MilliontoOne Chance
"A 10% chance is pretty unlikely, but everyone knows that a oneinamillion chance is a sure thing!" —Elan, The Order of the Stick

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 999,999 times. This is Truth in Television to a certain degree that it becomes likely that an extremely improbable event will occur to someone, and it's his story that's told.
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.
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 zeropoint(eleventy zillion zeroes)one percent; naturally, these things always happened. Though in fairness, they usually happened due to considerations not taken into account in the calculations.
 According to Ritsuko, the likelihood of anything actually succeeding at NERV is often so ridiculously low that they came up with a system to make counting the zeroes easier. The MAGI are certainly a pessimistic bunch of supercomputers.
 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.
 GaoGaiGar 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%. Not 0% as in "so close to zero it might as well be zero", but flatout impossible. 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 None 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 6yearold 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 YuGiOh!!, and all animes based on card games, for that matter: The Magic Poker Equation is in effect.
 Higurashi no Naku Koro ni has its entire premise based around this. It's about Rika living through every possible world in a Groundhog Day Loop, to try to find the one world where she doesn't get horribly killed.
 Actually a recurring theme in the When They Cry verse. In Umineko no Naku Koro ni, Kinzo relies on a huge gamble involving the epitaph to give Yasu the headship and get them to for give him as evidenced by the quote on top of the chapel: "You will only be blessed at a probability of a quadrillion to one. In the same EP, Bernkastel tells Lion and Will that the chances of Lion existing in a fragment is about 1 out of 2, 578, 917. And later on, cruelly reveals that in all those fragments, Beatrice/Lion suffers the same deadend fate. Not that it stopped either Will or Lion.
 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 realtime 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 was probably not used to show how miraculous the move was, but to show how skilled Lelouch was and how disciplined Suzaku was. The MilliontoOne Chance bit probably failed to calculate that Suzaku would magically know the exact moment to throw the eliminator thanks to the Geass effect.
 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 Gforces; 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 luck held up and they survived.
 Averted with Kaiji; whenever something extremely unlikely happens, it's always due to cheating of some type. When not Kaiji doing so, he tends to blame himself for not having good enough luck!
 Zigzagged in Akagi by the same author. Sometimes the mahjong version of The Magic Poker Equation is because of characters' luck, other times it's because they cheat.
 Subverted Trope in a chapter of Franken Fran. A Born Lucky serial killer dies to the astronomically high odds of being struck by lightning.
 In Bleach, being born with high enough reiatsu to possess Crazy Awesome powers is rare. Having enough power to become a Shinigami is even more rare. Becoming a seated officer is likewise unlikely. Possessing the power and training to become a Captain is apparently so rare that it only happens once every four generations.
 Subverted in Puella Magi Madoka Magica; Kyubey admits to Kyouko that It's theoretically possible to make witch!Sayaka human again, but extremely unlikely that it would work. Kyouko tries it anyway...and fails, because there's no indication that it is possible either. There's just no evidence that it isn't.
 In One Piece there's a special power called "Haki", one specific type called "Haoshoku Haki"(Color of the Supreme King) is said to be in one person per million, curiously the series have already shown seven.
 Well, if the world in One Piece has the same population count as the real world (or more), then 7 million isn't that much when (especially when compared to 6.5 billion [or more]).
 Considering the Loads and Loads of Characters in One Piece, plus the practically innumerable masses of Red Shirt Armies and civilians, seven isn't that many, and there's a damn good reason for them in particular to be showing up in the storyline.
 There's also the fact that the nature of the grand line means that it's basically been drawing and holding all the most powerful people in the world as a whole, so it makes sense that whatever portion of the world has this rare and powerful form of Haki, Most of them will be in the Grand Line.
 In Escaflowne, twin Catgirls Eriya and Naria had been augmented by Zeibach as "Intensified Luck" soldiers. Put simply, luck seems to go their way. Attacks heading their way misifre somehow while their own hits have more effect. Two catches. One, their power seems to be blunted around Hitomi—whether she is trumping luck manipulation with her innate reality manipulation or through the Power of Love is left unclear. Two, Their Days Are Numbered.
