Glossary of chance and probability
The vocabulary of chance, explained simply. 48 clear definitions, each illustrated with a concrete example drawn from our games and drawing tools.
Probability
Binomial distribution
The distribution of the number of successes obtained by repeating the same two-outcome trial a fixed number of times and independently.
Read the definitionConditional probability
The probability of an event computed given that another event has already occurred.
Read the definitionEquiprobability
A situation in which all the possible outcomes of an experiment have exactly the same probability of occurring.
Read the definitionEvent
A result, or set of results, of a random experiment, to which a probability can be assigned.
Read the definitionExpected value
The average value one can expect from a random experiment if it is repeated a large number of times.
Read the definitionFrequency
The proportion of times a result appears, relative to the total number of trials carried out.
Read the definitionIndependence
Two events are independent when the outcome of one does not change the probability of the other in any way.
Read the definitionLaw of large numbers
The principle that, when a random experiment is repeated a large number of times, the observed frequency of a result approaches its theoretical probability.
Read the definitionMean
The central value of a set of results, obtained by dividing their sum by their count.
Read the definitionProbability
A measure of how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain), or as a percentage.
Read the definitionProbability distribution
The way probabilities are spread across the full set of possible outcomes of an experiment.
Read the definitionRandom variable
A numerical quantity whose value depends on the outcome of a random experiment.
Read the definitionSample space
The set of all possible results of a random experiment.
Read the definitionStandard deviation
The square root of the variance; a measure of spread expressed in the same unit as the results.
Read the definitionUniform distribution
A distribution in which every possible outcome has exactly the same probability.
Read the definitionVariance
A measure of how spread out results are around their mean: the larger it is, the more scattered the results.
Read the definitionChance and randomness
Chance
The unpredictable nature of an event whose outcome can neither be controlled nor known in advance with certainty.
Read the definitionDeterminism
The idea that a result is entirely fixed by its causes and starting conditions — the opposite of chance.
Read the definitionEntropy
A measure of the disorder or unpredictability of a source: the higher the entropy, the harder the result is to predict.
Read the definitionMonte Carlo method
A technique that estimates a quantity by repeating a large number of random draws and observing the average results.
Read the definitionPseudo-random number generator
An algorithm that produces sequences of numbers that appear random but are entirely determined by a starting value called the seed.
Read the definitionRandom
Depending on chance; whose result cannot be predicted with certainty before it occurs.
Read the definitionSeed
The starting value that determines the sequence of numbers produced by a pseudo-random number generator.
Read the definitionRandom draws
Bias
A systematic deviation that makes a result unfair and pulls it away from what chance would normally produce.
Read the definitionLottery
A game of chance in which numbers are drawn at random and you win by having predicted the right ones.
Read the definitionRandom draw
A method of selecting one or more items at random from a set, giving each one a fair chance of being chosen.
Read the definitionSampling
Selecting a subset (the sample) from a larger set (the population) to represent it or to draw items from it.
Read the definitionSampling with replacement
A drawing mode where each item selected is put back into the set before the next draw; it can therefore come up again.
Read the definitionSampling without replacement
A drawing mode where the item selected is not put back into the set; it therefore cannot come up again.
Read the definitionShuffling
An operation that reorders the items of a set at random, so that every arrangement is as likely as any other.
Read the definitionUrn model
A classic model in which you draw balls from an urn to reason simply about probabilities.
Read the definitionGames of chance
Chance
The probability that a favourable result occurs; in everyday language, the luck that smiles on someone or not.
Read the definitionFairness
The property of a game or draw in which every possible outcome has exactly the expected probability, with no hidden advantage.
Read the definitionGambler's fallacy
The mistaken belief that an "overdue" result becomes more likely after a run of opposite results.
Read the definitionGame of chance
A game whose outcome depends essentially on chance, rather than on the player's skill or strategy.
Read the definitionHouse edge
A structural gap, built into the rules of a money game, that makes the player's expected value negative over the long term.
Read the definitionOdds
A way of expressing a probability as a ratio between the chances of success and the chances of failure.
Read the definitionPayout
What a player wins in case of a favourable result; to be weighed against the loss in case of failure.
Read the definitionStake
The sum or value a player commits to an uncertain result, which is lost or grows depending on the outcome.
Read the definitionMathematics
Arrangement
An ordered selection of elements taken without repetition from a set: order matters, but you do not reuse an element already chosen.
Read the definitionCombination
A way of choosing elements from a set without taking into account the order in which they are selected.
Read the definitionCombinatorics (counting)
Branch of mathematics that counts the number of possible arrangements, combinations and permutations.
Read the definitionFactorial
Product of all the integers from 1 up to a number n, written n!; it counts the number of ways to order n elements.
Read the definitionPermutation
A way of ordering elements where order matters; each different order is a distinct permutation.
Read the definitionCulture and beliefs
Destiny
The idea that the future is already fixed in advance — a view opposed to that of chance.
Read the definitionFatalism
A supposed force that makes certain events unavoidable, no matter what one does.
Read the definitionFortune
The personification or idea of luck distributing favorable and unfavorable outcomes, independently of merit.
Read the definitionSuperstition
A belief linking facts that have no real causal connection, such as a lucky charm thought to influence a draw.
Read the definition