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"Million-to-one chances crop up nine times out of ten."
If X is an event and Pr(X) is the event's Real Life probability, then the event's Hollywood probability is HPr(X) = 1 - Pr(X).
In layman's terms: if there's a million to one chance of something of vital importance happening, then it almost always will.
This comes up most frequently when characters say Never Tell Me The Odds, and occasionally when someone makes a few calculations.
It is still played straight, but it is also widely parodied.
A corollary of the Theory Of Narrative Causality.
Examples:
Literature
- Memorably invoked in the Discworld novel Guards, Guards, where the Watch try to make the odds exactly a million to one by use of a blindfold, rope and so on — but end up with one to ninehundredninetyninethousendninehundredninetynine to one chance, which isn't improbable enough. Though minutes later they survive an explosion because, the narrative hints, their chances of surviving it were exactly a million to one.
- Later on, they succeed in another million to one goal (well technically their pet swamp dragon does). And apparently, the reason they failed in shooting the big dragon with an arrow is they were aiming for "the voonerables", and the dragon was female.
- On the other hand, the reason the book gave was that chance has 999,999 casting votes. Plus Rule Of Drama demanded it.
- [[Introbulus This Troper]] always read that part as there being a "Million to One Chance" actually meaning "very likely in the literal sense".
- In the very next book, Death informs the mages that Rincewind has exactly one chance in a million of returning from the Dungeon Dimensions. At this stage, the book doesn't even bother to remind the reader of the rule.
- Equal Rites, the third book in the series, is the first one to state that "one-in-a-million chances crop up nine times out of ten", because of narrativium
- Also appears in the first Discworld game; Rincewind has to collect a number of Plot Tokens (tattoo, sword that goes *ting*, secret identity, camouflage...), but not before determining, with the aid of Nobby, which ones would land his chance of success at exactly a million to one.
- In The Hitchhiker's Guide to the Galaxy (book, radio show, tv show, movie, etc.), the spaceship "Heart of Gold" has an Infinite Improbability Drive which causes Million To One Chance events to occur all the time.
- Not just Million to One, infinity to one, hence the name of the drive. Million To One Chance events are generated by much simpler (finite) improbability generators, and it is by using one of these that the Infinite Improbability Drive is brought into existence (since such a device is a "virtual impossibility").
- Ciaphas Cain, HERO OF THE IMPERIUM! consciously exploits this. He usually justifies doing so in the narrative by saying that a Million To One Chance is better than no chance at all in those situations, which is what he would have if he didn't take the risk.
- Subverted viciously in the Doctor Who Expanded Universe novel The Book of the War, where the Remote, a race whose hat is being a living receiver for mass media, have been primed for battle by being exposed to endless transmissions glorifying battle in an effort to make them spontaneous and unpredictable. What the architects of this plan didn't realize was that the transmissions were so formulaic and full of cliches that it had the exact opposite effect. As a consequence, the Remote's first assault had the entire army take the Million to One Shot against the Evil Tower Of Ominousness.... and get mowed down by sniper fire. Also an interesting case of Death By Genre Savviness.
- From Bridge of Birds:
The gods will be forbidden to help you, and none but a mortal can restore you to heaven, and at a conservative estimate the odds against somebody pulling off a trick like that are one in ten thousand billion trillion.
- Of course, it happens by the end of the book.
- In Jacqueline Carey's Kushiels Legacy books, heroine Phèdre nó Delaunay is very frequently told (or admits herself) that her plans are madness and suicide. Yet, with the exception of a few Xanatos Sucker moments, they always work.
- Played straight as an arrow in "Day of the Ants". The one ant that was carrying a message from the humans trapped under the colony in the mad scientist's lair finds its way to the protagonist, who happens to be the cousin of one of the trapped human. The friend who was with her lampshades this by saying that even if it's a one to a million possibility, there's still one chance of it happening.
Western Animation
- Exception: Hey Arnold!, "Save The Tree": Arnold throws a mug at the lever of a bulldozer that's approaching the tree he's in in order to stop it. It's a long shot in more ways than one... and it misses completely. This could be considered an example of an Unspoken Plan Guarantee, since Arnold announces that he's aiming for the lever.
