A throw of which number on each of a pair of dice is known as Snake Eyes?
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Dice.txt Snake_eyes.txt
Dice Snake eyes
Dice (singular die or dice;  from Old French dé; from Latin datum "something which is given or played" ) are small throwable objects with multiple resting positions, used for generating random numbers. Dice are suitable as gambling devices for games like craps and are also used in non-gambling tabletop games.

A traditional die is a cube, with each of its six faces showing a different number of dots (pips) from 1 to 6. When thrown or rolled, the die comes to rest showing on its upper surface a random integer from one to six, each value being equally likely. A variety of similar devices are also described as dice; such specialized dice may have polyhedral or irregular shapes and may have faces marked with symbols instead of numbers. They may be used to produce results other than one through six. Loaded and crooked dice are designed to favor some results over others for purposes of cheating or amusement.

A dice tray, a tray used to contain thrown dice, is sometimes used for gambling or board games, in particular to allow dice throws which do not interfere with other game pieces.

History

Dice likely originated in the ancient Middle East. One of the oldest known dice games was excavated from a Mesopotamian tomb, dating to the 24th century BCE.  British archaeologist Leonard Woolley discovered the dice in the Royal Cemetery at Ur with a board game known as the Royal Game of Ur. Two types of dice, stick dice and tetrahedral dice (dice with four triangular surfaces), were found with the board game.  Unlike modern dice, the numbers on the opposite sides of Mesopotamian dice were consecutive numbers rather than numbers that add up to seven. 

The Egyptian game of Senet was played with dice. Senet was played before 3000 BC and up to the 2nd century AD. It was likely a racing game, but there is no scholarly consensus on the rules of Senet.  Dicing is mentioned as an Indian game in the Rigveda, Atharvaveda and Buddha games list.  There are several biblical references to "casting lots", as in Psalm 22, indicating that dicing (or a related activity) was commonplace when the psalm was composed. It is theorized that dice developed from the practice of fortunetelling with the talus of hoofed animals, colloquially known as "knucklebones", but knucklebones is not the oldest divination technique that incorporates randomness. Knucklebones was a game of skill played by women and children; a derivative form had the four sides of the bone receive different values and count as modern dice. 

Although gambling was illegal, many Romans were passionate gamblers that enjoyed dicing, which was known as aleam ludere ("to play at dice"). Dicing was even a popular pastime of emperors. Letters by Augustus to Tacitus and his daughter recount his hobby of dicing. There were two sizes of Roman dice. Tali were large dice inscribed with one, three, four, and six on four sides. Tesserae were smaller dice with sides numbered from one to six.  Twenty-sided dice date back to the 2nd century AD   and from Ptolemaic Egypt as early as 2nd century BC. 

Dominoes and playing cards originated in China as developments from dice. The transition from dice to playing cards occurred in China around the Tang dynasty, and coincides with the technological transition from rolls of manuscripts to block printed books.  In Japan, dice were used to play a popular game called sugoroku. There are two types of sugoroku. Ban-sugoroku is similar to backgammon and dates to the Heian period, while e-sugoroku is a racing game. 

Usage

Dice are thrown onto a flat surface either from the hand or from a container designed for this (such as a dice cup). The face of the die that is uppermost when it comes to rest provides the value of the throw. One typical dice game today is craps, where two dice are thrown simultaneously and wagers are made on the total value of the two dice. Dice are frequently used to randomize moves in board games, usually by deciding the distance through which a piece will move along the board; examples of this are backgammon and Monopoly.

The result of a die roll is determined by the way it is thrown, according to the laws of classical mechanics. A die roll is made random by uncertainty in minor factors such as tiny movements in the thrower's hand; They are thus a crude form of hardware random number generator. Perhaps to mitigate against concerns that the pips on the faces of certain styles of dice cause a small bias, casinos use precision dice with flush markings.

Construction

Arrangement

Common dice are small cubes most commonly  across, whose faces are numbered from one to six, usually by patterns of round dots called pips. (While the use of Hindu-Arabic numerals is occasionally seen, such dice are less common.) Opposite sides of a die traditionally add up to seven, implying that the 1, 2 and 3 faces share a vertex;  these faces may be placed clockwise or counterclockwise about this vertex. If the 1, 2 and 3 faces run counterclockwise, the die is called "right-handed", and if those faces run clockwise, the die is called "left-handed". Western dice are normally right-handed, and Chinese dice are normally left-handed. 

The pips on dice are arranged in specific patterns as shown. Asian style dice bear similar patterns to Western ones, but the pips are closer to the center of the face; in addition, the pips are differently sized on Asian style dice, and the pips are colored red on the 1 and 4 sides. One possible explanation is that red fours are of Indian origin.  In some older sets, the "one" pip is a colorless depression.

