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86-412: 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
172-400: 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
258-400: A standard , expresses a dice roll as n d s or n D s , where n is the number of dice rolled and s is the number of sides on each die; if only one die is rolled, n is normally not shown. For example, d4 denotes one four-sided die; 6d8 means the player should roll six eight-sided dice and sum the results. The notation also allows for adding or subtracting a constant amount c to
344-415: A counting sequence starting at one. One variation on the standard die is known as the "average" die. These are six-sided dice with sides numbered 2, 3, 3, 4, 4, 5 , which have the same arithmetic mean as a standard die (3.5 for a single die, 7 for a pair of dice), but have a narrower range of possible values (2 through 5 for one, 4 through 10 for a pair). They are used in some table-top wargames , where
430-414: A different color for the dots of each different end value (one-spots might have black pips while two-spots might be green, three red, etc.) to facilitate finding matching ends. Occasionally, one may find a domino set made of card stock like that for playing cards . Such sets are lightweight, compact, and inexpensive, and like cards are more susceptible to minor disturbances such as a sudden breeze. Sometimes,
516-600: A different number of dots ( pips ) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely. Dice may also have polyhedral or irregular shapes, may have faces marked with numerals or symbols instead of pips and may have their numbers carved out from the material of the dice instead of marked on it. Loaded dice are specifically designed or modified to favor some results over others for cheating or entertainment. Dice have been used since before recorded history, and their origin
602-437: A different way. On some four-sided dice, each face features multiple numbers, with the same number printed near each vertex on all sides. In this case, the number around the vertex pointing up is used. Alternatively, the numbers on a tetrahedral die can be placed at the middle of the edges, in which case the numbers around the base are used. Normally, the faces on a die will be placed so opposite faces will add up to one more than
688-546: A double- n set is found by: n ( n + 1 ) ( n + 2 ) 2 {\displaystyle {\frac {n(n+1)(n+2)}{2}}} i.e. the number of tiles multiplied by the maximum pip-count ( n ) e.g. a 6-6 set has (7 × 8) / 2 = 56/2 = 28 tiles, the average number of pips per tile is 6 (range is from 0 to 12), giving a total pip count of 6 × 28 = 168 The most popular type of play are layout games, which fall into two main categories, blocking games and scoring games. The most basic domino variant
774-436: A double- n set obeys the following formula: which is also the ( n +1)th triangular number , as in the following table. This formula can be simplified a little bit when n {\displaystyle n} is made equal to the total number of doubles in the domino set : ( n ) ( n + 1 ) 2 {\displaystyle {\frac {(n)(n+1)}{2}}} The total number of pips in
860-501: A double-six set. However, this is a relatively small number, especially when playing with more than four people, so many domino sets are "extended" by introducing ends with greater numbers of spots, which increases the number of unique combinations of ends and thus of pieces. Each progressively larger set increases the maximum number of pips on an end by three; so the common extended sets are double-nine (55 tiles), double-12 (91 tiles), double-15 (136 tiles), and double-18 (190 tiles), which
946-492: A line in the middle to divide it visually into two squares, called ends. The value of either side is the number of spots or pips. In the most common variant (double-six), the values range from six pips down to none or blank. The sum of the two values, i.e. the total number of pips, may be referred to as the rank or weight of a tile; a tile may be described as "heavier" than a "lighter" one that has fewer (or no) pips. Tiles are generally named after their two values. For instance,
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#17327732159751032-407: A method by which dice can be used to generate passphrases . Diceware is a method recommended for generating secure but memorable passphrases, by repeatedly rolling five dice and picking the corresponding word from a pre-generated list. In many gaming contexts, especially tabletop role-playing games, shorthand notations representing different dice rolls are used. A very common notation, considered
1118-435: A narrower range of numbers is required. Other numbered variations include Sicherman dice and intransitive 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,
1204-475: 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. This mitigates concerns that the pips will cause a small bias. 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
1290-515: A pair of boxcars on a freight train. Many rolls have names in the game of craps . Using Unicode characters, the faces can be shown in text using the range U+2680 to U+2685 or using decimal ⚀ to ⚅ , and the emoji using U+1F3B2 or 🎲 from the Miscellaneous Symbols and Pictographs block. A loaded, weighted, cheat, or crooked die is one that has been tampered with so that it will land with
1376-623: A single six-sided die yields a uniform distribution, where each number from 1 to 6 has an equal chance of appearing. However, when rolling two dice and summing the results, the probability distribution shifts, as some sums (like 7) become more likely than others (like 2 or 12). These distributions can model real-world scenarios or mathematical constructs, making dice a practical tool for teaching and exploring concepts in probability theory. Common dice are small cubes , most often 1.6 cm (0.63 in) across, whose faces are numbered from one to six, usually by patterns of round dots called pips . (While
