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98-447: Snake eyes is a roll of two dice , with one pip on each die. Snake Eyes or Snake Eye , may refer to: 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

196-481: A dumbbell -shaped board, counters and dice. Although its precise rules are unknown, it has been termed the Game of 20 Squares and Irving Finkel has suggested a possible reconstruction. The Royal Game of Ur from 2600 BC may also be an ancestor or intermediate of modern-day table games like backgammon and is the oldest game for which rules have been handed down. It used tetrahedral dice. Various other board games spanning

294-400: 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

392-589: A backgammon tournament system in 1963, then organized the first major international backgammon tournament in March 1964, which attracted royalty, celebrities and the press. The game became a huge fad and was played on college campuses, in discothèques and at country clubs; stockbrokers and bankers began playing at conservative men's clubs. People young and old all across the country dusted off their boards and pieces. Cigarette, liquor and car companies began to sponsor tournaments, and Hugh Hefner held backgammon parties at

490-414: A blot", "home", "doublet", "bear off" and "men" are recognisably the same as in the modern game; others, such as "binding a man" (adding a second man to a point) "binding up the tables" (taking all one's first 6 points), "fore game", "latter game", "nipping a man" (hitting a blot and playing it on forwards) "playing at length" (using both dice to move one man) are no longer in vogue. By no later than 1850,

588-555: A board when opened, for a tournament game, should be at a minimum of 44 cm by 55 cm to a maximum of 66 cm by 88 cm. Each side of the board has a track of 12 long triangles, called points . The points form a continuous track in the shape of a horseshoe , and are numbered from 1 to 24. In the most commonly used setup, each player begins with fifteen pieces; two are placed on their 24-point, three on their 8-point, and five each on their 13-point and their 6-point. The two players move their pieces in opposing directions, from

686-435: A computer this game was solved by Hugh Sconyers around 1994, meaning that exact equities for all cube positions are available for all 32 million possible positions. Nard is a traditional tables game from Persia which may be an ancestor of backgammon. It has a different opening layout in which all 15 pieces start on the 24th point. During play pieces may not be hit and there are no gammons or backgammons. Ban-sugoroku

784-415: 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

882-560: A decree prohibiting his court officials and subjects from playing. They were played in Germany in the 12th century, and had reached Iceland by the 13th century. In Spain , the Alfonso X manuscript Libro de los juegos , completed in 1283, describes rules for a number of dice and table games in addition to its discussion of chess. By the 17th century, games at tables had spread to Sweden . A wooden board and counters were recovered from

980-437: 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

1078-430: A direct descendant of the earlier Roman Ludus duodecim scriptorum ('Game of twelve lines') with the board's middle row of points removed, and only the two outer rows remaining. Ludus duodecim scriptorum used a board with three rows of 12 points each, with the 15 pieces being moved in opposing directions by the two players across three rows according to the roll of the three cubical dice. Little specific text about

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1176-494: A letter dated 1635. In English, the word "backgammon" is most likely derived from "back" and Middle English : gamen , meaning "game" or "play". Meanwhile, the first use documented by the Oxford English Dictionary was in 1650. In 1666, it is reported that the "old name for backgammon used by Shakespeare and others" was Tables. However, it is clear from Willughby that "tables" was a generic name and that

1274-407: 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

1372-435: 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,

1470-475: 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

1568-515: 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

1666-490: A player decides to double the opponent, the value is then a double of whatever face value is shown (e.g. if two automatic doubles have occurred putting the cube up to 4, the first in-game double will be for 8 points). The Murphy rule is not an official rule in backgammon and is rarely, if ever, seen in use at officially sanctioned tournaments. The "Jacoby rule", named after Oswald Jacoby , allows gammons and backgammons to count for their respective double and triple values only if

1764-460: A player is one point away from winning a match, that player's opponent will always want to double as early as possible in order to catch up. Whether the game is worth one point or two, the trailing player must win to continue the match. To balance the situation, the Crawford rule requires that when a player first reaches a score one point short of winning, neither player may use the doubling cube for

1862-459: A player to enter a checker from the bar, and that player stops rolling and playing until at least one point becomes open (occupied by one or zero checkers) due to the opponent's moves. A turn ends only when the player has removed his or her dice from the board. Prior to this moment, a move can be undone and replayed an unlimited number of times. When all of a player's checkers are in that player's home board, that player may start removing them; this

