History Main / MillionToOneChance

In layman's terms: ''if there's a million to one chance against something of vital importance happening, then it's that one time rather than the other nine-hundred-and-ninety-nine-thousand-nine-hundred-and-ninety-nine times''. This is TruthInTelevision in a sense, that if an extremely improbable event occurs to someone, chances are that it's [[AnthropicPrinciple his story that's told]]. What the trope hinges on is the reality that each audience member is an individual, and, thus, their own "number one": undeniably, each audience member is one in an increasing number from six billion, so, that single chance offers each of them the avenue to imbue it with themselves --- "you are the single chance"; if the chance is missed, it can break catharsis for the viewer, as they may feel, in a sense, that they are being left behind.

** In the very next book ''Literature/{{Eric}}'', 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.
*** Mentioning the odds here is more meant to refresh and emphasize Rincewind's ActionSurvivor nature rather than allude to the fact he's due to return.

* In ''Anime/TengenToppaGurrenLagann'', the odds of success were calculated to be 0%. Not 0% as in "so close to zero it might as well be zero", but ''flat-out impossible''. [[BeyondTheImpossible Naturally, the heroes succeed anyway]]. The main character also declares that if the odds of success are "nearly 0%", they might as well be 100%.

--->'''Rich Little:''' The Vegas odds tonight stand at an unprecedented 1000:0. A bet of zero dollars on Bender pays $1000 if he wins. Still, very few takers.\\

[[folder:Real Life]]
* [[http://www.ksl.com/index.php?nid=148&sid=11943102 This man]]--it's a "45 billion to one chance", rather!
* A literal million-to-one roll happens [[http://unicornjelly.com/urulesmystories.html#mil here]].
* 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.
* The managers of the hedge fund, Long Term Capital Management, said that there was only a one in a billion chance that their investment strategy would falter. Four years after it was founded, it collapsed, nearly taking the world economy with it.[[note]]One major reason for the collapse was that LTCM was no longer following that strategy, but rather a variant of it. Another reason is that they gamed their strategies using computer models, forgetting that actual investing is done by human beings, who do not always act with complete rationality.[[/note]]
* An exception to the rule is perhaps worth mention here. [[http://www.boingboing.net/2008/09/04/lhc-will-not-destroy.html One scientist]] has said that the Large Hadron Collider has less than a one in 10^billion*billion chance of destroying the world. Far more energetic events (meteoric impacts, volcanic eruptions, earthquakes, etc.) take place on Earth on a regular basis. Yet the [[GenreSavvy invocation of this]] [[WrongGenreSavvy trope to real life]] makes that chance seem far scarier than it should. (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.)
** 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.
* UsefulNotes/RichardDawkins 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, using one of the lower estimates of a billion billion planets in the universe (the actual figure is probably much higher). This astonishing figure relies on the fact that while a one in a billion chance is much too small for humans to comprehend comfortably, with a large enough sample a billion to one becomes a certainty. And the existence of life on this planet is an example of this certainty.
** The chances of life arising (and forming a technological civilization) are collected in the [[http://en.wikipedia.org/wiki/Drake_equation Drake Equation]], which predicts how many technologically advanced civilizations should be in existence. The problem is that the vast majority of terms in the equation are probabilities which require broad speculation. As we learn more about the nature of the universe, the ''uncertainty'' of terms in the equation goes down, which is not the same thing as the ''probability'' of other sapient, technologically advanced life existing.
*** There's also a discussion on the definition of probability here, where frequentists will claim the true probability is the same - it's just calculated it incorrectly. Another group disagrees and has a different definition. But that's a separate discussion.
* Rare diseases deserve a mention here. It's true that there are diseases that affect only one in every 10,000 or 100,000 people, but it's also true that ''hundreds'' of these conditions have been identified, and there are almost certainly hundreds more that are as yet unidentified. So don't be shocked if you or someone you know is diagnosed with a rare disease - perhaps ''that'' disease is rare, but rare diseases in total affect a lot of people. Odds are you know or will know someone with one.
** And so, JustForFun/TelevisionIsTryingToKillUs. The real-life lesson taught to all medical providers is summed up as, "When you hear hoofbeats, think horses, not zebras." [[CompletelyMissingThePoint Unless you're in Africa.]] In other words, when a patient comes in with a set of signs and symptoms, start looking for the common sources of those signs and symptoms before you start thinking about weird diseases. From a patient care viewpoint, it makes sense; if someone comes into the ER with low blood sugar and altered mental status, starting immediate treatment for diabetic shock is almost always better than figuring out all the other strange ways the patient might have low blood sugar and AMS. The problem is that thanks to Hollywood and the news, "millions of diabetics averting catastrophe and remaining fairly healthy thanks to managed diet, exercise, insulin," isn't news, but "man dies of rare illness doctors mistook for diabetes," is. The public winds up WrongGenreSavvy, often thinking they have weird diseases rather than simple ones, or else expecting whole battery of tests when the answer is obvious from just a couple of blood tests and a quick examination. [[Series/{{House}} Dr. House]] hasn't helped matters much, and countless medical practitioners subtly curse that show (even if they're some of the biggest fans). So ([[EaglelandOsmosis should you be an American)]], yeah, you will likely know one person in your life with Tay-Sachs, Gauchier's, Huntington's, or something equally rare. [[http://www.cdc.gov/NCHS/data/nvsr/nvsr58/nvsr58_19.pdf Almost everyone]] else you know will die to cardiovascular disease, malignant neoplasms, kidney or mental diseases, liver failure, the flu, and the occasional accident, murder, or suicide.
* This is pretty much how national/international lotteries can be successful. The chances of winning might be one in 75 million, i.e. all but impossible. But with hundreds of millions of entrants, there is in all probability going to be a few winners of the vast jackpot, which sells the dream to the next hundreds of millions of entrants.
* When dealing with continuous random variables (almost anything with an infinite number of possible outcomes), each individual outcome will occur with probability of one over infinity. They're not talking one-in-a-million, but so close to zero-in-a-million it can't be comprehended. However, one outcome ''always'' happens despite technically [[LiteralMinded being impossible]]. Hence the word ''almost''.
** Consider a square with sides one meter long. Now consider the diagonal of that square as a line. The probability of a randomly chosen point within that square - remembering that that square has an infinite number of points within - being within a certain region is P = (area of region) / (area of square). Now, a line has one dimension. Hence, the line has a length, but zero area. Therefore, the P of a randomly chosen point landing on the line segment = 0/1 = 0. Yet it's possible. This is where mathematicians split hairs between [[http://en.wikipedia.org/wiki/Almost_sure ''almost sure'']], happening with P = 1, and ''sure'', happening always, no matter what. As a matter of fact, whatever point does wind up chosen had a P = 0 chance of being chosen, so [[PuffOfLogic it had an assigned probability of 0, for no-way-no-how, but still happened.]]
** Whether the probability of such an event should ''actually'' be considered zero is subject to argument. There are number systems (for example, the hyperreal numbers) which permit "infinitesimal" values. This solves the apparent contradiction because then the probability of the events described above is not zero and it makes sense that they can occur. Such number systems bring in problems of their own, though, and currently suffer from a lack of popularity.
* Fans of TabletopGames are usually woefully unable to appreciate what the odds of something happening actually are. Consider a popular house rule for some games where an attack is rolled on a 20-sided dice. If a twenty is rolled, it is rerolled with a chance for [[CriticalHit massive bonus damage]]. If a second twenty is rolled, the target is dramatically slain. Now, let's say that each character is subjected to only twenty attacks in a game. The odds of any one attack pulls this off is only one in 400, so nothing to worry about, right? Well, over the course of ten gaming sessions, it becomes almost a 40% chance of being killed just by this mechanic. In a six person group, over ten sessions, it's more than 95% probably a player is instantly killed like this. And if you're playing the [[TabletopGame/DungeonsAndDragons granddaddy of TT games]], considering it usually takes at least four-six or so sessions to go up a level...
* Magic tricks abuse this all the time. The reason that a magician's ability to always cut to your card and produce it on command seems surprising is because you don't perceive the trick. Even if you know it's a trick, the visuals help maintain that what you saw happen was what actually happened. Therefore, the odds that the magician can successfully produce your card is apparently one in fifty two. Of course, it's really almost one in one, and if you know the secret to a given trick, it's obvious why.