1462-454: A specific side facing upwards more often or less often than a fair die would. There are several methods for making loaded dice, including rounded faces, off-square faces, and weights. Casinos and gambling halls frequently use transparent cellulose acetate dice, as tampering is easier to detect than with opaque dice. Various shapes such as two-sided or four-sided dice are documented in archaeological findings; for example, from Ancient Egypt and
1548-405: 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. 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
1634-494: A surface such as the polyominoes in Blokus . Dice A die ( sg. : die or dice ; pl. : dice ) is a small, throwable object with marked sides that can rest in multiple positions. Dice are used for generating random values , commonly as part of tabletop games , including dice games , board games , role-playing games , and games of chance . A traditional die is a cube with each of its six faces marked with
1720-403: A variety of probability distributions . 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 (tetrahedral) die does not have a side that faces upward when it is at rest on a surface, so it must be read in
1806-486: A winning score, the winning player from the previous round starts the next game with any tile in their hand and the game proceeds normally. Another variant of the blocking game is the Latin American version and is played in teams of two. The stock is divided equally among all players, each having seven tiles in hand. Players sitting on opposite ends of the table are part of the same team. The game ends when one of
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#17327732159751892-475: 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 introduce randomness into board games , where they are often used to decide the distance through which a piece will move along the board (as in backgammon and Monopoly ). Thrown or simulated dice are sometimes used to generate specific probability distributions, which are fundamental to probability theory . For example, rolling
1978-629: Is a member of two suits: for example, 🀴 belongs both to the suit of threes and the suit of blanks, or 0 suit. In some versions the doubles can be treated as an additional suit of doubles. In these versions, the 🁡 belongs both to the suit of sixes and the suit of doubles. However, the dominant approach is that each double belongs to only one suit. The most common domino sets commercially available are double six (with 28 tiles) and double nine (with 55 tiles). Larger sets exist and are popular for games involving several players or for players looking for long domino games. The number of tiles in
2064-492: Is called "left-handed". Western dice are normally right-handed, and Chinese dice are normally left-handed. The pips on standard six-sided 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. Red fours may be of Indian origin. Non-precision dice are manufactured via
2150-468: Is for two players and requires a double-six set. The 28 tiles are shuffled face down and form the stock or boneyard . Each player draws seven tiles from the stock. Once the players begin drawing tiles, they are typically placed on-edge in front of the players, so players can see their own tiles, but not the value of their opponents' tiles. Players can thus see how many tiles remain in their opponents' hands at all times. One player begins by downing (playing
2236-447: Is formed by a double. In Muggins, players score by ensuring the total pip count of the open ends is a multiple of a certain number. In variants of Muggins, the line of play may branch due to spinners. In the common U.S. variant known as Fives players score by making the open ends a multiple of five. In British public houses and social clubs, a scoring version of "5s-and-3s" is used. The game is normally played in pairs (two against two) and
2322-714: Is frequently used. Astrological dice are a specialized set of three 12-sided dice for divination; the first die represents the 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. Dice can be used to generate random numbers for use in passwords and cryptography applications. The Electronic Frontier Foundation describes
2408-462: Is played as a series of "ends". In each "end", the objective is for players to attach a domino from their hand to one end of those already played so that the sum of the end tiles is divisible by five or three. One point is scored for each time five or three can be divided into the sum of the two tiles, i.e. four at one end and five at the other makes nine, which is divisible by three three times, resulting in three points. Double five at one end and five at
2494-459: Is similar to backgammon and dates to the Heian period (794–1185 CE), while e-sugoroku is a racing game . Dice are thrown onto a surface either from the hand or from a container designed for this (such as a cup, tray, or tower ). The face (or corner, in cases such as tetrahedral dice, or edge, for odd-numbered long dice ) of the die that is uppermost when it comes to rest provides the value of
2580-586: Is the Manual of the Xuanhe Period which purports to be written by Qu You (1341–1427), but some scholars believe it is a later forgery. The traditional 32-piece Chinese domino set, made to represent each possible face of two thrown dice and thus have no blank faces, differs from the 28-piece domino set found in the West during the mid 18th century, although Chinese dominoes with blank faces were known during
