Dice in the context of Randomly

A tabletop role-playing game (TTRPG or TRPG), also known as a pen-and-paper role-playing game, is a kind of role-playing game (RPG) in which the participants describe their characters' actions through speech and sometimes movements. Participants determine the actions of their characters based on their characterization, and the actions succeed or fail according to a set formal system of rules and guidelines, usually involving randomization (such as through dice). Within the rules, players have the freedom to improvise, and their choices shape the direction and outcome of the game.Neither pen and paper nor a table are strictly necessary for a game to count as a TTRPG; rather, the terms pen-and-paper and tabletop are typically used to distinguish this format of RPG from role-playing video games or live action role-playing games. Online play of TTRPGs through videoconferencing has become common since the COVID-19 pandemic.

Some common examples of tabletop role-playing games include Dungeons & Dragons, Call of Cthulhu, and Pathfinder.

In common usage, randomness is the apparent or actual lack of definite patterns or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if there is a known probability distribution, the frequency of different outcomes over repeated events (or "trials") is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy.

The fields of mathematics, probability, and statistics use formal definitions of randomness, typically assuming that there is some 'objective' probability distribution. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness.

Information theory is the mathematical study of the quantification, storage, and communication of information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley. It is at the intersection of electronic engineering, mathematics, statistics, computer science, neurobiology, physics, and electrical engineering.

A key measure in information theory is entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip (which has two equally likely outcomes) provides less information (lower entropy, less uncertainty) than identifying the outcome from a roll of a die (which has six equally likely outcomes). Some other important measures in information theory are mutual information, channel capacity, error exponents, and relative entropy. Important sub-fields of information theory include source coding, algorithmic complexity theory, algorithmic information theory and information-theoretic security.

Cleromancy is a form of sortition (casting of lots) in which an outcome is determined by means that normally would be considered random, such as the rolling of dice (astragalomancy), but that are sometimes believed to reveal the will of a deity.

In geometry, an icosahedron (/ˌaɪkɒsəˈhiːdrən, -kə-, -koʊ-/ or /aɪˌkɒsəˈhiːdrən/) is a polyhedron with 20 faces. The name comes from Ancient Greek εἴκοσι (eíkosi) 'twenty' and ἕδρα (hédra) 'seat'. The plural can be either "icosahedra" (/-drə/) or "icosahedrons".

There are infinitely many non-similar shapes of icosahedra, some of them being more symmetrical than others. The best known is the (convex, non-stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles.

A game board (or gameboard; sometimes, playing board or game map) is the surface on which one plays a board game.

The oldest known game boards may date to Neolithic times; however, some scholars argue these may not have been game boards at all. Early Bronze Age artifacts are more universally recognized as game boards (for games such as Egyptian senet and mehen, and the Mesopotamian Royal Game of Ur). Most ancient board games were race games, utilizing random outcome generators like dice.

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' in its mathematical definition refers to neither randomness nor variability but instead is a mathematical function in which

• the domain is the set of possible outcomes in a sample space (e.g. the set ${\displaystyle \{H,T\}}$ which are the possible upper sides of a flipped coin heads ${\displaystyle H}$ or tails ${\displaystyle T}$ as the result from tossing a coin); and
• the range is a measurable space (e.g. corresponding to the domain above, the range might be the set ${\displaystyle \{-1,1\}}$ if say heads ${\displaystyle H}$ mapped to -1 and ${\displaystyle T}$ mapped to 1). Typically, the range of a random variable is a subset of the real numbers.

Informally, randomness typically represents some fundamental element of chance, such as in the roll of a die; it may also represent uncertainty, such as measurement error. However, the interpretation of probability is philosophically complicated, and even in specific cases is not always straightforward. The purely mathematical analysis of random variables is independent of such interpretational difficulties, and can be based upon a rigorous axiomatic setup.

In probability theory and logic, a set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the events 1, 2, 3, 4, 5, and 6 are collectively exhaustive, because they encompass the entire range of possible outcomes.

Another way to describe collectively exhaustive events is that their union must cover all the events within the entire sample space. For example, events A and B are said to be collectively exhaustive if

A quincunx (/ˈkwɪn.kʌŋks/ KWIN-kunks) is a geometric pattern consisting of five points arranged in a cross, with four of them forming a square or rectangle and a fifth at its center. The same pattern has other names, including "in saltire" or "in cross" in heraldry (depending on the orientation of the outer square), the five-point stencil in numerical analysis, and the five dots tattoo. It forms the arrangement of five units in the pattern corresponding to the five-spot on six-sided dice, playing cards, and dominoes. It is represented in Unicode as U+2059 ⁙ FIVE DOT PUNCTUATION or (for the die pattern) U+2684 ⚄ DIE FACE-5.

