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72-398: The 106 tiles are placed face down on the table and thoroughly mixed. Next, the players stacks the tiles faced down in groups of 5, creating a total of 21 stacks. There is no specific rule about how many stacks should be in front of each player. It is convenient to have at least six in front of the dealer, but this makes no real difference to the game. One tile remains unstacked and is kept by

144-400: 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

216-415: 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

288-437: 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

360-475: A game, as follows: If the game ends without any player exposing a winning hand (because there are no tiles left to draw, and the player whose turn it is cannot win by taking the previous discard), then there is no score. Play continues until any player's score reaches zero or less. The two players with the highest scores at that time are the winners and the two with the lowest scores are the losers. Some play that any player whose score reaches zero or less leaves

432-407: 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

504-406: A minimum of five doubles. Doubles are two identical tiles. If a player opens with doubles, they are not allowed to lay normal sets. They are, however, allowed to add tiles to existing sets from other players on the table. If all four players open with doubles within one round, that round gets canceled and replayed. No players receive any penalties. In order to complete a round, a player must play all

576-435: 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,

648-475: 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

720-515: 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

792-430: A player forms a winning hand and exposes it, ending the play. Discarded tiles are placed to the right of the player who discarded them, in a stack, so that only the most recent discard in the stack is visible. The usual rule is that the player is allowed to look through all the tiles in the discard stacks to their right (tiles they discarded) and to their left (tiles they had an opportunity to take), but they can only see

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864-478: A player's hand is 101. In order to open, the player needs to create sets of either 3 or 4 identical numbered tiles of different colors (e.g. black 5, red 5 & blue 5) or running numbers of the same color (e.g. red 7, red 8, and red 9). A set must have a minimum of three tiles. Players are only allowed to add to existing sets on the table after they have opened with a minimum of 101 points already. Players are, of course, allowed to open and then add to other sets within

936-623: 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

1008-454: 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

1080-405: 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

1152-463: A tile is turned up to be the joker. When drawing tiles during the play, any face down tile can be taken from the stock on the table. Some play that a player who wins a game with tiles of one colour only, the score is doubled: the other players lose 4 points if the winner discarded an ordinary tile, 8 points if the winner's final discard was a joker. Some only award this double score for a hand consisting entirely of red tiles or black tiles. This variant

1224-403: 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

1296-475: 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

1368-412: 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

1440-407: Is a run, and {black 5, green 5, yellow 5, false joker} is a set. If the player has a winning hand of groups and runs using at least one joker, they do not have to expose it immediately. If they wish, they can continue playing in the hope of forming a winning hand plus a joker. If the player is able to end the game by discarding a joker and exposing their remaining 14 tiles as a winning hand, their win

1512-492: 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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1584-714: 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

1656-402: Is made from three or four same-value tiles in distinct colors. Another type of winning hand consists of having at least seven pairs. Two identical tiles (same number and colour) is called a pair. If a player has a winning hand, he or she must show it to the other players. The other players then check whether all of 14 tiles of the player are grouped correctly. Apart from the discarded tiles and

1728-423: Is played with four players over multiple rounds. The object of the game is to collect as few points as possible at the end of the game. The player who has the fewest points, after all of the rounds are completed, is declared the winner. Points are determined according to the face value of the tile (e.g. a red 3 = 3 points & a black 11 = 11 points). A round is completed when there are no more tiles left to draw from

1800-459: 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

1872-437: 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

1944-459: 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

2016-400: Is worth twice as much as an ordinary win. Note that by continuing to play instead of exposing their ordinary win, the player run the risk that another player may complete a winning hand and expose it before they can achieve their double win, in which case they gain nothing for their concealed winning hand. Each player begins the game with 20 points and loses points each time another player wins

2088-529: 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

2160-483: 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

2232-779: 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

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2304-524: 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

2376-571: 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

2448-421: The bank and one tile which indicates what the joker will be is turned face up. The game is played counter-clockwise. The dealer starts the game by throwing away one of his tiles. The turn then goes to the player on his right. A player starts their turn by either taking a tile from the bank or taking the tile thrown away by the previous player. The player then either 'opens' (puts his sets on the table) and/or adds to