Manufacturing

Non-precision dice are manufactured via the plastic injection molding process. The pips or numbers on the die are a part of the mold. The coloring for numbering is achieved by submerging the die entirely in paint, which is allowed to dry. The die is then polished via a tumble finishing process similar to rock polishing. The abrasive agent scrapes off all of the paint except for the indents of the numbering. A finer abrasive is then used to polish the die. This process also creates the smoother, rounded edges on the dice. 

Precision casino dice may have a polished or sand finish, making them transparent or translucent respectively. Casino dice have their pips drilled, then filled flush with a paint of the same density as the material used for the dice, such that the center of gravity of the dice is as close to the geometric center as possible. All such dice are stamped with a serial number to prevent potential cheaters from substituting a die. Precision backgammon dice are made the same way; they tend to be slightly smaller and have rounded corners and edges, to allow better movement inside the dice cup and stop forceful rolls from damaging the playing surface.

Terms

While the terms ace, deuce, trey, cater, cinque and sice have been made obsolete by one to six, they are still used by some professional gamblers to designate different sides of the dice. Ace is from the Latin as, meaning "a unit";  the others are 2 to 6 in old French. 

Loaded dice

A loaded, weighted or crooked die is one that has been tampered with so that it will land with a specific side facing upwards more or less often than a fair die would. There are several methods for creating loaded dice, including round faces, off-square faces and weights. "Tappers" have a mercury drop in a reservoir at the center, with a capillary tube leading to another reservoir at a side; the load is activated by tapping the die so that the mercury travels to the side.

Another type of loaded die is hollow with a small weight and a semi-solid substance inside whose melting point is just lower than the temperature of the human body, allowing the cheater to change the loading of the die by applying body heat, causing the semi-solid to melt and the weight to drift down, making the chosen opposite face more likely to land up. A less common type of loaded die can be made by inserting a magnet into the die and embedding a coil of wire in the game table; running current through the coil increases the likelihood of a certain side landing on the bottom, depending on the direction of the current. Transparent acetate dice, used in all reputable casinos, are harder to tamper with than other dice.

A die may be shaved on one side, making it slightly shorter in one dimension, thus affecting its outcome. One countermeasure employed by casinos against shaved dice is to measure the dice with a micrometer before playing. 

Representation

Using Unicode characters, the faces ⚀ ⚁ ⚂ ⚃ ⚄ ⚅, can be shown in text using the range U+2680 to U+2685 or using decimal ⚀ to ⚅. 

Variants

Polyhedral dice

Around the end of the 1960s, non-cubical dice became popular among players of wargames,  and since have been employed extensively in role-playing games and trading card games. The numerals 6 and 9, which are reciprocally symmetric through rotation, are distinguished with a dot or underline.

Standard variations

Dice are often sold in sets, matching in color, of five or six different shapes. They are also sold frequently with a second 10-sided die of a complementary or contrasting color. Sometimes, dice are sold additionally with a die resembling the five Platonic solids, whose faces are regular polygons, or the pentagonal trapezohedron die, whose faces are ten kites, each with two different edge lengths, three different angles, and two different kinds of vertices.

The other four Platonic solids are the most common non-cubical dice; these can have 4, 8, 12, and 20 faces. The only other common non-cubical die is the 10-sided die. Using these dice in various ways, games can closely approximate the real probability distributions of the events they simulate. For instance, 10-sided dice can be rolled in pairs to produce a uniform distribution of random percentages; and summing the values of multiple dice will produce approximations to normal distributions. 

Unlike other common dice, a four-sided die does not have a side that faces upward when it is at rest on a surface, so it has to be read in a different way. Many such dice have the numbers printed around the points, so that when it settles, the numbers at the vertex pointing up are the same and the one counted. Alternately, the numbers on a tetrahedral die can be placed at the middles of the edges, in which case the numbers around the base are read.

Normally, the faces on a die will be placed so opposite faces will add up to one more than the number of faces (but in the case of a dice with 4 sides and dice with an odd-number of faces, this is simply not possible). Some dice, such as those with 10 sides, are usually numbered sequentially beginning with 0, in which case the opposite faces will add to one less than the number of faces.

Rarer variations

"Uniform fair dice" are dice where all faces have equal probability of outcome, which follows from the symmetry of the die (as it is face-transitive), and include:
* Platonic solids, the five regular polyhedra: 4, 6, 8, 12, 20 sides
* Catalan solids, the duals of the 13 Archimedean solids: 12, 24, 30, 48, 60, 120 sides
* Bipyramids, the duals of the infinite set of prisms, with triangle faces: any even number above 4, and usually divisible by 4 so that a face will face up
* Trapezohedrons, the duals of the infinite set of antiprisms, with kite faces: any even number above 4
* Disphenoids, an infinite set of tetrahedra made from congruent non-regular triangles: 4 sides

Dice with an odd number of flat faces can be made as "long dice".  They are based on an infinite set of prisms. All the (rectangular) faces they may actually land on are congruent, so they are equally fair. (The other 2 sides of the prism are rounded or capped with a pyramid, designed so that the die never actually rests on those faces.)