Saturnalia is an ancient Roman festival and holiday in honour of the god Saturn, held on 17 December in the Julian calendar and later expanded with festivities until 19 December. By the 1st century BC, the celebration had been extended until 23 December, for a total of seven days of festivities. The holiday was celebrated with a sacrifice at the Temple of Saturn, in the Roman Forum, and a public banquet, followed by private gift-giving, continual partying, and a carnival atmosphere that overturned Roman social norms: gambling was permitted, and masters provided table service for their slaves as it was seen as a time of liberty for both slaves and freedmen alike. A common custom was the election of a "King of the Saturnalia", who gave orders to people, which were followed and presided over the merrymaking. The gifts exchanged were usually gag gifts or small figurines made of wax or pottery known as sigillaria. The poet Catullus called it "the best of days".

Saturnalia was the Roman equivalent to the earlier Greek holiday of Kronia, which was celebrated during the Attic month of Hekatombaion in late midsummer. It held theological importance for some Romans, who saw it as a restoration of the ancient Golden Age, when the world was ruled by Saturn. The Neoplatonist philosopher Porphyry interpreted the freedom associated with Saturnalia as symbolizing the "freeing of souls into immortality". Saturnalia may have influenced some of the customs associated with later celebrations in western Europe occurring in midwinter, particularly traditions associated with Christmas, the Feast of the Holy Innocents, and Epiphany. In particular, the historical western European Christmas custom of electing a "Lord of Misrule" may have its roots in Saturnalia celebrations.

Gambling (also known as betting or gaming) is the wagering of something of value ("the stakes") on a random event with the intent of winning something else of value, where instances of strategy are discounted. Gambling thus requires three elements to be present: consideration (an amount wagered), risk (chance), and a prize. The outcome of the wager is often immediate, such as a single roll of dice, a spin of a roulette wheel, or a horse crossing the finish line, but longer time frames are also common, allowing wagers on the outcome of a future sports contest or even an entire sports season.

The term "gaming" in this context typically refers to instances in which the activity has been specifically permitted by law. The two words are not mutually exclusive; i.e., a "gaming" company offers (legal) "gambling" activities to the public and may be regulated by one of many gaming control boards, for example, the Nevada Gaming Control Board. However, this distinction is not universally observed in the English-speaking world. For instance, in the United Kingdom, the regulator of gambling activities is called the Gambling Commission (not the Gaming Commission). The word gaming is used more frequently since the rise of computer and video games to describe activities that do not necessarily involve wagering, especially online gaming, with the new usage still not having displaced the old usage as the primary definition in common dictionaries. "Gaming" has also been used euphemistically to circumvent laws against "gambling". The media and others have used one term or the other to frame conversations around the subjects, resulting in a shift of perceptions among their audiences.

A game of skill is a game where the outcome is determined mainly by mental or physical skill, rather than chance.

Alternatively, a game of chance is one where its outcome is strongly influenced by some randomizing device, such as dice, spinning tops, playing cards, roulette wheels, or numbered balls drawn from a container.

Trictrac (also tric trac or tric-trac) is a French board game of skill and chance for two players that is played with dice on a game board similar, but not identical, to that of backgammon (the difference being that the edges of a true trictrac board are perforated for score-marking purposes). It was "the classic tables game" of France in the way that backgammon is in the English-speaking world.

Trictrac's gaming interest lies in its multiple combinations, the importance of decision-making and its comprehensive rules which have been well documented and remained stable since the early 17th century. It requires constant attention from the players whether or not it is their turn. Its vocabulary, which is very rich, frequently occurs in French literature.

Dominoes is a family of tile-based games played with gaming pieces. Each domino is a rectangular tile, usually with a line dividing its face into two square ends. Each end is marked with a number of spots (also called pips or dots) or is blank. The backs of the tiles in a set are indistinguishable, either blank or having some common design. The gaming pieces make up a domino set, sometimes called a deck or pack. The traditional European domino set consists of 28 tiles, also known as pieces, bones, rocks, stones, men, cards or just dominoes, featuring all combinations of spot counts between zero and six. A domino set is a generic gaming device, similar to playing cards or dice, in that a variety of games can be played with a set. Another form of entertainment using domino pieces is the practice of domino toppling.

The earliest mention of dominoes is from Song dynasty China found in the text Former Events in Wulin by Zhou Mi (1232–1298). Modern dominoes first appeared in Italy during the 18th century, but they differ from Chinese dominoes in a number of respects, and there is no confirmed link between the two. European dominoes may have developed independently, or Italian missionaries in China may have brought the game to Europe.

A game of chance is in contrast with a game of skill. It is a game whose outcome is strongly influenced by some randomizing device. Common devices used include dice, spinning tops, playing cards, roulette wheels, numbered balls, or in the case of digital games random number generators. A game of chance may be played as gambling if players wager money or anything of monetary value.

Alternatively, a game of skill is one in which the outcome is determined mainly by mental or physical skill, rather than chance.

In probability theory, a probability space or a probability triple ${\displaystyle (\Omega ,{\mathcal {F}},P)}$ is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a dice.

A probability space consists of three elements: