100 Fun Facts About Probability

How many people in a room are needed before a shared birthday between two of them is more likely than not?

23 people are enough, because every pair in the room is a separate chance at a match and a group that size holds hundreds of pairs. With 70 people a shared birthday is 99.9% certain.

In the Monty Hall problem, what chance of winning the car does switching give once the host reveals a goat?

Switching wins 2/3 of the time, because it loses only when the first pick was already the car, a one-in-three event. Pigeons trained on the puzzle learn to switch faster than people do.

What do statisticians call the belief that a fair coin, after ten heads in a row, is 'due' to land tails?

It is the gambler's fallacy, also called the Monte Carlo fallacy, and it runs backwards: past flips leave no trace on a fair coin, so tails stays at exactly one half. The 'hot hand' is the mirror-image error.

How many riffle shuffles did Bayer and Diaconis show a 52-card deck needs before its order is effectively random?

7 riffle shuffles is the finding of the 1992 Bayer–Diaconis paper: after five the deck is still far from random, and around the seventh its order breaks down fast. A later study using a different yardstick argued that six are enough.

Roughly how many different orderings can a shuffled 52-card deck take, the number mathematicians write as 52 factorial?

A 52-card deck has 52! ≈ 8 × 10^67 orderings, so any properly shuffled deck is almost certainly in an order no deck in history has ever been in before.

What are the jackpot odds for a Powerball ticket matching five white balls from 69 and the red ball from 26?

1 in 292,201,338 has been the jackpot chance since 2015, when the white-ball pool grew from 59 to 69 and the odds lengthened from about 1 in 175 million, even as the chance of winning any prize improved to about 1 in 25.

By Persi Diaconis's physics model, which side is a caught coin slightly likelier to land on?

Whichever side started up wins about 51% of the time, because a tossed coin wobbles as it spins and spends slightly longer with that face up. A 2023 study of 350,757 tosses measured 50.8%.

Which physicist told Max Born in a 1926 letter that he was convinced God 'is not playing at dice'?

Albert Einstein was rejecting Born's proposal that quantum mechanics predicts only probabilities with no underlying cause. He never accepted it, and his argument with Bohr ran on for decades.

How many ways can a 63-game March Madness bracket be filled in if every game is treated as a coin flip?

There are 2^63, about 9.2 × 10^18 or 9.2 quintillion, possible brackets, more than the estimated 7.5 quintillion grains of sand on Earth. Knowing the sport only cuts the NCAA's estimate to around 1 in 120 billion.

In the secretary problem, what share of candidates do you reject before taking the first one better than all of them?

Rejecting the first 37% — one divided by e — and then taking the next best-so-far candidate lands the single best applicant about 37% of the time, whether there are 100 or 100 million of them.

With two fair dice, what is the probability of a double six, the only way to throw a total of twelve?

A double six comes up 1/36 of the time, since each die has six faces and the pair makes 36 equally likely combinations. A total of seven, by contrast, can be made six different ways.

What is the probability that three fair coins all land heads, one of the two outcomes that void a three-way flip?

All heads happens 1/8 of the time (½ × ½ × ½), which is why the three-way coin flip used to pick an odd one out works on 75% of attempts and is simply repeated otherwise.

What is the expected value of a single roll of a fair six-sided die, the average seen over thousands of throws?

The expected value is 3.5, a result the die can never actually show, because each face from one to six is equally likely and their mean is 21 divided by 6. A pair of dice averages exactly double that.

If 1 driver in 1,000 is drunk and a breathalyser flags 5% of sober ones, how likely is a flagged driver drunk?

Only about 2%: among 1,000 drivers the device flags roughly 50 sober people for every one who is truly drunk, a base-rate effect that also makes rare-disease screening positives mostly false alarms.

Which solicitor's 1999 murder conviction over her two sons' deaths hinged on a discredited '1 in 73 million' statistic?

Sally Clark's jury heard paediatrician Roy Meadow claim two cot deaths in one family had odds of 1 in 73 million, a figure that wrongly treated the deaths as independent. Her convictions were quashed in 2003.

Which sport did Gilovich, Vallone and Tversky study in the 1985 paper that called the 'hot hand' an illusion?

Basketball shooting was the test case: the paper found no evidence that a player who has just sunk several shots is likelier to sink the next. A 2018 reanalysis argued the original data did show streaks after all.