** Playing with the odds here leads to a fun trick, wherein the target picks a card, and then the "magician" finds all sorts of bizarre ways to ensure that the card cannot be tracked... then draws the top card of the deck. 51 times out of 52, it's a joke trick. The fifty-second, you blow someone's mind. Extra fun to use on magicians who are watching for the sleight, and will never find it.
*** You'll need to know quite a few magicians in order to have a good chance of pulling it off in front of even one. Also, most magicians are wise to such sophistry and if irked can really make the performer look like a fool. Just ask him to repeat it at the next gathering. And the one after that, if necessary. Then show them up with a few actual tricks.
* Affirmed in any case of the [[http://en.wikipedia.org/wiki/Birthday_Paradox Birthday Paradox]], where a group of just 23 people will have a 50% chance of having at least one birthday in common. The reason is because for every additional person added to a group you add a number of comparisons equal to the number of persons already in the group. Birthday Paradoxes often result in [[MindScrew counter-intuitive]] outcomes with UnfortunateImplications. For example a DNA test that can narrow down a match between two random people to a probability of 13 billion to one will on average yield [[http://freakonomics.blogs.nytimes.com/2008/08/19/are-the-fbis-probabilities-about-dna-matches-crazy/ 100 exact matches]] in a sample prison population of just 65,000. Can also be used [[http://en.wikipedia.org/wiki/Birthday_attack to attack]] high strength cryptographic algorithms.
* Steve Whiteley bet £2 on a horse that had lost the last 26 races. It won the race and as the only person who bet on this horse he won a jackpot of £1,445,671.71. [[http://www.racingpost.com/news/horse-racing/lupita-exeter-exeter-tote-small-stakes-racegoer-scoops-1-4m-jackpot/827203/]]
* The odds of a random person being struck by lightning and surviving in any given year are 1:280,000. The odds of three brothers all being struck by lightning and surviving is 1:345,000,000. The odds of three brothers all being struck by lightning ''in the order in which they were born'' and surviving is 1:2,700,000,000. This very thing happened to brothers Jack, Aaron, and Nathan Helms of Apopka, Florida.
** This is related to the rare diseases example above. A probability of 1 in 3 billion sounds very low, but you have to consider what the "positive" outcomes are. What if three cousins were hit in the order on which they were born? Or maybe in alphabetical order? If you count all newsworthy events you can quickly get a very reasonable probability.
* The Helms brothers have ''nothing'' on [[http://en.wikipedia.org/wiki/Roy_Sullivan Roy Sullivan]]. He was struck by lightning and survived on ''seven different occasions'', the odds of which being a whopping 1:10,000,000,000,000,000,000,000,000,000.
** Lightning strikes are not truly random occurrences. Roy Sullivan worked his entire life as a Virginia Park ranger, almost entirely outdoors in mountainous terrain which vastly increased his exposure to lightning storms. Still, seven strikes over his lifetime is incredibly rare, rare enough to make the Guinness Book of World Records.
** [[DeathByIrony And then he shot himself.]]
* NASA's management claimed that the risk of catastrophic malfunction on the shuttle was 1 in 100,000. After the Space Shuttle Challenger disaster, UsefulNotes/RichardFeynman immediately realized that this claim was risible on its face; as he described, this assessment of risk would entail that NASA could expect to launch a shuttle every day for the next 274 years while suffering, on average, only one accident.
* The chances of one meeting a frighteningly similar-looking {{Doppelganger}}, or DistaffCounterpart, to oneself on any given day are quite low but over the course of a lifetime the chances are good that people encounter a few.
* Chances are good that [[NamesTheSame someone out there shares your name]], even if it's a fairly unusual one. Not only might they have the same first name as you, they might even have the same last name! People tend to pick names for their kids that they like and/or find [[MeaningfulName meaningful]], and there's a good chance that what your parents thought was an AwesomeMcCoolName, another parent will too. Every year, there's a list of top-ten trendy baby names. Many parents also name their kids after a family member, a famous person, a saint, deity, or [[Literature/TheBible Biblical]] figure, etc.
* One micromort (the measurement of the probability of death) is equivalent to an activity that has a one-in-a-million chance of a fatal accident occurring.
* When you think about it, your own '''birth''' qualifies as this trope. While a human mother usually only has one egg cell in the fallopian tubes when she's able to get pregnant, a single ejaculation from a man can release anywhere from 40 million to 1.2 billion sperms cells. And ultimately, [[ThereCanOnlyBeOne only one sperm cell will be able to fertilize the egg]] while the others perish. This means that any individual sperm cell's chance of getting to fertilize is almost zero, and yet the fact remains that one sperm cell ''will'' get to fertilize the egg. Not only that, but an estimated ''30-90%'' of fertilized eggs either fail to implant in the uterus, or perish shortly thereafter. (And that's just under ''natural'' conditions.) In short, you simply being born the way you are pretty much fits this trope to a tee.
* Many animals, especially R-strategist ones such as fish, aquatic invertebrates, insects and rodents, tend to [[ExplosiveBreeder produce hundreds of eggs at a time]], the record holder being the Mola Mola, who can produce 300 million eggs in one spawn. The chances of offspring surviving to adulthood is so low that of those eggs, only one or two may make it to breed themselves.
* In January of 2016, off-duty sheriff's deputy Jose Marquez got into a shootout with two robbers in an apartment parking lot in Aurora, Colorado. During the gun battle, one of Marquez's bullets actually went straight down the barrel of a robber's gun. Police described such a shot as "one in a billion."[[http://www.cbsnews.com/news/deputy-fires-one-in-a-billion-shot-suspect-gun-barrel/]]
* Since there's currently 7 billion people in the world, there are roughly 7,000 Million to One chances occurring.
* While not necessarily one-to-a-million (more like one-to-a-thousand), one of the reason why students with nerdy and unusual interests will say that their time in college or university is better than high school is because those people have much more chance meeting people with the same interests as them in college or university than in high school simply because colleges and universities contain more students(50,000 - 100,000 students) than high school (~1,000 students).
* In 1835, Andrew Jackson became the first president to survive an assassination attempt. As he was leaving a funeral, 35-year old Richard Lawrence attempted to shoot him with a pistol, which misfired. The 67-year old Jackson then proceeded to beat Lawrence with his cane, but as Lawrence was being pummeled, he drew a second pistol and again tried to shoot Jackson. Amazingly, this second gun also misfired, and Lawrence was eventually subdued by bystanders. While it was not uncommon for the black powder guns of the early 19th century to misfire, it is astoundingly unlikely for two of them to do so in the same incident. There was nothing mechanically wrong with either pistol. Roughly 100 years later, the Smithsonian museum test fired both of them and they worked on the first try. Scientists estimated the odds of both guns misfiring in the same incident were roughly 1 in 125,000.
* The odds of [[MonkeysOnATypewriter a monkey typing out "Hamlet" on its first try]] is estimated to be 1 in 10^183,800. Taking capitalization, pronunciation, and spacing into account, it's estimated to be 1 in 10^360,783. Possibly the most unlikely thing predicted by man.
* A quite exhaustive list can be found [[https://www.youtube.com/watch?v=RV-WV2g2muE here.]]
[[/folder]]