Comic Books
 In the Disney Ducks Comic Universe, Gladstone Gander's luck usually beats all odds. Huey, Dewey and Louie even tried to use it against him in the Don Rosa story "Oolated Luck". Donald and Gladstone entered a raffle and Donald's nephews had one entry ticket with Donald's name and the others for Gladstone. Donald won the first prize (a trip in a cruise ship) and Gladstone won the second prize (a lifetime supply of oolated squigs). It turned out Gladstone was lucky for not winning the trip since the ship got stuck in an iceberg. (The Lucky Bastard didn't seem to be concerned for his cousin) And one of the squigs had swallowed a diamond.
Film
 In Titan A.E., the main character spacefloats 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."
 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.
 Theory of Narrative Causality: you also really can't end a goofy buddy comedy soft scifi piece on a Downer Ending like the end of all existence.
 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?"
 Sir, the possibility of successfully navigating an asteroid field is approximately 3,720 to 1!
 "Never tell me the odds!"
 Of course, in reality the milliontoone shot would be the probability of Han's attackers not getting through safely.
 "Great shot kid, that was oneinamillion!"
 This latter is actually an inversion, however, as Luke had actually used the Force to aim  or perhaps guide  the shot. Han, of course, doesn't believe in the Force and chalks it up to luck, but as ObiWan has already said, "In my experience, there's no such thing as luck."
 "Never tell me the odds!"
 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 backtoback 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.
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 ninehundred ninetynine thousand, ninehundred ninetynine 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.
 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 "oneinamillion 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 Coupons (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.
 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.
 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 MilliontoOne Chance events to occur all the time.
 Not just Million to One, infinity to one, hence the name of the drive. MilliontoOne Chance events are generated by much simpler (finite) improbability generators, and it is by using one of these that the Infinite Improbability Drive was brought into existence; since such a device is a "virtual impossibility" but not completely impossible, its existence was a finite, calculable probability. The man who programmed the computers to calculate the precise probability of the Drive's potential existence wound up discovering the exact scientific principles behind the Drive in his results.
 I think in the Hitchhiker's guide universe, most probabilities are distinct (ie rarely do two highly improbable events have the same probability) which is why it's possible to specify the event you want to occur using a finite/infinite improbability drive. You induce all events with that probability, but usually there's only one or the sideeffects of the others are trivial or at least benign. What's even more mindboggling is that the probability that a particularly notable improbable event will have a probability whose digits are particularly notable such as Ford and Arthur being rescued / 1 over 2 to the phone number of the party where Arthur first met Trillian is itself a number which can be plugged into the drive.
 In addition, any event that is infinitely improbable is most likely to instantly happen as soon as the field is turned on.
 Averted in most Asimov stories. He often has characters discuss probability and the remote dangers of Hyperspace travel. Never does a ship actually get torn apart by hyperspace or accidentally jump into the sun. Whenever something really improbable does happen such as a ship getting hit by an asteroid, it must be a major focus of the story and also must have not happened a million times before to show that it actually is one in a million.
 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.
 Although such an army should get mowed down even in cliched media, because of Conservation of Ninjutsu.
 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 Kushiel's 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 Unwitting Pawn 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 humans. 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.
LiveAction TV
 Spoofed in Red Dwarf with the luck virus. Lister, Cat, and Kryten travel to a certain planet to investigate the death of a bacteriologist. While there, Lister is injected with the virus, which allows him to pick all the aces out of a deck of cards. He also tries to hit a dartboard's bullseye while throwing over his shoulder, but the virus wears off and he instead hits the center of Kryten's forehead. In the climax of the episode, Rimmer goes insane and locks the three in quarantine, slowly draining out the oxygen. Due to the virus however, Lister successfully guesses the code to unlock the door, then manages to trip over the necessary components to cure the insanity while running backwards down a hallway.
 Lister, in another episode: "The chances of it happening are one in..." [big explosion] "...one."
 In the Doctor Who story "The Creature from the Pit", the Doctor's companion Romana tells him that the odds are 74,384,338 to 1 against his Crazy Enough to Work plan actually working. He tells her that 74,384,338 is his lucky number. (The plan works, of course.)
 A Seinfeld episode has Kramer marvelling at stories told by proctologists, which all end with the statement "It was a million to one shot, doc. Million to one," since none of their patients want to admit how whatever object is stuck really got there. At the end of the episode, Frank is the victim of such a million to one shot, falling on a pasta sculpture Kramer had made. Naturally, he leads with the same statement.
 Tomica Hero Rescue Force did this, When the Big Bad (Baatsu) is unhurt by the "Great God Striker" "Super Final Rescue" attack which cannot be used again Hikaru is told that there is a "Less than 0.1 percent chance of victory" instead of giving up he burrows into Baatsu's head and blows him apart from the inside delivering the line:
Hikaru: Your calculations were wrong to begin with! Humans have hearts for helping those in need! With that even 0.1 can be changed into 100 or 1000! 
 Captain James T. Kirk is a master at this  Spock repeatedly computes incredibly long odds for a successful execution of whatever Kirk's latest daring plan is, often citing denominators in the thousands, if not hundreds of thousands, and Kirk always wins. Always. Eventually, they start lampshading this.
 A specific example: In "The Naked Time", they have to implode the antimatter engines to prevent themselves from crashing into a planet that is itself imploding. The procedure has never been done before: Spock and Scotty have only minutes to prep the engines, and they only have one shot to get it right. Kirk insists, "We've got to take that 10,000 to 1 chance!" They do. It works.
 I guess this is sort of lampshading and subverting? In Covert Affairs at the end of season 1, Annie is undercover in London and needs to lose a lot of money in a nonsuspicious way so that she will not be allowed to the leave the country. She loses all her money playing craps, then takes out a loan for a few thousand dollars, and bets it all on snake eyes, which is of course very risky. She acts confident that she'll win but is secretly hoping she'll lose. The roll comes up snake eyes so now she has lots and lots of money. Now she has to look outwardly relieved, although internally she's freaking out because the whole point was to rack up massive debts. She bets it all on snake eyes again, and luckily this time, she loses.
 In an episode of Gilligan's Island, a radioactive meteorite falls on the island, and the crew is in danger of the radiation killing them. They learn of an incoming storm, and the Professor gets the idea of trying to put a lightning rod on it and hope lightning strikes it, but admits the chance is a million to one. When the Skipper asks what could be worse than that, Gilligan suggests, "A million to none?" Realizing that he has a point (slim chance is better than no chance) they try it, and it works.
Music
 Jeff Wayne's Musical Version of The War of the Worlds: "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 namedafter.
Professional Wrestling
 This trope is very common among the top babyfaces in Professonal Wrestling. So common, in fact, that the fans became very Genre Savvy when WWE attempted to invoke this trope on John Cena. Thanks to this, his already simmering and vocal Hatedom just got louder, citing his status as an Invincible Hero, and each pay per view ended up as a monthly "pay to watch John Cena overcome impossible odds once again" event to them. The culmination was at 2006's New Year's Revolution pay per view, where Cena was the first in the Elimination Chamber, surviving through 5 men while having about 90% of the fans in attendance against him. The crowd seemed ready to riot. Then Edge, one of the most hated men in the company at that time, backdoored his way into a match right after this and subverted this trope, defeating Cena to win his title despite being fresh and Cena having just fought through five men in a steel cage. The crowd was so happy to see this subverted that Edge became one of the biggest stars in the company almost overnight. Cena's hatedom has since cooled down when WWE downplayed him being a oneman odds beating machine.
 Of course, John Cena is far from the worst offender of invoking this trope. Hulk Hogan in WCW was doing this to such a degree that C3PO's head would explode trying to calculate the odds. The 1996 Uncensored PPV had Hulk Hogan team up with his then buddy Randy Savage to take on the Alliance to End Hulkamania. Ric Flair, Arn Anderson, Meng, The Barbarian, Lex Luger, Kevin Sullivan, ZGangsta (Zeus), and The Ultimate Solution. That's right, an 8 on 2 advantage, in a tripledecker steel cage! Hogan wins.
