---
title: "Board glossary"
url: https://lotto649.ws/glossary/
description: "Definitions of the vocabulary used across this board: expected value, house edge, overround, variance, par sheets, pari-mutuel pools and the rest."
---

# Board glossary

[Lotto649](https://lotto649.ws/)

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

[Board index](https://lotto649.ws/) › 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.