure him into a trap.
In Halo: Uprising, Colonel Ackerson convinces the Covenant not to blast Cleveland from orbit by making up an artifact called the "Key of Osanalan" which he told them was hidden somewhere in the city.
In the film The Usual Suspects, the police have captured one member of a criminal gang. They interrogate him, and the Suspect tells the story of the gang's exploits, leading up to the Suspect's capture.
The film The Princess Bride, this happens when Westley is captured by the Dread Pirate Roberts.
A variant occurs in The Dark Knight when the Joker is captured. He verbally manipulates a police officer into attacking him, then takes the officer hostage.
This trope is practically Captain Jack Sparrow's modus operandi in Pirates of the Caribbean. In the first movie, he successfully uses it twice on Captain Barbossa and crew, and he goes on to use it (still successfully) against Davy Jones, Beckett, and on his own crew in the sequels.
Made even more amusing by the fact that Captain Barbossa knows that Jack is using this on him. He closes his eyes and you can see him trying to will himself not to ask what Jack is babbling about this time. He fails, of course, by the very merit of this gambit.
James Bond saves himself from laser-based castration by convincing Goldfinger (in the movie of the same name) that he's more valuable alive as a prisoner.
BIONICLE: Web of Shadows puts a spin on it by having The Starscream Roodaka do one on behalf of the heroes, arguing that a spectacular execution would enhance Sidorak's reputation better than Just Shooting Them. Admittedly, she only wanted them killed differently for the purposes of her own schemes, but the effect is the same as it gave the Rahaga time to stage a rescue.
Played for Drama all throughout The Fall. Roy, the storyteller, tells 5-year-old Alexandria that he needs his pills to continue telling his bandit story, and she needs to go steal them for him like a good little bandit. The pills he wants her to steal are morphine. He plans to kill himself. Alexandra later uses the story to convince him to live.
The miniseries Arabian Nights makes use of this, which is not surprising since it is based on 1001 Arabian Nights. In this version, the Sultan went insane after his first wife betrayed him to his brother, and thus decides that while he must marry to keep the throne, he'll have his new wife killed at dawn so the same thing won't happen again. Scheherezade, who was friends with the Sultan as a child and loves him still, takes him up on the offer and craftily puts various morals and twists in the stories which the Sultan relates to. By the end, he trusts and loves her and is no longer mad.
The 'first wife betrayed him, he'll kill his new wife at dawn' part was in the original.
Bilbo in The Hobbit keeps Gollum from eating him by proposing a game of riddles, where if he loses, Gollum could eat him but if he wins, Gollum has to show him the way out.
A man was facing the firing squad and said "Can I have one last request? I've always liked singing, so I'd like to sing one last song." The captain decides it's a reasonable request and nods. The condemned man clears his throat and sings "One thousand and one bottles of beer on the wall, one thousand and one bottles of beer...."
The Trope Namer is One Thousand and One Nights, a collection of Middle Eastern folk tales. The framing device for the collection is the story of a sultan who takes a new wife every day, spends the night with her, then has her executed the next morning. He marries Scheherezade, the daughter of his vizier. That night, Scheherezade asks the sultan for a favor, and tells him she'd like to see her sister. The sister asks to hear a story. Scheherezade is such a gifted story-teller that the sultan is entranced. However, Scheherezade cleverly leaves the story unfinished, telling her sister and the sultan that she'll relate the ending tomorrow night. Thus, the sultan spares her life, because he wants to hear the end of the story. Every night thereafter, Scheherezade tells the ending of the previous story, and the beginning of another, so the sultan must keep delaying the execution. Eventually, Scheherezade runs out of stories, but by then the sultan has fallen in love with her (What they did on each of those thousand and one nights before the stories probably helped).
Worth mentioning that this was Scheherezade's plan from day one. She had to talk her father into it (naturally enough, he didn't like the idea of executing his own daughter).
Stephen King's novel Misery is about a Loony Fan kidnapping her favorite author and forcing him to write a book just for her. After a while, the writer begins to compare himself to Scheherezade, knowing that he will be kept alive at least as long as it takes him to finish the book.
In "Jack's Bean Problem" from Jon Scieszka's book The Stinky Cheese Man and Other Fairly Stupid Tales, the Giant kidnaps Jack the Narrator and gives an ultimatum: "Tell me a better story or I'll grind your bones to bake my bread. And when you're done I'll grind your bones to bake my bread anyway!" Jack then tells the Giant a recursive story, repeats it until the Giant falls asleep, and sneaks away.
