Never Tell Me the Odds

"C-3PO: Sir, the possibility of successfully navigating an asteroid field is approximately three thousand, seven hundred twenty to one. Han Solo: Never tell me the odds!"

- Star Wars Episode V: The Empire Strikes Back

A character is told by the Smart Guy that If His Calculations Are Correct then it's a Million-to-One Chance of them succeeding and/or surviving. Naturally, the Determinator presses on anyway. Naturally, he succeeds, proving statistical analysis to be useless.

And yes, no matter what, the moment ridiculous odds are mentioned, the probability of failure approaches zero (mostly due to the Million-to-One Chance). Bonus points if the odds given are absolute (as in 0% either or 100%), seeing as this is never correct.

The Other Wiki calls this "neglect of probability". Contrast I Like Those Odds, which have a similarly Badass sentiment.

Anime and Manga

 * Neon Genesis Evangelion: Misato ignores Ritsuko's estimations of the probability of success catching the tenth angel being 0.0000001% (one in a billion). Once you know more about the EVA-01, the odds may have been way higher in the first place...
 * GaoGaiGar does this several times. "With courage, 1% becomes 100%!"
 * Also happens enough times in Tengen Toppa Gurren Lagann, to the point of lampshading it once it goes to its logical extreme: a zero percent chance. As  states: "This operation had an almost zero percent chance of succeeding, but it seems that theoretical calculations are pointless with you."
 * In strict fairness,  probably wasn't taking into account that.
 * It doesn't matter though, like Simon said, its as good as 100%. Statistics only apply to other, less awesome people.
 * Inverted in Eyeshield 21, where not only does everyone want to know the odds, at one point Hiruma reminds the team that 99% chance of winning is still 1% chance of losing.
 * Although Hiruma will take the chance of winning if it is anything more than 0% (and he rarely says the odds are 0%)
 * Inverted in an episode of Dai-Guard: the Humongous Mecha's primary weapon is damaged. When it goes back into combat with a backup, one pilot asks their chances of winning. The response: "You'll fight much better if you don't know."
 * Averted in Kaiji, which is about gambling - the path to success is to find a strategy or cheat that leaves as little as possible to chance. In the first season finale,.
 * Code Geass' penultimate episode has a countermeasure for the FLEIJA superweapon; however, in order to work properly the user needs to input critical information 19 seconds before the explosion, and activated, the window of opportunity is only four-hundredths of a second.
 * Also in Code Geass in episode 2 Cecile says to Suzaku that "It's possible, but the chances are close to zero." It isn't directly stated, but she probably refers to Lancelot activation.
 * Dr. Ichigaki in Yu Yu Hakusho
 * In the first arc of Slayers Lina expresses a logical explanation for this trope: If you dwell on the fact that you only have a Million-to-One Chance, you'll go in expecting to fail, which guarantees that you will.

Films
"Tony: Take me to maximum altitude. JARVIS: With only 15% power, the odds of reaching that altitude are-- Tony: I know the math! Do it!"
 * The Empire Strikes Back is the trope namer here, although it happens elsewhere in the Star Wars works.
 * Interestingly enough, the exact quote suggests a very high probability of success. 3720 chances to succeed versus one chance to fail... Oh, right.
 * The Expanded Universe also defines this as a universal Corellian trait. Any Corellian character will most likely not care about the odds of success, or having been informed will take the odds as a challenge to be beaten.
 * Another bit of EU fluff has Leia finding out exactly why he doesn't want people to tell him the odds. He has no idea what they mean.
 * Iron Man features this exchange between Tony and his onboard AI during the final fight:

"Spooner: That girl was somebody's baby. 11% was more than enough. A human being would've known that."
 * In The Return Of The King, when Aragorn suggests that Gondor march against Mordor as a diversion, Gimli comments, "Certainty of death, small chance of success... What are we waiting for?"
 * The Expository Theme Tune of The Guns of Navarone mentions the incredible odds twice.
 * I, Robot has the premise of Will Smith as a robot-hating cop, due to a traffic accident in which a robot chose to save him instead of a small girl, simply because his chances of survival were better. In a flashback, Smith's character can be seen begging the NS-4 to save the girl instead of him.

"Orious: Numbers alone do not win a battle. Peter: No ... but I bet they help."
 * Before the Battle of Beruna in The Lion, The Witch and the Wardrobe, a Narnian soldier informs Peter and his centaur general Orious that the enemy has greater numbers.