1960-410: A roll of 5-5 allows the player to make four moves of five spaces each. On any roll, a player must move according to the numbers on both dice if it is at all possible to do so. If one or both numbers do not allow a legal move, the player forfeits that portion of the roll and the turn ends. If moves can be made according to either one die or the other, but not both, the higher number must be used. If one die

2058-623: 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

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2156-454: 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

2254-405: 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

2352-403: 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

2450-475: 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

2548-412: Is a cube with each of its six faces marked with 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

2646-413: Is a gammon or double game worth 2 points. A backgammon or triple game is worth 3 points and occurs when the losing player has borne off no pieces and has one or more on the bar and/or in the winner's home table (inner board). To speed up match play and to provide an added dimension for strategy, a doubling cube is usually used. The doubling cube is not a die to be rolled, but rather a marker, with

2744-498: Is a relatively modern American English term derived from another board game, draughts , which in US English is called checkers . The objective is for players to bear off all their disc pieces from the board before their opponent can do the same. As the playing time for each individual game is short, it is often played in matches where victory is awarded to the first player to reach a certain number of points. The dimensions of

2842-462: Is a two-player game of contrary movement in which each player has fifteen pieces known traditionally as men (short for 'tablemen'), but increasingly known as 'checkers' in the United States in recent decades, analogous to the other board game of checkers . The backgammon table pieces move along twenty-four ' points ' according to the roll of two dice . The objective of the game is to move

2940-412: Is called "bearing off". A roll of 1 may be used to bear off a checker from the 1-point, a 2 from the 2-point, and so on. If all of a player's checkers are on points lower than the number showing on a particular die, the player must use that die to bear off one checker from the highest occupied point. For example, if a player rolls a 6 and a 5, but has no checkers on the 6-point and two on the 5-point, then

3038-492: 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

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3136-714: 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

3234-410: Is often taken to be zero or one; for instance, when the dice roll determines the amount of damage to a creature. [REDACTED]   This article incorporates text from a publication now in the public domain :  Chisholm, Hugh , ed. (1911). " Dice ". Encyclopædia Britannica . Vol. 8 (11th ed.). Cambridge University Press. p. 176–177. Backgammon Backgammon

3332-458: Is similar or identical to earlier tables games that have been depicted for centuries in art, leading to the mistaken belief that backgammon itself is much older. The history of board games can be traced back nearly 5,000 years to archaeological discoveries of the Jiroft culture , located in present-day Iran , the world's oldest game set having been discovered in the region with equipment comprising

3430-459: 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

3528-437: 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

3626-406: Is the following: White doubles Black to 2 points, Black accepts then beavers the cube to 4 points; White, confident of a win, raccoons the cube to 8 points, while Black retains the cube. Such a move adds greatly to the risk of having to face the doubling cube coming back at 8 times its original value when first doubling the opponent (offered at 2 points, counter offered at 16 points) should the luck of

3724-689: Is the national authority and runs a backgammon championship   —   the Backgammon Galaxy UK Open Tournament   —   as well as club championships, online leagues and knockout tournaments. Like the USBGF they are active members of the World Backgammon Federation (WBF) and their tournament rules have been adopted in their entirety by the WBF. Backgammon entered the computer era in

3822-459: 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

3920-402: Is unable to be moved, but such a move is made possible by the moving of the other die, that move is compulsory. In the course of a move, a checker may land on any point that is unoccupied or is occupied by one or more of the player's own checkers. It may also land on a point occupied by exactly one opposing checker, or " blot ". In this case, the blot has been "hit" and is placed in the middle of

4018-586: The Playboy Mansion . Backgammon clubs were formed and tournaments were held, resulting in a World Championship promoted in Las Vegas in 1967. In the second half of the 20th century, new terms were introduced in America, such as 'beaver' and 'checkers' for men (although American backgammon experts Jacoby and Crawford continued to use both the older terms as well as the new ones). Most recently,

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4116-529: 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

4214-606: The expected value -driven game played in the 20th and 21st centuries. The popularity of backgammon surged in the mid-1960s, in part due to the charisma of Prince Alexis Obolensky who became known as "The Father of Modern Backgammon". "Obe", as he was called by friends, co-founded the International Backgammon Association, which published a set of official rules. He also established the World Backgammon Club of Manhattan, devised

4312-483: 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 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

