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A character is told by the Smart Guy or Straw Vulcan that If His Calculations Are Correct then it's a MilliontoOne 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 MilliontoOne Chance).
The Other Wiki calls this " neglect of probability". Contrast I Like Those Odds, which have a similarly Badass sentiment.
Examples:
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Anime & Manga
 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 fourhundredths of a second. Lelouch and Suzaku, working together, manage to pull it off.
 Also in Code Geass in episode 2 Cecile says to Suzaku that "It's possible, but the chances are close to zero." In one of the previous scenes he asked Cecile if his friend Lelouch can be alive. Unsurprisingly it turns out that he is alive and leads terrorist force against Britanian army.
 Inverted in an episode of DaiGuard: 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."
 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%)
 GaoGaiGar does this several times. "With courage, 1% becomes 100%!"
 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, Kaiji's rigged lottery fails and he panics, taking a blind chance for the first time and missing an opening purposefully left him by the Big Bad. He suffers a humiliating defeat.
 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 EVA01, the odds may have been way higher in the first place...
 The operations against Ramiel and Sahaquiel have a higher probability of success (still only a small fraction of a percent), which makes you wonder whether Ritsuko and the Magi supercomputers are cooking up numbers out of thin air.
 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 MilliontoOne Chance, you'll go in expecting to fail, which guarantees that you will.
 Also happens enough times in Tengen Toppa Gurren Lagann. When antispiral Nia tells Simon that the probability of success is less than one percent, Simon says that as long as it is not zero, it's as good as 100%. Lampshaded and taken Beyond the Impossible when the DaiGurren Dan is faced with an actual zero percent chance. As Lordgenome's head states: "This operation had a zero percent chance of succeeding, but it seems that theoretical calculations are pointless with you." Sheer awesomeness and Rule of Cool beat even impossible odds!
 In strict fairness, Lordgenome probably wasn't taking into account that King Kittan was carrying a used Giga Drill inside the Space King Kittan frame.
 Plus, in probability while an impossible event has a probability of zero, an event can have a probability of zero and not actually be impossible  it would simply have to be the one event out of an infinite number of possible outcomes, like picking out the exact number of a point randomly chosen between, say, zero and one.
 Dr. Ichigaki in YuYu Hakusho
 In the twopart episode of Yu Gi Oh Zexal where Yuma duels Charlie McCoy, Charlie's Number gives him unearthly luck, enabling him to roll a six on his gamblecards every time. Astral  who seems to have incredible skills with mathematics  keeps calculating how unlikely the odds of are of so many lucky rolls, and it gets annoying until it reaches the Stop Helping Me! level.
Films
 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:
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!
 In The Lord of the Rings: 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?"
 On the other hand, Gimli is almost definitely wellaware of their history of not only surviving such odds, but winning outright, so he may just be working off a different set of statistics.
 The Expository Theme Tune of The Guns of Navarone mentions the incredible odds twice.
 I Robot has the premise of Will Smith as a robothating 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.^{note }The robot was forced to do so based on The First Law of Robotics ("A robot may not injure a human being or, through inaction, allow a human being to come to harm") — Will Smith's character had the highest probability of survival, and logically the better choice to save first. In a flashback, Smith's character can be seen begging the NS4 to save the girl instead of him.
Spooner: That girl was somebody's baby. 11% was more than enough. A human being would've known that.
 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.
Orious: Numbers alone do not win a battle.
Peter: No ... but I bet they help.
 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 then misses, naturally.
 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 counterattacks, 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 milliontoone chances crop up nine times out of ten.
 That's because Discworld runs on the Theory of Narrative Causality, therefore milliontoone 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. (It does have consequences later, though.)
 Star Wars again: Rogue Squadron (mostly in the XWing novels, but also everywhere else) succeeds in so many "impossible" and "oneinamillion" missions that their unofficial motto is, "Impossible is our stock in trade". Given that they were founded by the only two XWing 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 Hitchhikers 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: Milo's quest was impossible, but he did it anyway, because nobody told him it was impossible until after he was done.
 Literal variant: In Robert A. Heinlein's Tunnel in the Sky, 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.
LiveAction TV
Videogames
 Inverted in Left 4 Dead 2
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.
 In Space Quest VI, the shuttle's automatic copilot, 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:
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 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 The End of the World as We Know It, this is a rather sensible reaction.
 In Ratchet & Clank: Up Your Arsenal:
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.
Webcomics
Western Animation
 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. It doesn't end well. But for different reasons...
 In Family Guy's The Empire Strikes Back parody "Something, Something, Something Dark Side":
C3PO/Quagmire: Sir, the odds of successfully navigating an asteroid field are 21!
Han/Peter: Never tell me the o... well that's not bad.
 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:
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 baabaa' zero? Which one, I'm just curious."
[...]
Willie:"Point zero zero three percent."
Palmer:"Sweet!"
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.