"Spock: Jim... the statistical likelihood that our plan will succeed is less than 4.3%. Kirk: It'll work. Spock: In the event that I do not return, please tell Lieutenant Uhura... Kirk: Spock. It'll work."
 * This exchange between Spock and Kirk in Star Trek:


 * In Apollo 13 When President Nixon starts asking for odds on the astronauts' safe return, Gene Kranz simply says, "We're not losing those men!" Inverted, in that he already knows the odds, but refuses to give them out.

Literature

 * In the Discworld book Guards Guards, the characters note that saying "It's a million to one chance but it just might work" practically guarantees success.
 * Needless to say, this leads to the comic relief team engaging in a painstaking process of rebalancing their odds of success to be EXACTLY one in a million. By the time they're done, the archer who's supposed to hit the dragon's weak point as it flies overhead has been handicapped to truly amazing levels..
 * He seems to only miss because they were aiming for the Dragon's Jewels, of which it had none.
 * Rather, he was aiming for the Vulnerable Spot, which all dragons (in some traditions) have, but missed because he got the balance of probability slightly off.
 * But then the dragon counter-attacks, knocking them off the roof, and their chances of hitting something soft on the fall were exactly a million to one chance...
 * In fact, it's a universal law in the Discworld that million-to-one chances crop up nine times out of ten.
 * That's because Discworld runs on the Theory of Narrative Causality, therefore million-to-one chances always succeed. The problem is to get them to be that difficult.
 * In Equal Rites Esk tries a feat of magic which, if she'd actually studied magic, she'd know is impossible. As she hasn't and doesn't, she succeeds.
 * Star Wars again: Rogue Squadron (mostly in the X-Wing novels, but also everywhere else) succeeds in so many "impossible" and "one-in-a-million" missions that their unofficial motto is, "Impossible is our stock in trade". Given that they were founded by the only two X-Wing pilots to survive the first Death Star...
 * In fact, disdain for the odds practically becomes Corellia's hat: Han Solo, Wedge Antilles, and Corran Horn all explain their Never Tell Me the Odds styles with "I'm Corellian." Though Wedge, at least, does look at the odds and try to compensate for them, and Corran is annoyed that Han's managed to reinforce that hat to the point where Corellians are commonly seen as reckless gamblers.
 * The Hitchhiker's Guide to the Galaxy parodies this with the Heart of Gold that's essentially powered by extremely slim odds of something happening.
 * In Towers of Midnight Birgette tells Mat that the odds of getting back from the Tower of Ghenji are one in a thousand. Mat responds by taking out ten coins and predicting that when he throws them every single one will land heads up (1/1024 chance if you were wondering). They do, and Mat remarks that "for me, one in a thousand is good odds." Being ta'veren means that when Mat is around one in a thousand actually IS good odds.
 * The Phantom Tollbooth:
 * Literal variant: In Tunnel In The Sky by Robert Heinlein, two students discuss whether to drop a survival course before their practical wilderness exam. One (who drops it) asks if the other has seen the casualty statistics on last year's class, and the other (who takes the exam and prevails) replies that he doesn't want to see them.

Live-Action TV
"Kirk: I take it the odds are against us and the situation is grim. Picard: You could say that. Kirk: You know, if Spock were here, he'd say that I was an irrational, illogical human being by taking on a mission like that. Sounds like fun!"
 * In Star Trek: The Original Series, Spock mentions the odds of the crew's success being very low. Naturally, Kirk presses on anyway.
 * Averted in "Errand of Mercy". Spock calculates very poor odds of attacking the Klingon headquarters. They attack anyway, and fail and are surrounded—though they do make it as far as the commander's office.
 * Lampshaded in the film Star Trek: Generations

"Inara: Any chance [Jubal Early] might survive? Mal: Air he had left, chance'd be one in about... a very big number."
 * Lampshaded in Star Trek: Voyager, Seven of Nine and Tuvok are discussing the captain's latest plan, Tuvok points out it isn't the first time the captain has beaten the odds. To which Seven replies "She does seem to succeed more than random chance would allow. I'll add that to my calculations."
 * Parodied in Firefly:

"Idris: You were thinking you could build a working TARDIS console out of broken remnants of a hundred different models and you don't care that it's impossible. Doctor: It's not impossible as long as we're alive."
 * The finale of Tomica Hero Rescue Force has the team repeatedly told that they only have a 0.1% chance of defeating the Big Bad. This just prompts Hikaru to claim that with the power of their "Rescue Souls", they'll make it one thousand percent.
 * Inverted in Doctor Who with "The Doctor Dances", where Captain Jack actually asks for his odds of survival (and then, of course, defies them anyway).
 * Notably, he doesn't try to fight them. Having been told he is dead, he has a drink and then gets rescued.
 * From The Doctor's Wife

Video Games
"Rochelle: Nick, what do you think the odds are that the swamp people are still alive? Nick: You mean, alive Infected, or alive and not zombies? Rochelle: Not zombies. Nick: 100 to 1. Rochelle: Sounds about right."
 * Inverted in Left 4 Dead 2:

"Roger: Why only 97.2 percent? Manuel: I judged 97.2 to sound more hip to our audience than would 100. You would have to mention it. Roger: Sorry. Manuel: Don't apologize to me. It's the players you ruined it for."
 * In Space Quest VI, the shuttle's automatic co-pilot, Manuel Override, tells Roger he's "97.2 percent certain" he can get the shuttle to Delta Burksulon V after damage caused by a Negative Space Wedgie is repaired. Roger questions the odds:

"Big Al: I estimate our odds at approximately 1 in 63 Million..give or take. Ratchet: Hey, that's uhh..well you know, not so bad."
 * Actually, the name is Auxverride, but it's pronounced the same.
 * In Derelict, during the mission Hail Mary, Lieutenant Mackie dismisses the odds and tells everyone to just get the job done. Considering the consequence for not getting the job done is, this is a rather sensible reaction.
 * In Ratchet & Clank: Up Your Arsenal:

Web Comics
"Minionbot: Why do you not simply ask either Carl or I to calculate those values? Vexxarr: Because my time is valuable and I can allocate only so many hours in a day to screaming in abject terror?"
 * Lampshaded in this Schlock Mercenary strip. True enough, they escape afterward, but they find an alternate—and more statistically sound—method to do so.
 * Both Elan and Vaarsuvius Lampshade this trope in Order of the Stick when a tiny demon succeeds in summoning a hugely powerful ally against all probability.
 * Parodied in Starslip Crisis here.
 * The classic Star Wars example is mocked and inverted in this Irregular Webcomic strip.
 * This page of Spacetrawler.
 * El Goonish Shive references the Star Wars example here.
 * Inverted in the author's notes of this Leftover Soup comic.
 * Vexxarr explains why:

Western Animation
"C-3PO/Quagmire: Sir, the odds of successfully navigating an asteroid field are 2-1! Han/Peter: Never tell me the o... well that's not bad."
 * In Transformers Animated, Sentinel Prime orders Jazz to bring the ship to full power and take the route through an ion storm, as it is the quickest way back to Cybertron. Jazz states why both reasons are a bad idea. His response: He pulls rank on him and threatens to throw him into the brig with the Decepticons imprisoned on the ship.
 * In Family Guy's The Empire Strikes Back parody "Something, Something, Something Dark Side":

"Palmer:"Willie! What are the odds [Titan] Maximum could make it through that beam without all our genitals fusing into glass?" Willie:"Um... zero percent." Palmer:"Zero zero? Or 'I'm a wah wah sissy baby and I want my blankie and my baa-baa' zero? Which one, I'm just curious." [...] Willie:"Point zero zero three percent." Palmer:"Sweet!""
 * One smart astronaut in the Samurai Jack episode "Jack in Space" kept giving impossibly high odds throughout the entire episode. Jack beat his odds every time.
 * This exchange from Titan Maximum:

Real Life

 * During the 1950s Korean war, General MacArthur gave his plan of landing 70,000 US troops far behind the North Korean lines a chance of 5000 to 1 of succeeding. It proved to be a dramatic turning point in a previously losing war.
 * Admiral John Jervis at the Battle of Cape St Vincent came up with a fairly good version of this. As his captain called out the number of enemy ships and reached 27 to Jervis's 15 he responded "Enough, sir, no more of that; the die is cast, and if there are fifty sail I will go through them". There were 28 ships in all, he did go through them and he did win.
 * Sun Tzu said the strength of an army is not measured in its numbers but in its unity. This has been borne out time and time again in history.