Contents 
6d8
or 2d6
; the former meaning "six eightsided dice," and the latter meaning "two sixsided dice." Addition or various other arithmetic operations are often added at the end as well, e.g. 3d6+4
"three sixsided dice plus four to the outcome thereof".Sides  Shape  Notes  

4  tetrahedron  Each face has three numbers: they are arranged such that the upright number (which counts) is the same on all three visible faces. Alternatively, all of the sides have the same number in the lowest edge and no number on the top. This die does not roll well and thus it is usually thrown into the air instead.  
6  cube  A common die. The sum of the numbers on opposite faces is seven.  
8  octahedron  Each face is triangular; looks like two square pyramids attached basetobase. Usually, the sum of the opposite faces is 9.  
10  pentagonal trapezohedron  Each face is a kite. The die has two sharp corners, where five kites meet, and ten blunter corners, where three kites meet. The ten faces usually bear numbers from zero to nine, rather than one to ten (zero being read as "ten" in many applications). Often all odd numbered faces converge at one sharp corner, and the even ones at the other.  
12  dodecahedron  Each face is a regular pentagon.  
20  icosahedron  Faces are equilateral triangles. Typically, opposite faces add to twentyone. A 2nd century AD Roman icosahedron die is in the collection of the British Museum, though the game it was used for is not known.^{[13]} 
Sides  Shape  Notes 

1  sphere  Most commonly a joke die^{[citation needed]}, this is just a sphere with a 1 marked on it. About spherical dice that may produce more than one result, see the section Noncubical dice above. 
2  cylinder  This is nothing more than a coin shape with 1 marked on one side and 2 on the other. While some tasks in roleplaying require flipping a coin, the game rules usually simply call for the use of a coin rather than requiring the use of a twosided die. It is possible, however, to find dice of this sort for purchase, but they are rare, and can typically be found among other joke dice. 
3  Roundedoff triangular prism  This is a roundedoff triangular prism, intended to be rolled like a rollingpin style die. The die is roundedoff at the edges to make it impossible for it to somehow land on the triangular sides, which makes it look a bit like a jewel. When the die is rolled, one edge (rather than a side) appears facing upwards. On either side of each edge the same number is printed (from 1 to 3). The numbers on either side of the upfacing edge are read as the result of the die roll. Another possible shape is the "American Football" or "Rugby ball" shape, where the ends are pointed (with rounded points) rather than just rounded. 
5  Triangular prism  This is a prism that is thin enough to land either on its "edge" or "face". When landing on an edge, the result is displayed by digits (2–4) close to the prism's top edge. The triangular faces are labeled with the digits 1 and 5. 
7  Pentagonal prism  Similar in constitution to the 5sided die. When landing on an edge, the topmost edge has pips for 1–5. The pentagonal faces are labeled with the digits 6 and 7. This kind of die is particularly odd since it has pips for five of its results and digits for two of them. Sevensided dice are used in a sevenplayer variant of backgammon. Some variants have heptagonal ends and rectangular faces. 
12  rhombic dodecahedron  Each face is a rhombus. 
14  heptagonal trapezohedron  Each face is a kite. 
16  octagonal dipyramid  Each face is an isosceles triangle. 
24  tetrakis hexahedron  Each face is an isosceles triangle. 
24  deltoidal icositetrahedron  Each face is a kite. 
30  rhombic triacontahedron  Each face is a rhombus. Although not included in most dice kits, it can be found in most hobby and game stores. 
34  heptadecagonal trapezohedron  Each face is a kite. 
50  icosakaipentagonal trapezohedron  Similar to the 14 and 16sided dice, the faces of the 50sided die are kites, although very narrow. 
100  Zocchihedron  100sided dice can be found in hobby and game stores, and such a die is used in some narrative roleplaying games such as Dungeons & Dragons. They are not, however, a true polyhedron. A 100sided die is made by flattening 100 facets on a sphere. The name Zocchihedron was taken from its creator, Lou Zocchi. A typical d100 will be hollow and filled with small plastic objects to dampen the die's momentum when rolled (lest it take off like a golf ball). A 100sided die is equivalent to a pair of tensided dice, and so, even in roleplaying games, the Zocchihedron is rarely seen and is generally more of a novelty item. 