4410-487: The 10th to 7th centuries BC have been found throughout modern day Iraq, Syria, Egypt and western Iran. The Persian tables game of nard or nardšir emerged somewhere between the 3rd and 6th century AD, one text ( Kār-nāmag ī Ardaxšēr ī Pāpakān ) linking it with Ardashir I (r. 224–41), founder of the Sasanian dynasty , whereas another ( Wičārišn ī čatrang ud nihišn ī nēw-ardaxšēr ) attributes it to Bozorgmehr Bokhtagan ,

4508-554: The 17th century. In medieval Italy, Barail was played on a backgammon board, with the important difference that both players moved their pieces counter-clockwise and starting from the same side of the board. The game rules for Barail are recorded in a 13th-century manuscript held in the Italian National Library in Florence. The earliest mention of backgammon, under the name Baggammon , was by James Howell in

4606-669: The 1990s when software was developed to play and analyze games, and for people to play one another over the internet. Real-time online play began with the First Internet Backgammon Server in July 1992, but there are now a range of options. Since 2018, backgammon has been overseen internationally by the World Backgammon Federation who set the rules of play for international tournaments. Backgammon playing pieces may be termed men, checkers, draughts, stones, counters, pawns, discs, pips, chips, or nips. Checkers

4704-402: The 24-point towards the 1-point. Points 1 through 6 are called the home board or inner board, and points 7 through 12 are called the outer board. The 7-point is referred to as the bar point, and the 13-point as the midpoint. The 5-point for each player is sometimes called the "golden point". To start the game, each player rolls one die, and the player with the higher number moves first using

4802-779: 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 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

4900-524: 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

4998-429: The 5-point using the die roll of 6; this is sometimes useful tactically. As before, if there is a way to use all moves showing on the dice by moving checkers within the home board or by bearing them off, the player must do so. If a player's checker is hit while in the process of bearing off, that player may not bear off any others until it has been re-entered into the game and moved into the player's home board, according to

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5096-450: The 6 and the 5 must be used to bear off the two checkers from the 5-point. When bearing off, a player may also move a lower die roll before the higher even if that means the full value of the higher die is not fully utilized. For example, if a player has exactly one checker remaining on the 6-point, and rolls a 6 and a 1, the player may move the 6-point checker one place to the 5-point with the lower die roll of 1, and then bear that checker off

5194-518: The English clergy. Edmond Hoyle published A Short Treatise on the Game of Back-Gammon in 1753; this described rules and strategy for the game and was bound together with a similar text on whist . The early form of backgammon was very similar to its predecessor, Irish. The aim, board, number of pieces or "men", direction of play and starting layout were the same as in the modern game. However, there

5292-591: The French Toutes Tables and Spanish Todas Tablas , the latter name first being used in the 1283 El Libro de los Juegos , a translation of Arabic manuscripts by the Toledo School of Translators . Irish had been popular at the Scottish court of James IV and considered to be "the more serious and solid game" when the variant which became known as Backgammon began to emerge in the first half of

5390-571: 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

5488-659: The United States Backgammon Federation (USBGF) was organized in 2009 to repopularize the game in the United States. Board and committee members include many of the top players, tournament directors and writers in the worldwide backgammon community. The USBGF has recently created Standards of Ethical Practice to address issues on which tournament rules fail to touch. In its country of origin, the UK Backgammon Federation

5586-425: The bar. A player may not move any other checkers until all checkers belonging to that player on the bar have re-entered the board. If a player has checkers on the bar, but rolls a combination that does not allow any of those checkers to re-enter, the player does not move. If the opponent's home board is completely "closed" (i.e. all six points are each occupied by two or more checkers), there is no roll that will allow

5684-449: The better record over a series of many games. With each roll of the dice, players must choose from numerous options for moving their pieces and anticipate possible counter-moves by the opponent. The optional use of a doubling cube allows players to raise the stakes during the game. The earliest specific reference to backgammon was in a letter dated 1635, when it was emerging as a variant of the popular medieval Anglo-Scottish game of Irish ;

5782-399: The board at the beginning of the game. The roll of 1-2 is given special consideration, allowing the player, after moving the 1 and the 2, to select any desired doubles move. A player also receives an extra turn after a roll of 1-2 or of doubles. Hypergammon is a game in which players have only three counters on the board, starting with one each on the 24, 23 and 22 points. With the aid of