2666-437: Is the 10-sided die, a pentagonal trapezohedron die, whose faces are ten kites , each with two different edge lengths, three different angles, and two different kinds of vertices. Such sets frequently include a second 10-sided die either of contrasting color or numbered by tens, allowing the pair of 10-sided dice to be combined to generate numbers between 1 and 100. Using these dice in various ways, games can closely approximate
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2752-449: Is the configuration of played tiles on the table. It starts with a single tile and typically grows in two opposite directions when players add matching tiles. In practice, players often play tiles at right angles when the line of play gets too close to the edge of the table. The rules for the line of play often differ from one variant to another. In many rules, the doubles serve as spinners, i.e., they can be played on all four sides, causing
2838-482: Is the maximum in practice. As the set becomes larger, identifying the number of pips on each domino becomes more difficult, so some large domino sets use more readable Arabic numerals instead of pips. In China, early "domino" tiles were functionally identical to playing cards . An identifiable version of Chinese dominoes developed in the 12th or 13th century. The oldest written mention of domino tiles in China dates to
2924-459: 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 produces 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
3010-414: Is uncertain. It is hypothesized that dice developed from the practice of fortune-telling with the talus of hoofed animals, colloquially known as knucklebones . The Ancient Egyptian game of senet (played before 3000 BCE and up to the 2nd century CE) was played with flat two-sided throwsticks which indicated the number of squares a player could move, and thus functioned as a form of dice. Perhaps
3096-747: The Caribbean " but is also popular with the Windrush generation (who have Caribbean heritage) in the UK. In the U.S. state of Alabama , although rarely prosecuted, it was illegal to play dominoes on Sunday within the state until the relevant section of the Alabama Criminal Code was repealed, effective April 21, 2015. Dominoes (also known as bones, cards, men, pieces or tiles), are normally twice as long as they are wide, which makes it easier to re-stack pieces after use. A domino usually features
3182-529: The ancient Indian Rigveda , Atharvaveda , Mahabharata and Buddhist games list . There are several biblical references to "casting lots" ( Hebrew : יפילו גורל yappîlū ḡōrāl ), as in Psalm 22 , indicating that dicing (or a related activity) was commonplace when the psalm was composed. Knucklebones was a game of skill played in ancient Greece ; a derivative form had the four sides of bones receive different values like modern dice. Although gambling
3268-475: The 13th century and comes from Hangzhou where pupai (gambling plaques or tiles) and dice are listed as items sold by peddlers during the reign of Emperor Xiaozong of Song (r. 1162–1189). It is not entirely clear that pupai means dominoes, but the same term is used two centuries later by the Ming author Lu Rong (1436–1494) in a context that clearly describes domino tiles. The earliest known manual on dominoes
3354-504: The 17th century. Each domino originally represented one of the 21 results of throwing two six-sided dice (2d6). One half of each domino is set with the pips from one die and the other half contains the pips from the second die. Chinese sets also introduce duplicates of some throws and divide the tiles into two suits : military and civil. Chinese dominoes are also longer than typical European ones. Modern dominoes first appeared in Italy during
3440-516: 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. Having been established in Italy, the game of dominoes spread rapidly to Austria , southern Germany and France . The game became fashionable in France in
3526-472: The 2nd century BCE. 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 (618–907 CE), 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
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3612-571: The Middle East. While the cubical six-sided die became the most common type in many parts of the world, other shapes were always known, like 20-sided dice in Ptolemaic and Roman times. The modern tradition of using sets of polyhedral dice started around the end of the 1960s when non-cubical dice became popular among players of wargames , and since have been employed extensively in role-playing games and trading card games . Dice using both
3698-477: The basic scoring unit, worth 1 game point. The game was played to 31 and employed a cribbage board to keep score. In 1864, The American Hoyle describes three new variants: Muggins , Bergen and Rounce; alongside the Block Dominoes and Draw Dominoes. In Muggins, the cribbage board was dropped, 5 spots scored 5 points, and game was now 200 for two players and 150 for three or four. Despite the name, there
3784-546: The blank-blank (0–0) combination. Subsequently 45-piece ( double eight ) sets appeared in Austria and, in recent times, 55-piece ( double nine ) and 91-piece ( double twelve ) sets have been produced. All the early games are still played today alongside games that have sprung up in the last 60 years such as Five Up , Mexican Train and Chicken Foot , the last two taking advantage of the larger domino sets available. Some modern descriptions of All Fives are quite different from