Non-numeric

The faces of most dice are labelled using sequences of whole numbers, usually starting at one, expressed with either pips or digits. However, there are some applications that require results other than numbers. Examples include letters for Boggle, directions for Warhammer Fantasy Battle, playing card symbols for poker dice, and instructions for sexual acts using sex dice.

Fudge dice are cubical dice featuring two sides marked with plus signs, two with minus signs, and two blank. These are rolled in groups of four, with each plus sign adding to the total, while each minus sign reduces it; blank sides are ignored. This generates a range between –4 and +4.  They are also used in the Fate role-playing game.

Spherical dice

A die can be constructed in the shape of a sphere, with the addition of an internal cavity in the shape of the dual polyhedron of the desired die shape and an internal weight. The weight will settle in one of the points of the internal cavity, causing it to settle with one of the numbers uppermost. For instance, a sphere with an octahedral cavity and a small internal weight will settle with one of the 6 points of the cavity held downwards by the weight.

Applications

Polyhedral dice are commonly used in role-playing games. The fantasy role-playing game Dungeons & Dragons (D&D) is largely credited with popularizing dice in such games. Some games use only one type, like Exalted which uses only ten-sided dice. Others use numerous types for different game purposes, such as D&D, which makes use of all common polyhedral dice. Dice are usually used to determine the outcome of events. Games typically determine results either as a total on one or more dice above or below a fixed number, or a certain number of rolls above a certain number on one or more dice. Due to circumstances or character skill, the initial roll may have a number added to or subtracted from the final result, or have the player roll extra or fewer dice. To keep track of rolls easily, dice notation is frequently used.

Many board games use dice to randomize how far pieces move or to settle conflicts. Typically, this has meant that rolling higher numbers is better. Some games, such as Axis & Allies, have inverted this system by making the lower values more potent. In the modern age, a few games and game designers have approached dice in a different way by making each side of the die similarly valuable. In Castles of Burgundy, players spend their dice to take actions based on the die's value. In this game, a six is not better than a one, or vice-versa. In Quarriors (and its descendent, Dicemasters), different sides of the dice can offer completely different abilities. Several sides often give resources while others grant the player useful actions. 

Dice can be used for divination and using dice for such a purpose is called cleromancy. A pair of common dice is usual, though other forms of polyhedra can be used. Tibetan Buddhists sometimes use this method of divination. It is highly likely that the Pythagoreans used the Platonic solids as dice. They referred to such dice as "the dice of the gods" and they sought to understand the universe through an understanding of geometry in polyhedra. 

Astrological dice are a specialized set of three 12-sided dice for divination; the first die represents planets, the Sun, the Moon, and the nodes of the Moon, the second die represents the 12 zodiac signs, and the third represents the 12 houses. A specialized icosahedron die provides the answers of the Magic 8-Ball, conventionally used to provide answers to yes-or-no questions.

Notation

In many gaming contexts, especially tabletop role-playing games, shorthand notations representing different dice rolls are used. A "d" or "D" is used to indicate a die with a specific number of sides; for example, d4 denotes a four-sided die. If several dice of the same type are to be rolled, this is indicated by a leading number specifying the number of dice. Hence, 6d8 means the player should roll six eight-sided dice and add the results. Modifiers to a die roll can also be indicated as desired. For example, 3d6+4 instructs the player to roll three six-sided dice, calculate the total, and add four to it. In gambling in general and the game of Craps in particular, snake eyes is the outcome of rolling the dice in a game and getting only one pip on each die. The pair of pips resembles a pair of eyes, which is appended to the term 'snake' because of the long-standing association of this word with treachery and betrayal. The dictionary of etymology traces that use of the term back to 1929,  although it may be traced all the way back to the ancient Roman dice games, where 'Dogs' represented two ones. They referred to this as "the dog throw". In modern parlance, it refers to such a roll in any game involving dice.

Because this is the lowest possible roll, and will often be a loser in many dice games, such as Craps, the term has been employed in a more general usage as a reference to bad luck. In some board games, such as Monopoly, house rules may decide that this roll earns the player a bonus due to it being rare and otherwise disadvantageous. 

Probability

The odds of rolling snake eyes on two six-sided dice are 1-in-36.
1 one One
1 one
one
Numerical
One
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