- In Titan AE, the main character space-floats around a docking bay, when his friend warns him against the chance of an actual docking ship. He responds with, "Oh, please, the chances of a ship docking here are a thousand to one." He then turns around and utters the line, "...and that would be the one."
Anime and Manga
- In Neon Genesis Evangelion, Dr. Akagi and her subordinates were fond of proclaiming that the chances of something necessary/spectacular would happen were zero point a-long-long-string-of-zeroes one percent; naturally, these things always happened. Though in fairness, they usually happened due to considerations not taken into account in the calculations.
- Played straight in Mermaid Saga. However, in this case, the million to one chance of mermaid's flesh granting immortality probably is really a million to one. Over the last eight hundred years, only four appear to have gained complete and uninhibited immortality.
- Gao Gai Gar actually lampshaded it with its famous catchphrase: "With courage, 1% becomes 100%!".
- Taken to the logical extreme in Tengen Toppa Gurren Lagann, where the odds of success were calculated to be 0%. Naturally, the heroes succeed anyway (see page quote). The main character also declares that if the odds of success are "nearly 0%", they might as well be 100%.
- TTGL may warrant its own subtrope of this; the Million to Zero Chance.
- A smattering of All There In The Manual makes this happen in Death Note: Tsugumi Ohba claims that any time L throws out a percentage chance of Light being Kira (normally 4 to 10 percent), it's really over 90%.
- Then again L may just be lying. Even in his private thoughts, he may just be calculating the number he'll tell Light instead of actually estimating anything.
- The entire premise of Detective Conan lies in the Million To One Chance that a poisonous pill would shrink him into a 6-year-old body instead of killing him. It was also pretty lucky that the creator of the drug was the other person to shrink, so that she could help him.
- It's not that unlikely; they explained that when testing it on mice, one mouse shrunk too.
- Exploited in every episode of Yu-Gi-Oh!, and all animes based on card games, for that matter: The Magic Poker Equation is in effect.
- Of course Yugi's superpowered side actually has an excuse for this. And any time a "Shadow Game" is in effect, there's also an excuse. But when neither explanation applies, it's something to do with the "heart of the cards", which didn't exist in the original.
- Also happens near the end of Code Geass. For Lelouch and Suzaku to break through the shield of and thus board the Damocles, they have to fly through the opening in the shield made to fire F.L.E.I.J.A.s. In order to do that, they essentially have to disarm a fired F.L.E.I.J.A. using Nina's F.L.E.I.J.A. Eliminator, but that requires real-time environment conditions to be input by Lelouch for 19 seconds before detonation and the Eliminator has to hit within .04 seconds of detonation. Odds of success: outrageously low, but the definition of this trope can tell you what happened...
- This is just Lelouch in action. On the other hand, in the first season, the chances of him geassing Euphemia li Britannia really were outrageously low. Rule of Drama demanded it though.
- At the end of Rocket Girls, the main characters, falling from 3000 km above the Earth, are expected to disintegrate and burn during reentry. However, they figure they can skip over the top of the atmosphere to shed the excess momentum that threatens them, but that doesn't work when Akane faints from the G-forces; since she can't provide the timing for rocket burns they need, Yukari has to fire and time the burns by instinct. The result is this charred body of the Mangosteen's pod... but somehow their Plot Armor held up and they survived.
Film
- In the first Ghostbusters movie, our heroes manage to stop Gozer by crossing the streams of their proton packs. Egon had earlier warned his comrades against "Crossing The Streams" on pain of being vaporized, but here states that there's "a slim chance" they'll survive. Since they're the heroes, they do.
- Played totally and completely straight in Baby Mama, where Tina Fey's chances of conceiving are a million to one. At first you think it's a subversion, as she goes out and gets a surrogate etc, but by the end of the movie, guess who's pregnant.
- Subverted in Dumb and Dumber. When the woman Lloyd is in love with tells him their chances of getting together are one in a million, his response is "So you're telling me there's a chance? YES!" Later he's outraged to find she's married: "What was all that one in a million talk?"
- "Never tell me the odds!"
- "Great shot kid, that was one-in-a-million!"
- Played straight by Chicken Run in the spirit of Screw Destiny. Being told that the chickens ever escaping Tweedy's Farm is a million to one chance, Ginger retorts "Then there's still a chance."
- "Certainty of death. Small chance of success. What are we waiting for?"
- In Run Lola Run, Lola wins back-to-back spins at roulette on the number 20. Not exactly one in a million, but one in 1,369 — A 0.073% chance of happening.
- Run Lola Run is an interesting case. Because we see multiple outcomes of the same situation, they probably all happened. The other possibilities are just not shown.
Live Action TV
Music
- Jeff Wayne's War of the Worlds adaptation: "The chances of anything coming from Mars are a million to one, he said. The chances of anything coming from Mars are a million to one... but still, they come." If not a trope namer, then surely a trope named-after.
Video Games
- In the original Half-Life, Gordon is cheerfully reminded by his fellow scientists that Explosive Overclocking of their Applied Phlebotinum is perfectly okay, because a "resonance cascade scenario is extremely unlikely". They also assure you that "nothing will go wrong"...
- Kyosuke Nanbu from Super Robot Wars loves this trope. After all, his Catch Phrase is "I don't mind betting on the tough odds!"
- Played with in Penny Arcade: OTRSPOD Episode 1, where the chance of a summon working is stated as 1 in millions (if not billions), but it's really more like 1 in 4.
- The final battle of Star Fox Assault has the final boss mention a zero chance of victory for the protagonists. It is entirely possible to win the battle; however, the announcement of the zero chance is in fact an attempted Mind Screw by the Big Bad.
Web Comics
- Subverted and lampshaded in Order Of The Stick #454
 , when Haley relies on her Genre Savviness a bit too much.
Durkon: Lass, it were an awful difficult shot.
Haley: Exactly! It was totally dramatic! How did I miss?
- Spoofed and lampshaded again in #584. Being even more Genre Savvy than the rest of the group (Durkon's response to the above is "I think maybe ye been spendin' too much time wit Elan"), Elan realizes that a 10% chance of an imp summoning a demonic ally isn't anything to worry about, but a million-to-one chance of the imp summoning a monster that could actually kill them is a sure thing. This results in one of the page quotes.
Real Life
- By assuming independence and selectively considering events anything can be considered a million-to-one shot. Rolling a six on a dice may be a one-in-six shot, but what about rolling a six on a Tuesday in a bar in Washington DC while wearing a blue shirt and jeans? That's got to be at least a million-to-one shot.
- A literal million-to-one roll happens here.
- The universe being as it is.
- It turns out, quite a lot of things in real life exhibit this trope. Many events that are assumed to have their chances controlled by the normal bell curve distribution, have actually been found to obey Mandelbrot's (yes, he of the pretty fractal patterns) fat-tailed distribution. Which means that improbable events actually happen more often than statisticians expect.
- A probable exception to the rule is perhaps worth mention here. A scientist has said that the Large Hadron Collider has less than a one in a billion * billion chance of destroying the world. Given the uncertainty of all human knowledge, it's probably considerably more than that, though perhaps even less than one in a million. This hasn't prevented the formation of a large set of luddites, paranoids, and conspiracy theorists from forecasting the imminent end of the world. The invocation of this trope (to real life) possibly forms a significant part in their justification of their fears. (The same scientist said, likely tongue-in-cheek, that one has a one in a hundred billion chance of spontaneously evaporating while shaving. It's probably less than that.)
- Incidentally, it's far more likely that a random radiation storm from a nearby supernova will wipe out all life on Earth without warning, than it is for the LHC to do anything to hinder human life. And at least in theory it is possible for matter to evaporate randomly as well — just incredibly unlikely.
- Not to mention, the Russian mathematicians Irina Aref'eva and Igor Volovich did the numbers and it turns out its rather more likely that someone in the future will lock onto one of the incidental wormholes the LHC's collisions might make for passing moments, and use them as a 'year zero' for a future time machine to come visit us.
- Richard Dawkins mentions in The God Delusion that if the chances of life arising on any given planet was one in a billion, then life would still have arisen on a billion planets in the universe. This is using a conservative estimate of a billion billion planets in the universe (the actual figure is probably much higher).
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