Which version of roulette adds a second green pocket, the 00, nearly doubling the house edge to 5.26%?

American wheels kept the double zero that the Blanc brothers dropped at Bad Homburg in 1843 to compete with rival casinos; a single-zero wheel's edge is 2.7%, one pocket in 37.

At Monte Carlo in 1913, how many spins in a row came up black while bettors lost millions of francs backing red?

Black came up 26 times running while the crowd kept piling onto red, sure the run had to end — the textbook case of the error named after that casino. A one-colour run that long has odds of roughly 1 in 68 million.

Which game show, where players traded prizes for what hid behind numbered doors, gave the Monty Hall problem its name?

Let's Make a Deal was hosted by Monty Hall from its 1963 debut, and its audience 'traders' gambling on unseen prizes inspired the three-door puzzle. Hall himself noted that real play on the show never followed the puzzle's rules.

In a normal bell curve, what share of values fall within one standard deviation either side of the mean?

About 68% lies within one standard deviation, 95% within two and 99.7% within three — the empirical rule that lets a single number say how unusual a height, a test score or a blood reading is.

Which Toulouse lawyer's 1654 letters with Blaise Pascal on a gambling problem founded probability theory?

Pierre de Fermat, who treated mathematics as a hobby beside his legal career, worked out with Pascal how to split the stakes of an interrupted game, the 'problem of points'. His famous Last Theorem was a margin note.

Which man of letters brought the 'problem of points', on splitting an unfinished game's pot, to Pascal in 1654?

The Chevalier de Méré, born Antoine Gombaud, was a writer and salon wit whose questions about dice and stakes drew Pascal into the subject. Within months Pascal and a correspondent in Toulouse had its foundations.

Which Italian polymath's Liber de ludo aleae, written around 1564, was the first systematic treatment of probability?

Gerolamo Cardano kept himself solvent at the gaming table, and his book, unpublished until 1663, includes a section on effective cheating beside the first definition of odds as favourable against unfavourable outcomes.

Which Dutch scientist, famed for the pendulum clock, wrote the first published treatise on probability, in 1657?

Christiaan Huygens took up games of chance after a 1655 visit to Paris, where he heard of the Pascal correspondence, and his De Ratiociniis in Ludo Aleae set out the idea of expected value, the average payoff of a bet.

Which Swiss mathematician's posthumous Ars Conjectandi of 1713 proved the law of large numbers, his 'golden theorem'?

Jacob Bernoulli spent over 20 years proving that a coin's observed share of heads settles toward its true probability as tosses mount, and the book appeared eight years after his death. His nephew Daniel gave fluids their principle.

Which Huguenot exile in London described the bell curve in 1733 and wrote The Doctrine of Chances?

Abraham de Moivre's 1733 result was the first statement of the normal curve as an approximation to the binomial, and legend says he predicted the date of his own death by noticing he slept 15 minutes longer each night.

Thomas Bayes, whose theorem updates a probability on new evidence, earned his living in what profession?

Bayes was a Presbyterian minister at the Mount Sion Chapel in Tunbridge Wells, and his theorem was never published in his lifetime; it surfaced only after his death in 1761.

Which Welsh philosopher edited Bayes's essay and sent it to the Royal Society in 1763, two years after its author's death?

Richard Price, who also helped found actuarial science and defended the rebel colonists in a 1776 pamphlet, spent two years editing the paper and added his own introduction; some writers now speak of the Bayes–Price rule.

Which Soviet mathematician's 1933 Foundations of the Theory of Probability gave the subject its modern axioms?

Kolmogorov built probability on measure theory — an event is a set and its probability a measure that sums to one — and the same man went on to found the mathematics of turbulence and of algorithmic complexity.

Which Los Alamos mathematician dreamed up the Monte Carlo method in 1946 while playing solitaire during an illness?

Stanisław Ulam wondered what the odds were that a Canfield solitaire would come out, and decided to just lay out a hundred hands and count; the code name came from the casino where his uncle gambled with borrowed money.

Which mathematician, interned in Nazi-occupied Denmark, tossed a coin 10,000 times to test the law of large numbers?

John Kerrich, raised in South Africa and caught visiting in-laws in Copenhagen in April 1940, recorded 5,067 heads — a proportion that crept ever closer to one half as the tosses mounted, exactly as the theorem predicts.