3870-440: The board geometry during play. Each tile has a back (undifferentiated) side and a face side. Domino tiles are usually rectangular, twice as long as they are wide and at least twice as wide as they are thick, though games exist with square tiles, triangular tiles and even hexagonal tiles. Modern games may use unconventional non-tileable shapes such as the curved-shaped Bendominoes , or use many different shapes that together tile
3956-400: The dice cup and stop forceful rolls from damaging the playing surface. The word die comes from Old French dé ; from Latin datum "something which is given or played". While the terms ace , deuce , trey , cater , cinque and sice are generally obsolete, with the names of the numbers preferred, they are still used by some professional gamblers to designate different sides of
4042-526: The dice. Ace is from the Latin as , meaning "a unit"; the others are 2 to 6 in Old French . When rolling two dice, certain combinations have slang names. The term snake eyes is a roll of one pip on each die. The Online Etymology Dictionary traces use of the term as far back as 1919. The US term boxcars , also known as midnight , is a roll of six pips on each die. The pair of six pips resembles
4128-431: The double-six tile starts by downing that tile on the table and the game then proceeds counter-clockwise. Since there is no boneyard, a player without a matching tile passes their turn. A player that is unable to play is called a downed or sitting player. A less common alternation of the middle eastern game requires the player to the left of the sitting player to transfer one of their tiles (not necessarily playable) tile to
4214-433: The downed player. In this variant, if the transferred tile can be played, they have to down it. Similar to a normal blocking game, the game ends when a player empties their hand or the game is blocked. If the game is blocked, the player with the lightest hand receives points equal to the sum of all losing players' hands. A set of games ends when any player reaches a set amount of points, in which they win. If no player reached
4300-467: The duplicates that went with them. Moreover, according to Michael Dummett , in the Chinese games it is only the identity of the tile that matters; there is no concept of matching. Instead, the basic set of 28 unique tiles contains seven additional pieces, six of them representing the values that result from throwing a single die with the other half of the tile left blank, and the seventh domino representing
4386-666: The ends accumulating towards a total. The game ends when one of the pair's total score exceeds a set number of points. A running total score is often kept on a cribbage board. 5s-and-3s is played in a number of competitive leagues in the British Isles. Tile-based game A tile-based game is a game that uses tiles as one of the fundamental elements of play. Traditional tile-based games use small tiles as playing pieces for gambling or entertainment games. Some board games use tiles to create their board, giving multiple possibilities for board layout, or allowing changes in
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#17327732159754472-416: The first tile) one of their tiles. This tile starts the line of play, in which values of adjacent pairs of tile ends must match. The players alternately extend the line of play with one tile at one of its two ends; if a player is unable to place a valid tile, they must continue drawing tiles from the stock until they are able to place a tile. The game ends when one player wins by playing their last tile, or when
4558-429: The following are descriptions of the tile 🁄 bearing the values two and five: A tile that has the same pips-value on each end is called a double or doublet , and is typically referred to as double-zero 🀱 , double-one 🀹 , and so on. Conversely, a tile bearing different values is called a single . Every tile which features a given number is a member of the suit of that number. A single tile
4644-557: The game in England were the Block Game and Draw Game . The rules for these games were reprinted, largely unchanged, for over half a century. In 1863, a new game variously described as All Fives, Fives or Cribbage Dominoes appeared for the first time in both English and American sources; this was the first scoring game and it borrowed the counting and scoring features of cribbage, but 5 domino spots instead of 15 card points became
4730-405: The game is blocked because neither player can play. If that occurs, whoever caused the block receives all of the remaining player points not counting their own. A common variant of the blocking game that is played in the Middle East features four players with slightly altered rules. The stock is divided equally on all players, each having seven tiles in hand. After drawing the tiles, the player with
4816-401: The game starts with a spinner from which various trains branch off. Most trains are owned by a player and in most situations players are allowed to extend only their own train. In blocking games, scoring happens at the end of the game. After a player has emptied their hand, thereby winning the game for the team, the score consists of the total pip count of the losing team's hands. In some rules,
4902-636: The game to Europe. The name "domino" is probably derived from the resemblance to a kind of carnival costume worn during the Venetian Carnival , often consisting of a black-hooded robe and a white mask. Despite the coinage of the word " polyomino " as a generalization, there is no connection between the word "domino" and the number 2 in any language. The most commonly played domino games are Domino Whist, Matador , and Muggins (All Fives). Other popular forms include Texas 42 , Chicken Foot , Concentration, Double Fives, and Mexican Train . In Britain,