5880-468: The board on the bar that divides the two sides of the playing surface. A checker may never land on a point occupied by two or more opposing checkers; thus, no point is ever occupied by checkers from both players simultaneously. There is no limit to the number of checkers that can occupy a point or the bar at any given time. Checkers placed on the bar must re-enter the game through the opponent's home board before any other move can be made. A roll of 1 allows

5978-461: The board. Modern backgammon follows the same rules as tabula for hitting a blot and for bearing off; and the rules for re-entering pieces in backgammon are the same as those for initially entering pieces in tabula. The name Tavli ( τάβλι ) is still used in Greece for various tables games, which are frequently played in town plateias and cafes. The τάβλι of Emperor Zeno's time is believed to be

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6076-405: The checker to enter on the 24-point (opponent's 1), a roll of 2 on the 23-point (opponent's 2), and so forth, up to a roll of 6 allowing entry on the 19-point (opponent's 6). Checkers may not enter on a point occupied by two or more opposing checkers. Checkers can enter on unoccupied points, or on points occupied by a single opposing checker; in the latter case, the single checker is hit and placed on

6174-408: The cube has already been offered and accepted. This encourages a player with a large lead to double, possibly ending the game, rather than to play it to conclusion hoping for a gammon or backgammon. The Jacoby rule is widely used in money play but is not used in match play. The "Crawford rule", named after John R. Crawford , is designed to make match play more equitable for the player in the lead. If

6272-400: The cube, doubling the value of the game again, while retaining possession of the cube. A variant of the doubling cube "beaver" is the "raccoon". Players who doubled their opponent, seeing the opponent beaver the cube, may in turn then double the stakes once again ("raccoon") as part of that cube phase before any dice are rolled. The opponent retains the doubling cube. An example of a "raccoon"

6370-417: The dice change. Some players may opt to invoke the "Murphy rule" or the "automatic double rule". If both opponents roll the same opening number, the doubling cube is incremented on each occasion yet remains in the middle of the board, available to either player. The Murphy rule may be invoked with a maximum number of automatic doubles allowed and that limit is agreed to prior to a game or match commencing. When

6468-400: 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

6566-526: 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

6664-416: The doubled stakes or resign ("drop") the game immediately. Whenever a player accepts doubled stakes, the cube is placed on their side of the board with the corresponding power of two facing upward, to indicate that the right to redouble, which is to offer to continue doubling the stakes, belongs exclusively to that player. If the opponent drops the doubled stakes, they lose the game at the current value of

6762-437: The doubling cube. For instance, if the cube showed the number 2 and a player wanted to redouble the stakes to put it at 4, the opponent choosing to drop the redouble would lose two, or twice the original stake. There is no limit on the number of redoubles. Although 64 is the highest number depicted on the doubling cube, the stakes may rise to 128, 256, and so on. In money games, a player is often permitted to "beaver" when offered

6860-415: The fifteen pieces around the board and be first to bear off , i.e., remove them from the board. The achievement of this while the opponent is still a long way behind results in a triple win known as a backgammon , hence the name of the game. Backgammon involves a combination of strategy and luck from rolling dice. While the dice may determine the outcome of a single game, the better player will accumulate

6958-480: The following game, called the "Crawford game". After the Crawford game, normal use of the doubling cube resumes. The Crawford rule is routinely used in tournament match play. It is possible for a Crawford game to never occur in a match. If the Crawford rule is in effect, then another option is the "Holland rule", named after Tim Holland , which stipulates that after the Crawford game, a player cannot double until after at least two rolls have been played by each side. It

7056-409: The game. These other tables games commonly have a different starting position, restrict certain moves, or assign special value to certain dice rolls, but in some geographic games even the rules and direction of movement of the counters change, rendering them fundamentally different. Acey-deucey is a relative of backgammon in which players start with no counters on the board, and must enter them onto

7154-550: The gameplay of Ludus duodecim scriptorum has survived; it may have been related to the older Ancient Greek dice game Kubeia . The earliest known mention of the game is in Ovid 's Ars Amatoria ('The Art of Love'), written between 1 BC and 8 AD. In Roman times, this game was also known as alea . Tables games first appeared in France during the 11th century and became a favourite pastime of gamblers. In 1254, Louis IX issued

7252-801: 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

7350-456: The latter was described as a better game. By the 19th century, however, backgammon had spread to Europe, where it rapidly superseded other tables games like Trictrac in popularity, and also to America, where the doubling cube was introduced. In other parts of the world, different tables games such as Nard or Nardy are better known. Backgammon is a recent member of the large family of tables games that date back to ancient times. Its equipment