Sum 












Probability 











Probability (simplified) 











d6
, and the notation for rolling two such dice is 2d6
. A constant bias may be added or subtracted by ordinary arithmetic: for example, 2d6+4
adds a 4 point bonus, while 2d62
subtracts a 2 point penalty. Games which use only one type of dice rarely require complex dice notation.1d100
or 1d%
. Since actual hundredsided dice are large, almost spherical, and difficult to read, percentile rolls are usually handled by rolling two tensided dice together, using one as the "tens" and the other as the "units". A roll of ten or zero on either die is taken as a zero, unless both are zeros or tens, in which case this is 100 (rather than zero). To avoid this confusion, some sets of percentile dice exist where one is marked in tens (00, 10, 20... up to 90) and the other from 0 to 9. White and black percentile dice are also used, and are commonly found in colorcoded dice sets, or sold separately.
A die (plural dice, from Old French dé, from Latin datum "something given or played"^{[1]}) is a small throwable object with multiple resting attitudes, used for generating random numbers or other symbols. This makes dice suitable as gambling devices, especially for craps or sic bo, or for use in nongambling tabletop games.
A traditional die is a cube (often with corners slightly rounded), marked on each of its six faces with a different number of circular patches or pits called pips. All of these pips have the same appearance within a set of dice, and are sized for ease of recognizing the pattern formed by the pips on a face. The design as a whole is aimed at each die providing one randomly determined integer, in the range from one to six, with each of those values being equally likely.
More generally, a variety of analogous devices are often described as dice, though the word "dice" used without qualifiers refers to traditional dice by default. Such specialized dice may have polyhedral or irregular shapes, with faces marked with various collections of symbols, and be used to produce other random results than one through six. There are also "loaded" or "crooked" dice (especially otherwise traditional ones), meant to produce skewed or even predictable results, for purposes of deception or amusement.
Contents 
dice.]]
Common dice are small cubes 1 to 3 cm along an edge (16 mm being most common), whose faces are numbered from one to six (usually by patterns of round dots called pips). Since classical antiquity^{[2]} it is traditional to arrange the numbers so that opposite faces add to seven; this implies that the faces 1, 2 and 3 meet at a common vertex. This constraint leaves one more abstract design choice: the faces representing 1, 2 and 3 respectively can be placed in either clockwise or counterclockwise order about this vertex. If the 1, 2 and 3 faces run counterclockwise around their common vertex, the die is called "righthanded"; if they run clockwise it is called "lefthanded". Standard modern Western dice are righthanded, whereas Chinese dice are often lefthanded.^{[3]}
The pips on traditional European dice are arranged in specific patterns. These can be conveniently described by pairs: one pair of pips in opposite corners; the next pair in the remaining corners; and a last pair in the middles of two opposite sides. For odd numbers, a dot is added in the center of the face; thus "three" is a diagonal row, and "five" a quincunx. Asianstyle dice bear similar patterns, but the pips are typically closer to the centre of the face; the "one" pip is larger than the others; and the "one" and "four" pips are coloured red. In some older sets the "one" pip is a colorless depression. It is suggested^{[who?]} that an entirely black and white color combination on the "one" side would be unlucky and red (a lucky color in Chinese culture) would counteract this. In some Asian languages, the word "four" sounds similar to the word "death" and is considered unlucky. Several legends^{[citation needed]} also mention that the "four" side is colored red because a Chinese emperor (one legend said it was a Ming dynasty emperor, while another stated it was Chung Tsung) ordered it as "fours" helped him win a dice game (sugoroku) against his empress. This story, however, is questionable at best, as it is also probable that "red fours" are also of common Indian origin.^{[3]}^{[4]} Another reason why the "four" side might be colored red is because in Asian cultures, the number four is seen as unlucky, like the number thirteen in Western culture, and as mentioned before, it is colored red so that the luckiness of the red counteracts the unluckiness of the four.