2520-406: The bank or when one of the players has completed his/her hand (tiles on the rack). A game is played over a predetermined number of rounds (e.g. 3,5,7,9 or 11 rounds). All of the rounds must be completed before a winner is declared, not just a best of rounds. After a random dealer is chosen, each player is given 21 tiles except for the dealer, who gets 22 tiles. The rest of the tiles go face down into

2592-402: The count will continue using the stacks in front of the player to dealer's right, and one of these will be selected. The selected stack now has six tiles. Next, the dealer throws the die for a second time to determine which tile will be shown face-up. The second throw selects one of the tiles in the selected stack, counting upwards from the bottom of the stack. The selected tile is extracted from

2664-410: The dealer briefly. The dealer is randomly chosen at the start and passes to the right after every round. The dealer then throws a die to determine on which stack the one remaining tile will be placed upon. For example if a 6 is thrown, the tile is placed on the sixth stack in front of the dealer (counting from left). If the number thrown is greater than the number of stacks in front of the dealer, then

2736-400: 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

2808-526: 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

2880-415: The exposed top tiles of the two discard stacks on the other side of the table. Tiles are always drawn from the top of the next available stack. When only the final stack of 6 tiles remains, the exposed tile is removed from the top of this stack and the other five tiles are drawn in order. The exposed tile (the red 4 in the example diagrams) can never be drawn. When there are no tiles left in the centre except

2952-402: The face up tile on top of the six-tile stack, no tiles are exposed until a player shows a winning hand: no sets or runs are exposed during the game. The 1 can be used as the lowest tile, below the 2, or as the highest tile, above the 13, but not both at once. So black 1-2-3 or black 12-13-1 would be valid runs, but black 13-1-2 would not be valid. As previously explained, the two tiles that are

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3024-430: The face-up tile. If the player doesn't show the tile to others, it will miss out the point. Now the player to the dealer's right begins the play by discarding one tile, face up. After this, each player in turn may either take the tile just discarded by the previous player, or draw the next tile from the supply in the centre of the table, and must then discard one unwanted tile. This continues in anticlockwise rotation until

3096-414: The game, but the other players continue to play. Some play that the players sitting opposite each other are partners. In practice partners cannot help each other much, except by cheating(!) [In the partnership game, presumably each team starts with 20 points, and when a player exposes a winning hand, the opposing team loses 2 or 4 points as appropriate. If a player shows the tile matching the exposed tile at

3168-644: The indicator tile is a 13 the joker then becomes a 1. Sets of the same number are not allowed to have the same color in them (e.g. A blue 10, a red 10 & a blue 10 is not allowed). Running sets are not allowed to continue from 13 to the 1 (e.g. black 13, black 1 & black 2 is not allowed). 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

3240-801: 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

3312-541: The joker tile are free to assign for themselves which color and number the joker tile will represent. The face-up tile on top of the stack also helps determine the false joker. The false jokers are not wild - they are used only to represent the tiles that have become jokers. So for example, if the red 11s became the jokers, then the false jokers are played as red 11s (and cannot represent any other tile). New players may wonder why false joker tiles aren't used as joker themself. A possible reason can be that through any defect in

3384-475: 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

3456-516: 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

3528-515: 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

3600-411: 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

3672-411: 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

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3744-482: 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

3816-404: The players should arrange their tiles so that they can see their faces but the other players cannot. Wooden racks are often used for this. The remaining tiles are left for the players to draw from during the game. They are moved to the middle of the table, without looking at them or disturbing their order. Before the round starts, a player can score a point if the player holds the tile that matches

3888-405: The right of the dealer takes the next stack after (to the right of) the selected stack with the face up tile on top of it, then the player opposite the dealer takes the following stack, and so on anticlockwise around the table, until each player has two stacks (10 tiles). Now the player to the dealer's right receives the whole of the next stack, but the player sitting opposite the dealer is given only