Which Victorian polymath invented the 'bean machine', a pegboard down which balls fall to pile up in a bell curve?

Francis Galton, Darwin's half-cousin, presented the board in 1874 to show the central limit theorem in action; he also coined 'regression to the mean', devised fingerprint classification and, less happily, eugenics.

Which statistician's 'lady tasting tea' experiment tested Muriel Bristol's claim to tell if milk was poured first?

Ronald Fisher's test gave her eight cups, four of each kind, in random order; by a colleague's later account she got all eight right, something chance alone would manage once in 70 tries — the experiment that introduced the null hypothesis.

Who built a life table from Breslau's death records in 1693, showing how to value life annuities by the buyer's age?

Edmond Halley, better known for his comet, used records sent from Breslau by the clergyman Caspar Neumann to work out how many people of each age survive — the root of actuarial science.

Which Danish engineer, sizing the Copenhagen telephone company's circuits, founded queueing theory in 1909?

Agner Erlang's name is now the unit of telephone traffic, and his formulas still size call centres and networks by working out how many circuits keep callers from finding every line busy.

Which distribution did Ladislaus Bortkiewicz famously fit in 1898 to Prussian cavalrymen killed by horse kicks?

The Poisson distribution fitted twenty years of deaths across fourteen army corps, and Bortkiewicz titled his book The Law of Small Numbers: even rare chance accidents followed a predictable pattern.

Which mathematician's 1962 book Beat the Dealer proved blackjack could be beaten by counting cards?

Edward Thorp ran the strategy on an IBM 704 before testing it in Reno and Las Vegas in disguise, and with Claude Shannon built the first wearable computer to predict roulette — a device Nevada outlawed in 1985.

In what ratio did yellow and green peas reappear in the second generation of Gregor Mendel's crosses?

The 3:1 ratio arises because each parent passes on one of two gene versions at random, so a quarter of offspring get two copies of the recessive green. Mendel's counts were later judged suspiciously close to perfect.

How many other people must be in a room before one of them more likely than not shares your own birthday?

It takes 253 other people, far more than for any two sharing, because every match must now involve you: each person is compared with you once, instead of every pair in the room being compared.

Which Parade columnist, once Guinness's highest-IQ holder, drew some 10,000 letters with her 1990 Monty Hall answer?

Marilyn vos Savant told readers to switch, and around 10,000 wrote in to say she was wrong; she was right, and about half of the published letter-writers later admitted they had changed their minds.

Which university's 1973 admissions figures are the textbook Simpson's paradox, reversing once split by department?

UC Berkeley's overall figures showed men admitted at a clearly higher rate, but the gap vanished department by department: women had applied in larger numbers to the most competitive programmes, which rejected everyone more often.

Which Scientific American columnist's 1959 'three prisoners' puzzle is Monty Hall with a pardon instead of a car?

Martin Gardner's puzzle has a warden name one of two condemned cellmates; the asker's own odds do not improve at all, while the unnamed prisoner's do — a result readers fought just as hard three decades later.

Which city names the paradox of a coin-flip game whose payout doubles each round, giving an infinite expected value?

The St. Petersburg paradox takes its name from the academy journal in which its 1738 analysis appeared, arguing that people value money by its usefulness rather than its face amount — the birth of the idea of diminishing utility.

What is the chance of being dealt a five-card royal flush, ten to ace in one suit, from a 52-card deck?

A royal flush comes up 1 in 649,740 deals, so a player dealt 50 hands an hour would wait about 18 months of continuous play to see one on average.

How many six-number combinations can a 6/49 lottery draw — the tickets needed to guarantee the jackpot?

There are 13,983,816 combinations, the result of 49 × 48 × 47 × 46 × 45 × 44 divided by the 720 orderings of six numbers, so a single line faces odds of about 1 in 14 million.

Under Benford's law, roughly what share of numbers in real-world data such as street addresses begin with the digit 1?

About 30% of leading digits are 1 and fewer than 5% are 9, a skew so reliable that forensic accountants use it to flag invented figures.

Whose 'law' holds that an ordinary person should expect a one-in-a-million event — a 'miracle' — about once a month?

J. E. Littlewood's law took this form from the physicist Freeman Dyson in 2004: alert for about eight hours a day, we notice roughly one event a second, a million a month, so a monthly 'miracle' is only to be expected.

Which betting system, popular in 18th-century France, doubles the stake after each loss so one win recovers everything?