Puppet Shows
 Played straight in Thunderbirds, of course. "That thing [aircraft heading towards the tower they're in] is never going to hit us! It's a million to one chance!" Guess what happens. Go on.
Video Games
 In the original HalfLife, 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.
 In Portal 2, GLaDOS gives this evaluation of the player character's chances of beating Wheatley:
GLaDOS: I'll be honest, the odds are a million to one, and that's with some generous rounding. But if we're going to explode, let's at least explode with some dignity! 
Web Comics
 Subverted and lampshaded in The Order of the Stick #454, when Haley relies on her Genre Savviness a bit too much.
Durkon: Lass, it were an awful difficult shot. 
 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 milliontoone chance of the imp summoning a monster that could actually kill them is a sure thing. This results in one of the page quotes.
 Subversion in Girl Genius:
Abner: There's a million reasons why that is not going to work. 
 In Homestuck, Vriska's entire plan to take out Jack Noir relies on rolling the best possible result on eight magical eightsided dice (a 16,777,216 to 1 chance), unleashing their ultimate magical attack. It would have worked—because she'd been "stealing ALL of the luck" from her entire team.
Web Original
 In Tabletop, The odds of Ryan Higa's feat of rolling ten brains on his first turn in Zombie Dice approach infinity. Wil Wheaton speculates that, in order to balance his luck out, somewhere in the universe a planet spontaneously imploded.
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.
 Inverted in an episode of Dynomutt Dog Wonder. Dynomutt is reprogrammed for evil and given the task of killing his master, Blue Falcon. Falcon, knowing Dynomutt's tendencies all too well, announces that the odds are a million to one... in his favor. (And yes, the odds do hold up this time.)
Real Life
 This man—it's a "45 billion to one chance", rather!
 A literal milliontoone roll happens 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) fattailed distribution. Which means that improbable events actually happen more often than statisticians expect.
 The managers of the hedge fund LongTerm 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.
 An exception to the rule is perhaps worth mention here. One scientist has said that the Large Hadron Collider has less than a one in a 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 invocation of this trope to real life makes that chance seem far scarier than it should. (The same scientist said, likely tongueincheek, 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.
 This was most likely misprinted, and should have been one in 10^billion*billion. That is, a one followed by a billion times a billion zeroes. Of course, this doesn't account for such things as it being physically quite easy to destroy the Earth, and all the physicists just forgot about those laws, along with many other highly unlikely but still much more likely possibilities.
 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, 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 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  we just calculated it incorrectly. Another group disagrees and has a different definition. But that's a separate discussion.
 The chances of life arising (and forming a technological civilization) are collected in the 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.
 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, Television Is Trying to Kill Us. The reallife lesson taught to all medical providers is summed up as, "When you hear hoofbeats, think horses, not zebras." 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 Wrong Genre Savvy, 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. Dr. House hasn't helped matters much, and countless medical practitioners subtly curse that show (even if we're some of the biggest fans). So (should you be an American), yeah, you will likely know one person in your life with TaySachs, Gauchier's, Huntington's, or something equally rare. 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 infinite. Not oneinamillion, almost zeroinamillion. And always, one outcome actually happens despite being impossible.
 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 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 it had an assigned probability of 0, for nowaynohow, 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 Tabletop Games 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 20sided die. If a twenty is rolled, it is rerolled with a chance for 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 granddaddy of tabletop roleplaying games, considering it usually takes at least foursix 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 fiftysecond, 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.
 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 fiftysecond, you blow someone's mind. Extra fun to use on magicians who are watching for the sleight, and will never find it.
 Affirmed in any case of the 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 counterintuitive outcomes with Unfortunate Implications. 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 100 exact matches in a sample prison population of just 65,000. Can also be used to attack highstrength 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. (Racing Post article here.)
 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 1:3,105,000,000. This very thing happened to brothers Jack, Aaron, and Nathan Helms of Apopka, Florida.
 This is related to the rare deceases 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.