4988-801: The infinite set of prisms . All the rectangular faces are mutually face-transitive, so they are equally probable. The two ends of the prism may be rounded or capped with a pyramid, designed so that the die cannot rest on those faces. 4-sided long dice are easier to roll than tetrahedra and are used in the traditional board games dayakattai and daldøs . 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 , Fudge dice , playing card symbols for poker dice , and instructions for sexual acts using sex dice . Dice may have numbers that do not form
5074-437: The line of play to branch. Sometimes, the first tile is required to be a double, which serves as the only spinner. In some games such as Chicken Foot , all sides of a spinner must be occupied before anybody is allowed to play elsewhere. Matador has unusual rules for matching. Bendomino uses curved tiles, so one side of the line of play (or both) may be blocked for geometrical reasons. In Mexican Train and other train games,
5160-571: The mid-18th century. The name domino does not appear before that time, being first recorded in 1771, in the Dictionnaire de Trévoux . There are two earlier recorded meanings for the French word domino , one referring to the masquerades of the period, derived from the term for the hooded garment of a priest, the other referred to crude and brightly colored woodcuts on paper formerly popular among French peasants. The way by which this word became
5246-475: 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 descendant, Dice Masters ), different sides of the dice can offer completely different abilities. Several sides often give resources while others grant
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#17327732159755332-478: The most popular league and pub game is Fives and Threes . Dominoes have sometimes been used for divination , such as bone throwing in Chinese culture and in the African diaspora. European-style dominoes are traditionally made of bone, silver lip ocean pearl oyster shell (mother of pearl), ivory , or a dark hardwood such as ebony , with contrasting black or white pips ( inlaid or painted ). Some sets feature
5418-474: The name of the game of domino remains unclear. The earliest game rules in Europe describe a simple block game for two or four players. Later French rules add the variant of Domino à la Pêche ("Fishing Domino"), an early draw game as well as a three-hand game with a pool . From France, the game was introduced to England by the late 1700s, purportedly brought in by French prisoners-of-war. The early forms of
5504-516: The number of faces. (This is not possible with 4-sided dice and dice with an odd number of faces.) 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. Some twenty-sided dice have a different arrangement used for the purpose of keeping track of an integer that counts down, such as health points. These spindown dice are arranged such that adjacent integers appear on adjacent faces, allowing
5590-515: The numerals 6 and 9, which are reciprocally symmetric through rotation, typically distinguish them with a dot or underline. Dice are often sold in sets, matching in color, of six different shapes. Five of the dice are shaped like the Platonic solids , whose faces are regular polygons . Aside from the cube, the other four Platonic solids have 4, 8, 12, and 20 faces, allowing for those number ranges to be generated. The only other common non-cubical die
5676-609: The oldest known dice were excavated as part of a backgammon -like game set at the Burnt City , an archeological site in south-eastern Iran , estimated to be from between 2800 and 2500 BCE. Bone dice from Skara Brae , Scotland have been dated to 3100–2400 BCE. Excavations from graves at Mohenjo-daro , an Indus Valley civilization settlement, unearthed terracotta dice dating to 2500–1900 BCE, including at least one die whose opposite sides all add up to seven, as in modern dice. Games involving dice are mentioned in
5762-453: The original, having lost much of their cribbage character and incorporating a single spinner, making it identical, or closely related, to Sniff . Most published rule sets for Muggins include the rule that gives the game its name, but some modern publications omit it even though the muggins rule has been described as the unique feature of this game. Dominoes is now played internationally. It is recognized as an "ingrained cultural activity within
5848-442: The other makes 15, which is divisible by three five times (five points) and divisible by five three times (three points) for a total of eight points. An "end" stops when one of the players is out, i.e., has played all of their tiles. In the event no player is able to empty their hand, then the player with the lowest domino left in hand is deemed to be out and scores one point. A game consists of any number of ends with points scored in
5934-411: 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
6020-462: The pip count of the remaining stock is added. If a game is blocked because no player can move, the winner is often determined by adding the pips in players' hands. In scoring games, each individual can potentially add to the score. For example, in Bergen, players score two points whenever they cause a configuration in which both open ends have the same value and three points if additionally one open end