--->'''Leela:''' This is, by a wide margin, the ''least likely thing that has ever happened!''\\

* While not necessarily one-to-a-million (more like one-to-a-thousand), one of the reason why students with nerdy interests will say that college/university is better than high school is because those nerds have much more chance meeting people with the same intersts as them in college/university than in high school simply because college/university contain more students(avg 50,000 - 100,000) than high school (avg 1,000 students).

* The story of ''Literature/TheHungerGames'' is started with this. Prim is selected to be the female tribute of District 12 over any other older girls who have more tickets submitted, on her first day Reaping, where she doesn't pick Tesserae so she doesn't have to insert additional tickets. There is literally just ''one'' ticket with Prim's name on it in a container full of other names, some duplicates of each other, yet she is selected anyway. Katniss, who herself has 20 tickets by virtue of picking Tesseare for the whole family for five years straight, even lampshades this bitterly after the Reaping: why it has to be Prim?

* The story of ''Literature/TheHungerGames'' is started with this. Prim is selected to be the female tribute of District 12 over any other older tributes who have more tickets submitted, on her first day Reaping, where she doesn't pick Tesserae so she doesn't have to insert additional tickets. There is literally just ''one'' ticket with Prim's name on it in a container full of other names, some duplicates of each other, yet she is selected anyway. Katniss, who herself has 20 tickets by virtue of picking Tesseare for the whole family for five years straight, even lampshades this bitterly after the Reaping: why it has to be Prim?

* In the story of Gideon in the [[Literature/TheBible biblical]] ''Literature/BookOfJudges'', {{God}} instructs Gideon to reduce his army to only 300 men and arm them only with torches and pitchers, just so it would be even more obvious that the battle was won thanks to [[DeusExMachina divine intervention]].

* The story of the ''Literature/TheHungerGames'' is started with this. Prim is selected to be the female tribute of District 12 over any other older tributes who have more tickets submitted, on her first day Reaping, where she doesn't pick Tesserae so she doesn't have to insert additional tickets. There is literally just ''one'' ticket with Prim's name on it in a container full of other names, some duplicates of each other, yet she is selected anyway. Katniss, who herself has 20 tickets by virtue of picking Tesseare for the whole family for five years straight, even lampshades this bitterly after the Reaping: why it has to be Prim?

* The odds of [[MonkeysOnATypewriter monkey typing out "Hamlet" on its first try]] is estimated to be 1 in 10^183,800. Taking capitalization, pronunciation, and spacing into account, it's estimated to be 1 in 10^360,783. Possibly the most unlikely thing predicted by man.

* In a 1963 ''Franchise/{{Peanuts}}'' [[https://vignette.wikia.nocookie.net/peanuts/images/b/b1/19630123.gif/revision/latest?cb=20130923020509 comic strip]], Schroeder says the odds of him marrying Lucy are a googol (10^100). She asks how much that is and the comic '''actually shows one followed by a hundred zeroes'''. It's pretty much a WallOfText.

** Memorably [[InvokedTrope invoked]] in the novel ''Discworld/GuardsGuards''. The men of the City Watch are camped out on a rooftop to try to bring down a dragon by [[AttackItsWeakPoint shooting it in its "voolnerables."]] Problem is, they're all GenreSavvy about it, and after considering the situation - their archer used to win prizes for his marksmanship, he's using his lucky arrow, a dragon's "voolnerables" might be quite big - they think that it might ''not'' be a million-to-one-chance of success, but could be a near-certainty, or some awkward number like 999,943-to-one. So they end up trying to handicap their bowman by blindfolding him, putting soot on his face, and making him stand facing the wrong way on one leg while singing [[BawdySong the Hedgehog Song]], but still end up missing the shot. Then the dragon retaliates by flaming the building they are standing on. Which is a [[StuffBlowingUp distillery]]. Luckily, as the narration points out, the odds of the Watch surviving a jump from the (exploding) roof into a nearby pond ''do'' happen to be exactly a-million-to-one. [[spoiler:Later we learn their odds of hitting the dragon's "voolnerables" were more like zero - it was female.]]
** In the very next book ''Discworld/{{Eric}}'', 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.

** ''Discworld/EqualRites'', 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 [[TheoryOfNarrativeCausality narrativium]]
** Viciously questioned in ''Discworld/TheLastHero'' by Cohen, one of the last surviving barbarian heroes. When he meets the Lady, he tears into her about how many of his fellow heroes died due to taking million-to-one chances that failed them. As he points out, she's the million-to-one chance, and ''also'' all the chances of ''dying''. As such, Cohen has no respect whatsoever for her.

* ''Film/TheLordOfTheRings'': "Certainty of death. Small chance of success. What are we waiting for?"

** "Great shot kid, that was one-in-a-million!"

** A weird, kind of reversed[[note]]not InvertedTrope, however[[/note]] example appears with the "Holdo maneuver" in ''Film/TheLastJedi'' and ''Film/TheRiseOfSkywalker''. In the earlier movie, Vice Admiral Holdo does the maneuver, namely [[spoiler: a devastatingly effective suicide attack against enemy spaceships by jumping with your ship into lightspeed while going right at them.]] It doesn't look remotely chancy, it looks like exactly what should happen if you do that. Only it raises FridgeLogic about why nobody ever does that before or since. This is HandWaved in the latter movie by someone saying that the odds for it succeeding are a million to one.

* ''Film/StarWars'':

** ''Film/TheEmpireStrikesBack'':
*** [=C3P0=] actually does this many times in that movie, sort of a RunningGag. Every time, the heroes seem able to beat the odds he gives them.

*** "Great shot kid, that was one-in-a-million!"

** A weird, kind of reversed[[note]]not InvertedTrope, however[[/note]] example appears with the "Holdo maneuver" in ''Film/TheLastJedi'' and ''Film/TheRiseOfSkywalker''. In the earlier movie, Vice Admiral Holdo does the maneuver, namely [[spoiler: a devastatingly effective suicide attack against enemy ships by jumping into lightspeed while going right at them.]] It doesn't look remotely chancy, it looks like exactly what should happen if you do that. Only it raises FridgeLogic about why nobody ever does that before or since. This is HandWaved in the latter movie by someone saying that the odds for it succeeding are a million to one.

* ''Film/TheEmpireStrikesBack'':
** [=C3P0=] actually does this many times in that movie, sort of a RunningGag. Every time, the heroes seem able to beat the odds he gives them.

** "Great shot kid, that was one-in-a-million!"