Randomness, A to Z: a plain-language glossary

A tilt. A biased coin, die or generator favours some results over others. Bias can be built in (a lopsided die), introduced by sloppy maths (see modulo bias), or deliberate (see the weighted balls of 1980).

The surprising fact that in a room of just 23 people there is a better-than-even chance two share a birthday. Repeats happen far sooner than intuition expects, because every pair of people is a chance for a match.

A statistician’s first check on a pile of results: are the counts as even as chance allows? It compares what you saw with what a fair source would produce on average and turns the difference into a single number and a p-value.

Seeing clumps in truly random scatter and concluding that something must be causing them. Random points are lumpier than people expect; perfectly even spacing is the unusual thing.

The oldest two-way decision. A fair coin gives each side a 50% chance on every toss; previous tosses do not change the next one.

A choice where order does not matter. Picking 6 lottery numbers from 49 is a combination; there are 13,983,816 of them, which is why the jackpot odds are 1 in 13,983,816.

A pseudo-random generator built so that even someone who sees a long stretch of its output cannot predict the next value or work backwards to earlier ones. Browsers expose one through Web Crypto.

Shorthand from tabletop games: “2d6” means roll two six-sided dice and add them; “d20” is a single twenty-sided die.

The full picture of how likely each possible result is. A single die has a flat (uniform) distribution; the total of two dice has a triangle peaking at 7; many dice added together approach a bell curve.

In this context, unpredictability measured in bits. One fair coin toss is one bit of entropy; a fair d8 roll is three. Computers collect entropy from unpredictable physical events to seed their generators.

The long-run average of a random quantity. A single d6 has an expected value of 3.5 — a number you can never roll, yet the average of many rolls creeps towards it.

Giving every outcome its proper chance: a fair coin is 50/50, a fair d6 gives each face one chance in six, a fair raffle gives every entry the same chance. Fairness is about the odds, not about results looking tidy.

The standard way to put a list in random order on a computer: walk from the last item to the first, swapping each with a randomly chosen item at or before it. Done right, every ordering is equally likely.

The belief that after a run of one result the other is “due”. For independent events it is simply false: the coin, wheel or generator has no memory.

A device that makes random numbers from a physical process — electrical noise, radioactive decay, light, even lava lamps — rather than from arithmetic. Also called a true random number generator (TRNG).

The feeling that a player on a streak is more likely to succeed next time. Whether it exists in sport is a long-running research debate; in a random number generator it does not.

Events where one outcome tells you nothing about the other. Successive coin tosses, dice rolls and taps on this generator are independent. Draws from a hat without putting names back are not.

As you repeat a random experiment, the average result settles towards its expected value. It says nothing about any single result and does not require streaks to “even out” — the early lean is simply drowned by the later volume.

One of the oldest families of computer random number generators: multiply the previous value, add a constant, keep the remainder. Simple and fast, with well-known weaknesses when poorly tuned.

John von Neumann’s early recipe: square the previous number and keep its middle digits. Easy to run by hand, and famous for collapsing into short loops or sticking at zero.

The slight unevenness you get by taking a big random number and keeping only the remainder when dividing by your range size. Fixed by rejection sampling.

Solving a hard problem by running it many times with random inputs and looking at the spread of results. Named after the casino, and one of the reasons researchers once needed printed tables of random digits.

The bell curve. It appears whenever many small independent influences add up — heights, measurement errors, the total of lots of dice.

Probability is a share: 1 in 6, or 16.7%. Odds compare the two sides: 5 to 1 against. Lotteries usually say “1 in N”, which is a probability written as a fraction.

The chance that a fair source would produce results at least as extreme as the ones you observed. Small p-values are a prompt to look closer, not a verdict: a fair generator produces p < 0.05 about one run in twenty.

How long a pseudo-random generator runs before its sequence starts over. The middle-square method has tiny periods; modern generators have periods far longer than the age of the universe in nanoseconds.

An arrangement where order matters. A shuffled deck is one permutation of 52 cards; there are 52! (about 8 × 10⁶⁷) of them.

An algorithm that produces a long, random-looking sequence from a starting value (the seed). Deterministic — the same seed gives the same sequence — which is a feature for simulations and a hazard for lotteries.

A lottery ticket whose numbers are chosen by the terminal’s random number generator instead of by the player. Statistically no better or worse than chosen numbers, but less likely to share a jackpot with people who picked the same “lucky” pattern.

A subset chosen so that every member of the group had the same chance of being included. The foundation of polling, quality control and clinical trials.

A public service that publishes fresh random values on a schedule, signed so anyone can verify them later — useful when a draw must be checkable by strangers.

Throwing away the random draws that would tilt the odds and drawing again, so what remains is perfectly even. It is how this site fits 64 random bits to a range like 1–6.

Drawing with replacement puts each result back before the next draw, so repeats are possible (this generator). Drawing without replacement removes it, so every result is different (a raffle with one prize per person).

Splitting a deck in two and letting the halves fall together. A single riffle leaves obvious order; about seven are needed to mix a 52-card deck thoroughly.

A stretch of the same result in a row. Runs are longer and more common than intuition suggests: in 100 coin tosses, a run of six or more is more likely than not.

The starting value a pseudo-random generator grows its whole sequence from. Keep the seed secret and unpredictable and the sequence is safe; reuse it and every “random” result repeats.

Choosing people for office or duty by lot rather than by vote or appointment. Classical Athens ran much of its government this way; modern juries and citizens’ assemblies still use it.

Any of a family of checks that look for patterns a random source should not have: uneven counts, too few or too many runs, repeated templates, and so on. Passing many tests builds confidence; no test can prove randomness.

A formal word for “involving randomness”. A stochastic process unfolds step by step with chance at each step — a random walk, a queue, the weather.

Every outcome equally likely. It is what you want from a die, a lottery machine and a random number generator, and what the chi-square test checks for.

John von Neumann’s 1949 trick for getting a perfectly fair result from a biased coin: toss it twice, call heads-tails “heads” and tails-heads “tails”, and throw away matching pairs. As long as tosses are independent the result is exactly 50/50. Hardware random generators still use versions of it to strip out bias.

The browser’s cryptography toolkit. Its getRandomValues() function supplies cryptographically strong random bytes from the device’s own secure source, and it is where this site’s numbers begin.

A draw where outcomes deliberately have different chances — a loaded die, a prize wheel with wide and narrow slices, or a raffle where some people hold more tickets.