6106-411: The plastic injection molding process, often made of polymethyl methacrylate (PMMA) . The pips or numbers on the die are a part of the mold. Different pigments can be added to the dice to make them opaque or transparent, or multiple pigments may be added to make the dice speckled or marbled. The coloring for numbering is achieved by submerging the die entirely in paint, which is allowed to dry. The die
6192-482: 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
6278-493: The players has no tiles left or when the game is blocked. In the first case, the team of the player without any tiles left earns the sum of the points left in the opposing teams' hands. When the game is blocked, the team with the least points in its hands earns the points left in the opposing teams' hands. If both teams have the same points, the team that started wins the round. In a draw game (blocking or scoring), players are additionally allowed to draw as many tiles as desired from
6364-497: 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
6450-406: The resulting products are usually much more expensive than polymer materials. Modern commercial domino sets are usually made of synthetic materials, such as ABS or polystyrene plastics, or Bakelite and other phenolic resins ; many sets approximate the look and feel of ivory while others use colored or even translucent plastics to achieve a more contemporary look. Modern sets also commonly use
6536-414: The roll. When an amount is added, the notation is n d s + c or n D s + c ; for example, 3d6+4 instructs the player to roll three six-sided dice, calculate the total, and add four to it. When an amount is to be subtracted, the notation is n d s - c or n D s - c; so 3d6-4 instructs the player to subtract four from the result of rolling 3d6 . If the result of a modified dice roll is negative, it
6622-456: The stock before playing a tile, and they are not allowed to pass before the stock is (nearly) empty. The score of a game is the number of pips in the losing player's hand plus the number of pips in the stock. Most rules prescribe that two tiles need to remain in the stock. The draw game is often referred to as simply "dominoes". Adaptations of both games can accommodate more than two players, who may play individually or in teams. The line of play
6708-398: The throw. The result of a die roll is determined by the way it is thrown, according to the laws of classical mechanics (although luck is often credited for the results of a roll). 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 . One typical contemporary dice game
6794-486: The tiles have a metal pin (called a spinner or pivot) in the middle. The traditional domino set contains one unique piece for each possible combination of two ends with zero to six spots, and is known as a double-six set because the highest-value piece has six pips on each end (the "double six"). The spots from one to six are generally arranged as they are on six-sided dice , but because blank ends having no spots are used, seven faces are possible, allowing 28 unique pieces in
6880-527: The top half thickness in MOP, ivory, or bone, with the lower half in ebony. Alternatively, domino sets have been made from many different natural materials: stone (e.g., marble , granite or soapstone ); other woods (e.g., ash , oak , redwood , and cedar ); metals (e.g., brass or pewter ); ceramic clay, or even frosted glass or crystal . These sets have a more novel look, and the often heavier weight makes them feel more substantial; also, such materials and
6966-509: The two. This confusion continues to the present day with some publications equating the names and others describing All Fives as a separate game. In 1889, dominoes was described as having spread worldwide, "but nowhere is it more popular than in the cafés of France and Belgium. From the outset, the European game was different from the Chinese one. European domino sets contain neither the military-civilian suit distinctions of Chinese dominoes nor
7052-481: The universe through an understanding of geometry in polyhedra. 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
7138-399: The use of Arabic numerals is occasionally seen, such dice are less common.) Opposite sides of a modern die traditionally add up to seven, requiring the 1, 2, and 3 faces to share a vertex . The faces of a die may be placed clockwise or counterclockwise about this vertex. If the 1, 2, and 3 faces run counterclockwise, the die is called "right-handed". If those faces run clockwise, the die
7224-603: The user to easily find the next lower number. They are commonly used with collectible card games . "Uniform fair dice" are dice where all faces have an equal probability of outcome due to the symmetry of the die as it is face-transitive . In addition to the Platonic solids, these theoretically include: Two other types of polyhedra are technically not face-transitive but are still fair dice due to symmetry: Long dice and teetotums can, in principle, be made with any number of faces, including odd numbers. Long dice are based on
7310-403: Was illegal, many Romans were passionate gamblers who enjoyed dicing, which was known as aleam ludere ("to play at dice"). 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 CE and from Ptolemaic Egypt as early as
7396-532: Was no 'muggins rule' as in cribbage to challenge a player who fails to declare his scoring combinations. This omission was rectified in the 1868 edition of The Modern Pocket Hoyle , but reprints of both rule sets continued to be produced in parallel for around twenty years before the version with the muggins rule prevailed. From around 1871, however, the names of All Fives and Muggins, became conflated and many publications issued rules for 'Muggins or All Fives' or 'Muggins or Fives' without making any distinction between
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