Dice are thrown to provide random numbers for gambling and other games, and thus are a type of hardware random number generator. The result of a die roll is random in the sense of lacking predictability, not lacking cause. Exactly how dice are thrown determines how they will land according to the laws of classical mechanics. However, dice also can exhibit sensitive dependence on initial conditions, making it difficult to predict the outcome of a die roll even with good information about exactly how it is thrown. Some people claim that the pips on the face of certain styles of dice can cause a small bias, but there is no research to support this claim.^{[citation needed]} The supposed bias is reduced somewhat in the Japanese die with its oversized single pip (pictured).^{[citation needed]} Casino dice have markings that are flush, offering the assurance that this brings them very close to providing true uniformly distributed random numbers.^{[citation needed]}
Dice are thrown, singly or in groups, from the hand or from a cup or box designed for the purpose, onto a flat surface. The face of each die that is uppermost when it comes to rest provides the value of the throw. A typical dice game today is craps, wherein two dice are thrown at a time, and wagers are made on the total value of upfacing pips on the two dice. They are also frequently used to randomize allowable moves in board games, usually by deciding the distance through which a piece will move along the board; examples of this are ludo and backgammon.
Precision casino dice, used for the game of craps, may have a polished finish, making them transparent, or a sand finish, making them translucent. Casino dice have their pips drilled, and then filled flush with a paint of the same density as the acetate used for the dice, such that the dice remain in balance. In casino play, a stick of 5 dice is used, all stamped with a matching serial number to prevent a cheater from substituting a die.
Precision backgammon dice are also made with the pips filled in as with casino dice. While casino dice are noticeably larger than common dice, with sharp edges and corners, precision backgammon dice tend to be slightly smaller. Their corners and edges are rounded to allow better movement inside the dice cup and to stop chaotic rolls from damaging the playing surface.
Some computer games, such as clones of board games, must use computer generated dice. The values are usually determined by a random number generator, then displayed as a visual representation of a die.
by both Confederate and Union forces at separate times. The fort was also used in 1898 in the SpanishAmerican War.]] die, made of Steatite]]
]]Dice have been used throughout Asia since before recorded history.
The oldest known dice were excavated as part of a 5000yearold backgammon set, at Shahri Sokhta, the Burnt City, an archeological site in southeastern Iran.^{[5]}
Excavations from ancient tombs in the Harappan civilization,^{[6]} seem to further indicate a South Asian origin. Dicing is mentioned as an Indian game in the Rig Veda, Atharva Veda^{[7]} and Buddha games list. It also plays a critical role in the great Hindu epic, the Mahabharata, where Yudhisthira plays a game of dice against the Kauravas for the northern kingdom of Hastinapura, which becomes the trigger for a great war. There are several biblical references to "casting lots", as in Psalm 22, indicating that it had become commonplace in the region as of the time of King David. In its primitive form knucklebones was essentially a game of skill played by women and children. In a derivative form of knucklebones, the four sides of the bones received different values and were counted as with modern dice. Gambling with three or sometimes two dice was a very popular form of amusement in Greece, especially with the upper classes, and was an almost invariable accompaniment to symposia.
(However, the "dice game" mentioned in Rigveda book 10 hymn 34 (which is about the harm that gambling addiction causes) is a game played with about 150 nuts from a tree called Vibhīdaka (Terminalia bellerica).)
Dice were probably originally made from the ankle bones (specifically the talus or "astragalus") of hoofed animals (such as oxen), colloquially known as "knucklebones", which are approximately tetrahedral. Modern Mongolians still use such bones, known as shagai, for games and fortunetelling. In addition to bone, ivory, wood, metal, and stone materials have been commonly used. Recently, the use of plastics, including cellulose acetate and Bakelite, is nearly universal. It is almost impossible to trace clearly the development of dice as distinguished from knucklebones, because ancient writers confused the two. It is certain, however, that both were used in prehistoric times.