In another "Jack And The Beanstalk" adaptation, Jack says he can recite poetry, in an attempt to prevent the Giant from killing him. I don't think he actually recites it, but in his first attempt he puts the Giant to sleep. He isn't so lucky the second time.
The Kelx religion in Neal Stephenson's novel Anathem is built on a cosmology of a Magistrate and a Condemned Man; each day, the Condemned Man tells a story, to prove the value of every soul (as every soul can create entire worlds). The Kelx believe that they, and their world, are the Condemned Man's stories. If the Magistrate ever finds the content of the stories to be overly sinful, the Condemned Man and thus our universe will be executed.
In Stephenson's The Baroque Cycle, Eliza does this to her traveling companion to make sure he doesn't abandon her: she tells him the story of her life, pausing at a suspenseful point right as they approach a town and not resuming until they've passed it. The victim takes a while to catch on, mostly because he was never intending to abandon her anyway. Since Eliza is an escaped harem slave, she presumably learned about this trick directly.
In Robert A. Heinlein's Time Enough For Love, Lazarus and Ira embark on what they call a "reverse Scheherazade". Lazarus agrees to not suicide if Ira shows up faithfully every day to listen to him (Lazarus will accept an occasional suitable substitute if Ira's official duties prohibit him showing up in person). In a subversion, Lazarus has no way to measure the passage of time, so Ira has him kept unconscious for days at a time, until it's convenient for Ira to show up.
I Claudius takes the popular position that Claudius used Obfuscating Stupidity to appear as a bumbling, stuttering clown to keep himself alive during the reign of The Caligula. It worked. When the Praetorians assassinated Caligula and his family, they found Claudius hiding behind a curtain and crowned him Emperor. To everybody's surprise, Claudius was actually a good ruler. He even had the ringleaders of the conspiracy executed. (They did it once, so they could do it again.)
More to the point, they'd killed not only Caligula (which Claudius doesn't mind at all) but also his wife and infant child.
In Gail Carson Levine's The Two Princesses of Bamarre, the dragon Vollys deliberately invokes this - she keeps her human prisoners alive as long as they amuse her, with even a point system to measure how far they are from death. The catch is that she always gets bored eventually.
Meta: The entire Star Wars Expanded Universe would cease to exist without gobs and gobs of Continuity Porn. Every single character with a name has to be explained; even characters which don't have names, such as the wampa whose arm Luke cut off (not the same wampa that captured him, mind you, but its mate), have backstories. Done exactly like Scheherezade.
Keturah Reeve of Keturah and Lord Death meets Death, come to claim her life, after she becomes lost in a forest. She persuades him to grant her a reprieve by putting her storytelling skills to use in the fashion of this trope, winning herself a number of extra days by drawing out the story (although it becomes clear that Death is already inclined to be generous; on one of the nights he comes for her, Keturah doesn't have a story prepared but is allowed another day anyhow).
In The Hobbit, Bilbo's first idea to keep the mysterious Gollum from attacking is to propose a riddle-game. He's lucky that Gollum isn't hungry at the moment. Bilbo also takes advantage of this ploy: if he wins the game, Gollum has to show him the way out.
In too many episodes to list, the Doctor, with an enemy poised to kill him, starts thinking out loud about how to escape. The villain is so mesmerized by the process that he's allowed to keep going until he comes up with an idea.
Indeed, at one point The Master, his arch-rival, was persuaded to rescue him. The Master couldn't allow someone else, after all, to have the victory... and indeed, as he puts it, "A universe without The Doctor... is scarcely worth thinking about."
More recently the tactic has become to make the enemy want to interrogate him first.
Not just recently. This occurred at least as long ago as "Genesis of the Daleks" where Davros had The Doctor literally at his mercy, in the middle of his base, disarmed, isolated from his companions, and on a torture rack. He COULD have killed him then, but wanted to get the information about the Dalek defeats the Doctor knew about. Earlier in the same adventure, the first activated Dalek tried to kill The Doctor when it detected he was an alien, and one of the Kaled scientists intervened because they hadn't finished questioning him yet.
Parodied by Bob the Angry Flower when Bob persuades the Daleks to interrogate him inside an exclusive members-only club that he had been trying to get into for some time.
Rory does it to House in The Doctor's Wife. This results in some serious Mind Screw for him and Amy.