The Martingale is certain to win only with infinite money and no table limit; in practice a run of six losses at even-money roulette odds, about a 2% event per sequence, wipes out 63 units and the plan collapses.

Which constant did the Comte de Buffon show can be estimated by dropping needles onto a floor of parallel planks?

The chance that a needle as long as the plank width crosses a line works out to 2/π, so counting crossings estimates π — one of the earliest problems in geometric probability, posed in the 18th century.

Which French mathematician posed the 'box paradox' of gold and silver coins, identical in structure to Monty Hall?

Joseph Bertrand put the puzzle in his Calcul des Probabilités: the intuitive answer of one half for the coin left in the box leads to a contradiction, he showed, so it cannot be right.

In the famous theorem about random typing eventually producing Shakespeare, which animal is at the keyboard?

Monkey typists got a real trial when six macaques at Paignton Zoo were given a keyboard. They produced five pages, mostly the letter S, and the lead male attacked it with a stone.

Which French philosopher grew rich by joining mathematician La Condamine's scheme to buy up a government lottery?

Voltaire joined the consortium that bought up the lottery and earned perhaps a million livres. Invested cleverly, the winnings left him indisputably rich.

The numbers on a roulette wheel, 0 through 36, add up to which total?

666 is the total of every pocket from 0 through 36. François Blanc, who launched the single-zero wheel with his twin brother Louis, later made Monte Carlo a gambling mecca.

In The Empire Strikes Back, who snaps 'Never tell me the odds' when C-3PO rates an asteroid field at 3,720 to 1?

Han Solo flies into the asteroid field anyway and shakes off the Imperial fighters chasing him. Odds of 3,720 to 1 against work out to a chance of success of roughly 0.03%.

Paul, who correctly picked the winner of all eight of his 2010 World Cup matches from two food boxes, was which animal?

Octopus Paul chose between two boxes of food marked with team flags at his aquarium in Oberhausen, Germany. Calling eight two-way results in a row by luck alone is a 1-in-256 shot.

Which fairy-tale heroine names a probability puzzle about a woman woken once or twice depending on a coin toss?

Sleeping Beauty is given a drug that wipes her memory of each waking, then asked how likely it is that the coin landed heads. Philosophers divide into 'halfers' and 'thirders' over the answer.

Which 2008 film about MIT students beating Las Vegas casinos at card counting features the Monty Hall problem?

21 was inspired by Ben Mezrich's book Bringing Down the House, about the real MIT Blackjack Team. Its hero catches his professor's eye by solving the three-door puzzle in class.

Which grid diagram, named for a British geneticist, shows the probability of each genotype in two parents' offspring?

Punnett square boxes are all equally likely, so two carriers of a recessive gene can read off a 25% chance of an affected child. Reginald Punnett devised the method in 1905.

What nickname do craps players give a roll of two ones, the lowest total that a pair of dice can show?

Snake eyes is bad news on a come-out roll in craps. Along with a 3 or a 12 it counts as 'crapping out', and everyone betting the pass line loses.

Which London diarist wrote to Isaac Newton in 1693 asking which of three dice wagers was the likeliest to win?

Samuel Pepys fancied the bet needing three sixes from 18 dice. Newton showed that the simplest wager, at least one six from six dice, wins most often: about 66.5% of the time.

Which French mathematician, Napoleon's examiner at military school, put odds on the sun rising tomorrow?

Pierre-Simon Laplace applied his rule of succession to the sunrise, then added that anyone who understood the heavens would rate the chance far higher. Napoleon later made him interior minister and replaced him after six weeks.

Which playwright opened Rosencrantz and Guildenstern Are Dead with a coin landing heads 92 times in a row?

Tom Stoppard has Rosencrantz bet heads every time and win, while Guildenstern hunts for a reason the laws of chance have failed. A fair coin would manage it about once in 5 octillion tries.

Which statistical effect explains the Sports Illustrated cover jinx, where athletes slump after a standout season?

Regression to the mean says an extreme result is usually followed by a more ordinary one. Athletes make the cover after a career-best run, so a dip afterwards is what chance predicts, not a curse.

Which bird names Nassim Taleb's term for a rare, unpredictable event with extreme consequences?

Black swan was once a byword for the impossible, since Europeans had only ever seen white ones. Then, around 1697, Dutch mariners saw the real thing living in Australia.