3960-414: 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

4032-441: The same colour as the face up tile and one greater in number are the jokers. These tiles can be used to represent any tile the holder desires, in order to complete a set or run. Assuming a round with red 5 as being the joker: The two false jokers - the tiles without numbers - are used only to represent the joker tiles. So for example when red 5s are jokers, the false jokers are played as red 5s: for example {red 4, false joker, red 6}

4104-404: The same turn. If a player takes the discarded tile from the previous player, they must always use that tile. If the player has not opened yet, he/she must open with that tile included. The player is not allowed to keep the tile in their hand. A player is allowed to take the discarded tile and then return it and still take from the bank without receiving a penalty. Another way to open a hand is with

4176-400: The selected stack and placed it on top. It is a red 4, so red 5s will be jokers for this deal. Now player 2 must take stack 'a', player 3 stack 'b', player 4 'c', player 1 'd', player 2 'e', player 3 'f', player 4 'g', player 1 'h' and player 2 'i'. Next player 3 takes the top 4 tiles of stack 'j', player 4 the last tile of 'j' and three from 'k', and player 1 two from 'k' and two from 'l'. All

4248-436: The sets already on the table. If the player cannot open they finish the turn by throwing away one of the tiles from their hand. A player must always throw away a tile to finish the turn, even when finishing their entire hand. The tile that indicates what the joker will be changes each individual round. The two joker tiles (also called 'false jokers') are the same value as this tile's value plus 1. These jokers look different from

4320-404: The sets from their hand and finish with discarding a tile. The other players receive penalty points. When all of the rounds have finished, all penalty and minus points of all of the rounds are added together and the player with the fewest points is the winner. Players receive an additional penalty of 101 for the following actions. These penalties are added to the total points for that round. If

4392-446: The single exposed tile, if the next player to play does not want to take the previous player's discard, the play ends because there are no cards left to draw. There are multiple ways for a player to win a round. The object of the game is to have a rack full of runs, sets or seven pairs. A run is composed of three or more, same-colored tiles, in consecutive number order. (After 13, a 1 may follow but it can't continue after 1) A set

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4464-404: The stack and placed face-up on top of it. If the selected tile is a false joker, it is returned to the selected stack and the second throw of the die is repeated until a numbered tile is selected. This face-up tile helps determine the "joker" ( okey ) and "false joker" ( sahte okey ) for the game. The color and value of the joker and the false joker changes every round. The face-up tile on top of

4536-426: The stack helps determine the joker. The joker has the same color as this face-up tile. And its number for is +1 of this tile. For example, if the face up-tile is the red 10, the red 11s become jokers. If the face up tile is a 13, the 1s of the same colour become jokers. The joker is a very useful tile, because it functions as a wild tile that can be used to represent other tiles to complete a combination. Players with

4608-402: The standard tiles and vary in appearance according to the tile set used. The actual jokers (which can represent any tile in the game) are the actual tiles that get replaced by the false jokers. If, for example, the indicator tile is a blue 5, the actual jokers are the two blue 6 tiles and the joker tiles (or false jokers) have the value of the blue 6. The minimum number of points required to open

4680-408: The start, the other team loses 1 point.] Some players use the exposed tile as the last tile to be drawn from the centre, when all the other tiles have been taken. Some players omit the formal procedure for choosing the joker and distributing the tiles. Having shuffled the tiles face down on the table, each player simply takes any 14 tiles from the table (the player chosen to play first taking 15) and

4752-398: 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

4824-429: The tiles, some players learn to recognise the false jokers from the back, that would give them an unfair advantage. If a different tile is used as the joker in each game, recognising a joker from the back becomes much more difficult. After determining the joker and the false joker, the stacks of tiles are distributed among the players. The player to dealer's right will receive 15 tiles and the others 14 each. The player to

4896-411: The top 4 tiles of the following stack. The player to the dealer's left receives the last tile of this stack and 3 tiles from the top of the next stack, and finally the dealer takes the last 2 tiles from this stack and 2 from the next stack. In the above diagram the dealer threw a 5, placed the spare tile on top of the 5th stack from her left. She then threw a 2, and took the second tile from the bottom of

4968-481: 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

5040-399: 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

5112-603: 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

5184-403: 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

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