Rose pulls this on the Daleks in one episode, claiming knowledge of the Time War. Mickey and a scientist who's also in the room quickly follow her lead.
Kind of subverted in the fact that the Daleks did need one of them (Either/Or) and the scientist quickly turned out to be a Mauve Shirt ...
Criminal Minds, "Damaged": Spencer Reid puts his well-honed capacity for statistical and psychological babble to life-saving use.
One of this character's more quietly badass moments.
HARDWICK: ::To Reid, as the guards come rushing back in to rescue him:: "Is that true? Did I really never have a chance?" REID: :: On his way out the door:: "I don't know. Maybe."
Pretender: You won't kill me! You don't know who I am.
Robin Hood: I don't care who you are.
In an episode of the The Twilight Zone from the 1980's, a teacher is told that one of her student's must be allowed to take books home, though why he must is not given. When the student falls during recess and must be taken to the hospital overnight, she finds out that the boy's grandfather is home and waiting for the concluding half of the last night's story. She offers to fill in for the student. Many years later she sees the now-grown man hurrying home and follows him, wondering if the grandfather is still alive. Just as she is about to open the door to the room where they are, she stops telling the narrative to her mother, who must now wait until the next day to hear the conclusion.
We Will Rock You, based on the music of Queen, has an opening scrawl where Brian May was about to be executed, but was allowed to play one last solo first. Two days later, they executed him.
A Pirates of the Caribbean game has Jack Sparrow's allies betray him the second the tutorial level is beaten. The majority of the game is his story of what really happened, which he's telling the executioners as he is about to be hanged. (It is, of course, Blatant Lies.)
Later on, Jigsaw finds out (via Melody and Binary) that because she's already on the reality show, she's too high profile for them to let her die (since either her death will arouse suspicion, or won't be able to be covered up).
In the Tom And Jerry version of The Nutcracker Suite, the Sugar Plum Fairy gets locked in a cage and manages to steal the keys. The head cat catches her with them, but he thinks she wants to play with him, so she goes along with this misunderstanding; this leads to her being in possession of the right key later.
Done in one Family Guy episode where Stewie was the king of England, and his entertainers simulated television. When you get canceled, you get canceled.
The American Dad multi-parter "Stan of Arabia" sees Roger get bought as a bride for an oil baron. In order to get out of "the Beast with Two Backs", he tells the man the plots of Beverly Hills 90210 and Melrose Place. Subverted in Roger runs out of episodes, but when he learns that the man wants sex, he's okay with it.
In an episode of The Beatles ("The Word"), The Beatles accidentally see a sheik's harem unveiled and get sentenced to death. They delay their execution by playing a song, obviously.
Happens in one of The Simpsons Halloween specials. The three wicked witches go to the Expy Flanders' house intending to eat their children. The mother convinces the witches they'd rather have some gingerbread children and bakes them some. The witches enjoy this so much they get the idea of going to other families and threatening to eat their children in exchange for more treats. And this is apparently how Trick-or-Treating came about.
Older Than Feudalism: Caractacus was a British Celtic chieftain, who led an uprising against the Romans. He was defeated and captured, and Romans had that habit of making triumphant entries, of which decapitation of defeated and captured enemy leader was a major part. Caractacus persuaded the emperor that leaving him alive would be a better paragon of his magnificence than killing him. He lived wealthily ever after in Rome.
The Jewish rebel Josephus pulled more or less the same stunt as Caractacus during the Jewish Revolt of 66-70 CE, convincing the Roman commander Vespasian that he (Josephus) was a prophet, and predicting that Vespasian could become Emperor. Sure enough, 69 CE was the "Year of the Four Emperors," and come the end of the year, who was in charge? Why, Vespasian, of course. Josephus received Roman citizenship and Imperial patronage, got himself a state pension, and spent the rest of his life in Rome writing books. He ended up being one of the more important historians of the Jews, providing valuable information about Judea and Judaism in the first century which, for those of you living under a rock, is when the Jews were evicted from their traditional homeland and when a certain Yeshua ben Yosef got himself nailed to a stick for some things he said...
French artist Marie Tussaud was arrested and sentenced to death during the French Revolution, but was eventually released and employed to make wax death masks for famous guillotine victims. After the revolution, she set up a wax museum in London. This museum (called "Madame Tussauds") is still a major tourist attraction in London, displaying wax sculptures of modern and historical figures alike. It has branches in several major cities around the world.