7448-475: 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

7546-411: The normal movement rules. The first player to bear off all fifteen of their own checkers wins the game. When keeping score in backgammon, the points awarded depend on the scale of the victory. A player who bears off all fifteen pieces when the opponent has borne off at least one, wins a single game worth 1 point. If all fifteen have been borne off before the opponent gets at least one checker off, this

7644-516: 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

7742-421: The numbers 2, 4, 8, 16, 32, and 64 inscribed on its sides to denote the current stake. At the start of each game, the doubling cube is placed on the midpoint of the bar with the number 64 showing; the cube is then said to be "centered, on 1". When the cube is still centered, either player may start their turn by proposing that the game be played for twice the current stakes. Their opponent must either accept ("take")

7840-423: The numbers shown on both dice. If the players roll the same number, they must roll again until they roll different numbers. Both dice must land completely flat on the right-hand side of the gameboard. The players then take alternate turns, rolling two dice at the beginning of each turn. After rolling the dice, players must, if possible, move their pieces according to the number shown on each die. For example, if

7938-515: 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

8036-411: 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

8134-476: The phrase "playing at tables" was used in a similar way to "playing at cards". The first known rules of "Back Gammon" were produced by Francis Willughby around 1672; they were quickly followed by Charles Cotton in 1674. In the 16th century, Elizabethan laws and church regulations had prohibited "playing at tables" in England, but by the 18th century, Backgammon had superseded Irish and become popular among

8232-411: 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

8330-405: The player rolls a 6 and a 3 (denoted as "6-3"), the player must move one checker six points forward, and another or the same checker three points forward. The same checker may be moved twice, as long as the two moves can be made separately and legally: six and then three, or three and then six. If a player rolls two of the same number, called doubles, that player must play each die twice. For example,

8428-482: 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

8526-414: 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

8624-498: The rules of play had changed to those used today. Tables boards were now made with a 'bar' in the centre and men that were hit went onto the bar. Winning double or by "two hits" was achieved by bearing all one's men off before the other has borne any —  this was now called a gammon . If the winner bore off all men while the loser still had men in his adversary's table, it was a back-gammon and worth "three hits", i.e., triple. The most recent major development in backgammon

8722-398: 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

8820-481: 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

8918-399: 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

9016-603: 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

9114-551: The vizier of Khosrow I (r. 531–79), who is credited with the invention of the game. The earliest identifiable tables game, Tabula , meaning 'table' or 'board', is described in an epigram of Byzantine Emperor Zeno (AD 476–491). The overall aim was to be first to bear one's pieces off; the board had the typical tables layout, with 24 points, 12 on each side; and there were 15 counters per player. However, unlike modern Western backgammon, there were three cubical dice not two, no bar nor doubling die , and all counters started off

9212-539: The wreck of the Vasa among the belongings of the ship's officers. Tables games appear widely in paintings of this period, mainly those of Dutch and German painters, such as Van Ostade , Jan Steen , Hieronymus Bosch , and Bruegel . Among surviving artworks are Cardsharps by Caravaggio . Backgammon's immediate predecessor was the 16th century tables game of Irish . Irish was the Anglo-Scottish equivalent of

9310-520: Was common in tournament play in the 1980s, but is now rarely used. Minor variations to the standard game are common among casual players in certain regions. For instance, only allowing a maximum of five men on any point (Britain) or disallowing "hit-and-run" in the home board (Middle East). There are also many relatives of backgammon within the tables family with different aims, modes of play and strategies. Some are played primarily throughout one geographic region, and others add new tactical elements to

9408-403: 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

9506-447: Was no doubling die, there was no bar on the board or the bar was not used (men simply being moved off the table when hit) and the scoring was different. The game was won double if either the winning throw was a doublet or the opponent still had men outside the home board. It was won triple if a player bore all men off before any of the opponent's men reached the home board; this was a back-gammon . Some terminology, such as "point", "hitting

9604-580: Was the addition of the doubling cube. Doubles had originally been recorded by placing "common parlour matches" on the bar in the centre of the board. A doubling cube was first introduced in the 1920s in New York City among members of gaming clubs in the Lower East Side . The cube required players not only to select the best move in a given position, but also to estimate the probability of winning from that position, transforming backgammon into

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