Volatility, variance and the words around a game’s statistics

Volatility / variance

Volatility describes how dispersed a game’s outcomes are. Variance is a specific mathematical measure of dispersion, based on squared distances from the mean. The words are related, but they should not be assumed to name the same numeric quantity.

The Commission’s monitoring guidance says standard deviation is most commonly used to represent game volatility.

In a casino’s game information, a label such as “high volatility” is not a variance calculation. Without the publisher’s scale and definition, it cannot be converted into an exact figure or reliably compared with another supplier’s label. Record it as the description supplied, not as a universal unit.

The distinction is between a product description and a defined statistic. Neither tells you what the next result will be. A low-volatility label is also not a statement that gambling is harmless or suitable for an individual.

For the longer discussion of return figures and sessions, read RTP and your session; this entry only fixes the vocabulary.

Sources: Live return to player performance monitoring of games of chance; 1.3.5.6. Measures of Scale.

Variance / standard deviation

Standard deviation is the square root of variance. The distinction matters because squaring changes the units: if observations are expressed in pounds, their variance is expressed in squared pounds and their standard deviation returns to pounds. They are connected measures, not identical numbers with different names.

An invented variance of 9 squared units corresponds to a standard deviation of 3 units. That small calculation identifies the relationship only. It is not the variance of any casino game, a predicted loss or a way to choose how much to stake.

A published figure also needs its measurement basis: pounds, stake multiples or another defined unit.

If you are copying a number, copy its label and unit too. “Volatility 3” without those details is insufficient to reconstruct what was calculated. Do not square an unexplained star rating or adjective scale and call the result variance.

Odds & Ends covers the longer mathematical context; this entry is a definition and a units check.

Sources: 1.3.5.6. Measures of Scale.

Range / variance

Range is the largest value minus the smallest value in a set. Variance concerns distances from the mean across the set. Range therefore uses the extremes, whereas variance contains information about the observations between them.

A maximum-prize headline is not either of these complete statistics.

For a minimal invented comparison, take the sets 0, 0, 10 and 0, 5, 10. Each has a range of 10, although its values are arranged differently. You do not need to calculate a casino’s volatility to see that matching extremes do not describe the whole pattern.

These are abstract numbers, not a prize table or recorded play.

When a page uses “range”, check whether it actually means an observed minimum-to-maximum span, a permitted stake interval or a list of possible configurations. The label needs that object. A provider’s range of RTP settings is not a measure of outcome dispersion.

The general comparison of casino probabilities belongs with Odds & Ends, rather than a longer glossary calculation here.

Sources: 1.3.5.6. Measures of Scale.

Mean / median

The arithmetic mean is the sum of observations divided by their count. The median is the middle observation once the values are ordered, or the mean of the two middle observations when the count is even. Both describe the centre of a set; neither is a measure of its spread.

With the invented values 0, 0 and 30, the mean is 10 and the median is 0. The calculation is (0 + 0 + 30) ÷ 3 = 10; the middle ordered value is 0. Calling either one simply “the typical result” would conceal which summary was used.

No real game or player dataset is represented.

For a statement about customers, sessions or payouts, ask what each observation represents before comparing averages. An average per account is not automatically an average per person. Casino Data Desk explains those measurement questions in longer form.

Here the useful distinction is centre versus spread, followed by mean versus median within the centre category.

Sources: 1.3.5.1. Measures of Location.

Theoretical RTP / actual RTP

Theoretical RTP is the designed return percentage under the relevant game conditions. Actual RTP is calculated from the returns and stakes recorded in a specified body of play. The Commission’s monitoring guidance treats them as separate measures when assessing operational game performance.

If an invented dataset contains £200 in total stakes and £180 in returns, its actual return percentage is £180 ÷ £200 × 100 = 90%. That arithmetic alone does not identify the designed RTP, establish a defect or predict another session. It describes only the supplied totals.

The dataset here is fabricated for explanation, not presented as a measurement.

The label “actual” therefore needs a period and a dataset. It does not mean a universally truer percentage that replaces the game’s design figure. A personal session is also not a substitute for an operator’s monitoring evidence.

RTP and your session covers the slot-specific interpretation; the glossary distinction is between a design quantity and an observed summary.

Sources: Live return to player performance monitoring of games of chance; Remote gambling and software technical standards (RTS) - RTS 3 – Rules, game descriptions and the likelihood of winning.

RTP / house edge

RTP describes the long-run share of stakes returned under the specified conditions. House edge expresses the casino’s expected retained share. When both are defined for the same game, rules and stake basis, they are complementary descriptions: an illustrative 96% RTP corresponds to a 4% house edge, because 100% − 96% = 4%.

The qualification about the same basis matters. Do not combine a headline percentage from one mode with an edge quoted for another set of rules. Neither percentage is a fee charged identically on every round, and the illustration does not promise that a £100 deposit will end as £96.

Deposits and the total amount staked are different objects.

This entry names the relationship without offering a strategy or comparing operators. How the house edge actually works supplies the longer explanation. Knowing the vocabulary does not remove the risk of losing money, and increasing play to try to approach an average is not a conclusion these definitions support.

Sources: Return to player - how much gaming machines payout; Remote gambling and software technical standards (RTS) - RTS 3 – Rules, game descriptions and the likelihood of winning.

Prize frequency / prize size

Prize frequency concerns how often a defined prize event occurs. Prize size concerns the amount awarded when it does. A paytable can describe the second without giving enough information to calculate the first.

“Up to” a particular amount is not the probability of receiving it.

Keep the event definition beside the frequency. Does the wording count any positive award, an award above the stake, or entry into a feature? Those are different events.

Without the game’s definition, a quoted frequency cannot tell you how often a player finishes a round ahead. No frequency for a named game has been verified for this article.

The quick-reference table keeps the questions separate. Its purpose is to select the correct label before looking for the number, not to infer missing odds from artwork. For the longer game-specific explanation, use Reel & Story; for any actual title, use that title’s rules.

A prominent prize amount is still only the information its document supports.

Sources: Remote gambling and software technical standards (RTS) - RTS 3 – Rules, game descriptions and the likelihood of winning.

Probability / observed frequency

Probability is a model’s likelihood of an event. Observed frequency counts how often the event appeared in a particular dataset. They can be compared, but a short observed run does not automatically replace the model or establish that its probabilities changed.

In an invented record of ten events, three occurrences give an observed frequency of 3 ÷ 10 = 30%. That calculation says nothing by itself about the next event. It also does not establish a 30% designed probability.

The event definition, selection of observations and relevant model would all need to be specified.

The Commission’s standards distinguish expected probabilities from game outputs, while its monitoring guidance requires context when interpreting deviations. This glossary has not tested an RNG or analysed a game. For the mathematical treatment of independence and uncertainty, follow Odds & Ends.

The short definition ends at a disciplined sentence: “three of the ten recorded events”, rather than a claim about what a player is due next.

Sources: Remote gambling and software technical standards (RTS) - RTS 7 – Generation of random outcomes; Live return to player performance monitoring of games of chance.