What two-word term did Karl Pearson coin in 1905 for the unpredictable path traced by a staggering drunkard?

Random walk maths has a punchline from Shizuo Kakutani: 'A drunk man will find his way home, but a drunk bird may get lost forever.' On a flat grid the wanderer is all but certain to return; in 3D, not so.

Which Russian mathematician tested his 'chains' of dependent events on the vowels and consonants of Eugene Onegin?

Andrey Markov sorted the first 20,000 letters of Pushkin's verse novel into vowels and consonants to show how each depends on the one before. Google's PageRank is defined by the same kind of chain.

Which American military analyst gives his name to a 1961 urn paradox showing people prefer known odds to unknown ones?

Daniel Ellsberg is far better known for what he did a decade later: leaking the Pentagon Papers to the press. His paradox is taken as evidence of 'ambiguity aversion'.

Which Italian scientist studied dice throws around 1620, noting that some totals appear more often than others?

Galileo Galilei reasoned that a total turns up more often when more combinations of the dice produce it. Three dice can make a ten in 27 ways but a nine in only 25.

Which Cambridge economist published A Treatise on Probability in 1921, fifteen years before his General Theory?

John Maynard Keynes argued that probability is a strictly logical relation between evidence and hypothesis, not just a frequency. The book grew out of his King's College fellowship dissertation.

In probability, what name is given to the set of all possible outcomes of an experiment, such as heads and tails?

Sample space for a single card drawn from a standard deck has 52 members, one for each card. Every probability is a share of this set, so listing it is the first step of most problems.

Which kind of probability is estimated from actual trials, such as counting 53 heads in 100 coin flips?

Empirical probability, also called experimental probability, is only ever an estimate: 53 heads in 100 flips suggests 0.53. Keep flipping a fair coin and the figure drifts toward the theoretical 0.5.

What single word do British bookmakers use for odds of 1/1, where a winning £10 stake earns £10 profit?

Evens means the bookmaker rates the bet a 50% chance, the same as a coin toss. In decimal odds the same price is written 2.00, because a winner gets back double the stake.

What are the odds against a randomly chosen day of the week falling on a weekend?

5:2 sets the five weekdays against the two weekend days. The probability is a different figure, 2/7, because it compares the weekend with the whole week.

Among all two-child families with at least one boy, what fraction have two boys, not the half most people guess?

1/3 is right because such families come in three equally likely kinds: boy-boy, boy-girl and girl-boy. Only one of the three has two sons.

What value on the probability scale is given to an event that can never happen, like rolling 9 on a six-sided die?

0 marks the impossible end of the scale and 1 the certain end, so every probability sits somewhere between them. An even chance lands halfway, at 0.5.

What is the probability of drawing a king from a shuffled standard 52-card deck, which holds one in each suit?

1/13 comes from four kings among 52 cards. The same figure holds for any single rank, from aces to queens, since each appears once per suit.

What name is given to the dots on dice, a word also used for the spots on dominoes?

Pips also name the suit symbols on playing cards. On a traditional die they run from one to six, with a different count on each face.

The 'knucklebones' that ancient Greeks threw as early dice came from which joint of a sheep?

Ankle bones called astragali can come to rest on only four sides, so each throw had four possible results rather than a cube's six.

Which Platonic solid, with twenty triangular faces, gives the 20-sided dice of tabletop role-playing games their shape?

Icosahedron dice long predate modern role-playing games: a twenty-sided die inscribed with Greek letters survives from Ptolemaic Egypt. Each face of a fair one comes up 5% of the time.

Which error in reasoning treats a one-in-a-million DNA match as a one-in-a-million chance the defendant is innocent?

Prosecutor's fallacy was named by William Thompson and Edward Schumann in 1987. In a city of ten million people, a one-in-a-million match would still fit about ten of them, so the match alone proves little.

Which reasoning error does the 'Linda problem' expose, where a feminist bank teller seems likelier than any bank teller?

Conjunction fallacy answers break a basic rule: two things together can never be more probable than either one alone. Most people still get Linda wrong because the detailed option feels more 'representative'.

Which psychologist won the 2002 economics Nobel for work, begun with Amos Tversky, on judgment under uncertainty?

Daniel Kahneman said Amos Tversky would have shared the prize had he not died in 1996. He later summarised their research in the bestseller Thinking, Fast and Slow.

