A reference board on games of chance, their mathematics and their history

Board glossary

20 terms defined, in alphabetical order, revised 17 August 2026. Each definition restates only what is derived elsewhere on this board.

Definitions

Binomial coefficient: The count of distinct unordered selections of k items from a pool of n, written as n choose k. It gives the number of possible tickets in a draw matrix.
Conditional probability: The probability of an event given that something else is already known. It is the working tool for card games, where each exposed card changes what remains.
Decimal odds: A price expressed as the total return per unit staked, including the stake. It is the fractional figure plus one, and its reciprocal is the implied probability.
Expected value: The average result of a wager, found by multiplying each outcome by its probability and adding the products. It describes the design of a game, not any single play.
Fractional odds: A price expressed as profit against stake. Odds of a/b imply a probability of b divided by the sum of a and b.
Gambler's fallacy: The belief that an outcome becomes more likely because it has not occurred recently. Independent mechanisms have no memory, so nothing about the past alters the next trial.
Hit frequency: The proportion of plays that return anything at all. It is independent of theoretical return, and two machines with the same return can differ widely in it.
Hold: The share of the money brought to a game that is not carried away. It exceeds the house edge because returned money is frequently staked again.
House edge: The expected cost per unit staked, arising because the paytable pays less than the true odds of the event it pays on.
Implied probability: The probability that would make a quoted price break even. It is a statement about the price, not about the world.
Independence: The property that the outcome of one trial leaves the probabilities of the next unchanged. Dice, wheels and properly seeded generators have it; a dealt deck does not.
Law of large numbers: The theorem that the observed average of independent trials converges towards the expected value as the number of trials grows.
Overround: The amount by which the implied probabilities of a complete set of quoted prices exceed one. It is the margin built into the book.
Par sheet: The document specifying every symbol, weight and payout of a reel machine, and therefore its complete probability model.
Pari-mutuel: A pool arrangement in which a fixed proportion of stakes is distributed among winners, so the operator's margin does not depend on the outcome.
Return to player: The complement of the house edge: the proportion of each unit staked returned as winnings on average across a complete cycle.
Rollover: The carrying forward of an unwon prize tier to the next draw. Matrix size is chosen largely to control how often it happens.
Variance: A measure of how widely results scatter around their average. It is separate from expected value and governs what a short run feels like.
Virtual stop: A weighted position behind a display reel symbol, allowing a symbol's visual frequency to differ from its actual probability.
Volatility: The practical description of variance in a machine's design: how the same theoretical return is distributed between frequent small returns and rare large ones.