Which betting formula, described by a Bell Labs researcher in 1956, sizes each stake for the fastest long-run growth?

Kelly criterion stakes maximise the long-term growth rate of wealth, but the swings along the way are brutal. Gamblers in practice prefer 'fractional Kelly', betting only part of what the formula says.

Which unit of risk, introduced by decision analyst Ronald Howard, stands for a one-in-a-million chance of death?

Micromort joins 'micro', a millionth, to 'mortality'. Tables of them make very different dangers comparable, from a skydive to a long car journey.

Which 0-to-10 rating, named after an Italian city, grades the danger that an asteroid or comet will hit Earth?

Torino scale ratings combine the probability of a collision with the energy it would release into one threat value. The name comes from a 1999 conference in Turin where a revised version was presented.

Which adjective for randomly determined processes comes from a Greek word meaning 'to aim at' or 'guess'?

Stochastic first meant 'pertaining to conjecture' when it entered English in the 1660s. Its Greek root, stokhos, was the target that archers shot at.

Which view of probability, usually set against the Bayesian one, treats it as an outcome's share of endless trials?

Frequentism holds that probabilities can be found, in principle, by a repeatable objective process such as sampling again and again, leaving no room for personal degrees of belief.

Which profession uses probability and statistics to price the risks behind insurance policies and pension funds?

Actuary work grew out of 17th-century studies of probability and annuities, which first let insurers measure risk scientifically. Qualifying takes years of structured exams.

Which puzzle argues that swapping your unopened prize for one worth double or half always pays?

Two envelopes problem reasoning says a swap risks halving your money but might double it, so you should always switch, and then switch back, forever. It descends from an older puzzle about neckties.

Which Franciscan friar, called the father of accounting, tackled the gamblers' 'problem of points' in a 1494 textbook?

Luca Pacioli got it wrong: as Tartaglia later noticed, his rule could hand the whole pot to whoever won a single early round. A sound way to split the stakes took another 160 years.

Which Yorkshire businessman is said to have 'broken the bank at Monte Carlo' by exploiting biased roulette wheels?

Joseph Jagger is reputed to have won over 2 million francs in a matter of days. Each table began the day with a 100,000-franc reserve called 'the bank', and emptying it was 'breaking' it.

Which 17th-century English leader names the rule that no uncertain claim should get a probability of exactly 0 or 1?

Oliver Cromwell earned the honour with a 1650 plea to the Church of Scotland: 'I beseech you, in the bowels of Christ, think it possible that you may be mistaken.' Statistician Dennis Lindley named the rule.

Which English word for danger began as the name of a medieval dice game that later evolved into craps?

Hazard gets a mention in Chaucer's Canterbury Tales and was a favourite at Crockford's Club in London. By the 1540s the word had also come to mean any chance of loss or harm.

Romans called coin flipping 'navia aut caput', meaning head or which other image stamped on some of their coins?

Ship designs filled the reverse of some Roman coins, with a head on the other side. In England the same game was long known as 'cross and pile'.

What name is given to the event 'A does not happen', whose probability is always 1 minus that of A?

Complement events are the shortcut behind many hard problems. The chance of at least one six in several rolls is easiest to find as 1 minus the chance of rolling none.

Which English earl names a bridge hand with no card above a nine, a deal he would bet £1,000 to £1 against?

Yarborough was on to a good thing at the whist table, because the true odds against such a hand are about 1,827 to 1. He pocketed a pound every time it failed to appear.

Which Scottish botanist, watching pollen in water in 1827, gave his name to the random jitter of tiny particles?

Robert Brown was studying plant reproduction when he saw that tiny particles from the grains would not keep still. In 1900 Louis Bachelier used the mathematics of that motion to analyse the stock market.

Which ancient city-state used a slotted stone device called a kleroterion to pick jurors and officials at random?

Athens drew citizens by lot for its council, most state offices and court juries. Coloured dice dropped down a tube on the machine decided which rows of name tokens were picked.

Roulette, likely developed from the Italian game Biribi, takes its name from a French word meaning what?

Little wheel is all the name means. Many historians believe Blaise Pascal built a primitive version in the 17th century while hunting for a perpetual motion machine.

What two-word phrase do mathematicians use for an event of probability 1 that could, in principle, still fail?

Almost surely matters once outcomes are infinite. A fair coin tossed forever shows a head with probability 1, yet an endless run of tails is still a possible outcome.