The Romans were passionate gamblers, especially in the luxurious days of the Roman Empire, and dicing was a favorite form, though it was forbidden except during the Saturnalia. Horace derided what he presented as a typical youth of the period, who wasted his time amid the dangers of dicing instead of taming his charger and giving himself up to the hardships of the chase. Throwing dice for money was the cause of many special laws in Rome. One of these stated that no suit could be brought by a person who allowed gambling in his house, even if he had been cheated or assaulted. Professional gamblers were common, and some of their loaded dice are preserved in museums. The common publichouses were the resorts of gamblers, and a fresco is extant showing two quarrelling dicers being ejected by the indignant host. Twentysided dice date back to Roman times, as far back as 2nd century AD.^{[8]}
Tacitus states that the Germans were passionately fond of dicing, so much so, indeed, that, having lost everything, they would even stake their personal liberty. Centuries later, during the Middle Ages, dicing became the favorite pastime of the knights, and both dicing schools and guilds of dicers existed. After the downfall of feudalism the famous German mercenaries called landsknechts established a reputation as the most notorious dicing gamblers of their time. Many of the dice of the period were curiously carved in the images of men and beasts. In France both knights and ladies were given to dicing. This persisted through repeated legislation, including interdictions on the part of St. Louis in 1254 and 1256.
In China, India, Japan, Korea, and other Asiatic countries, dice have always been popular and are so still. The markings on Chinese dominoes evolved from the markings on dice, taken two at a time.
While the terms ace, deuce, trey, cater, cinque and sice are hardly common today having been replaced with the ordinary names of the numbers one to six, they are still used by some professional gamblers to describe the different sides of the dice. Ace is from the Latin as, meaning "a unit";^{[9]} the others are the numbers 2–6 in old French. (The dice game marketed as Kismet uses ace, deuce, and trey.)
In many modern gaming contexts, the count and number of sides of dice to be rolled at any given time is reduced to a common set of notations. Typically this involves the lowercase letter "d", preceded by a die count and followed by (optionally) the number of sides of the dice. For example, 6d8
or 2d6
; the former meaning "six eightsided dice," and the latter meaning "two sixsided dice." Addition or various other arithmetic operations are often added at the end as well, e.g. 3d6+4
"three sixsided dice plus four to the outcome thereof".
"Crooked dice" refers to dice that have been altered in some way to change the distribution of their outcome.
A loaded (or gaffed or cogged or weighted or crooked or gag) die is one that has been tampered with to land with a selected side facing upwards more often than it otherwise would simply by chance. There are methods of creating loaded dice, including having some edges round and other sharp and slightly off square faces. If the dice are not transparent, weights can be added to one side or the other. They can be modified to produce winners ("passers") or losers ("missouts"). "Tappers" have a drop of mercury in a reservoir at the center of the cube, with a capillary tube leading to another mercury reservoir at the side of the cube. The load is activated by tapping the die on the table so that the mercury leaves the center and travels to the side. Often one can see the circle of the cut used to remove the face and bury the weight. In a professional die, the weight is inserted in manufacture; in the case of a wooden die, this can be done by carving the die around a heavy inclusion, like a pebble around which a tree has grown.
A variable loaded die is hollow with a small weight and a semisolid substance inside, usually wax, whose melting point is just lower than the temperature of the human body. This allows the cheater to change the loading of the die by breathing on it or holding it firmly in hand, causing the wax to melt and the weight to drift down, making the chosen opposite face more likely to land up. A less common type of variable die can be made by inserting a magnet into the die and embedding a coil of wire in the game table. Then, either leave the current off and let the die roll unchanged or run current through the coil to increase the likelihood that the north side or the south side will land on the bottom depending on the direction of the current.
Transparent acetate dice, used in all reputable casinos, are harder to tamper with.
Cheat dice (see below) are often sold as loaded dice but usually are not technically loaded.
A die can be "shaved" on one side i.e. slightly shorter in one dimension, making it slightly rectangular and thus affecting its outcome. One countermeasure employed by casinos against shaved dice is to measure the dice with a micrometer.^{[10]}
Iced dice have lead in them, making them land on the 6 side more often. The "ice" refers to the lead in the dice.
If a die is heated in an oven for 10–15 minutes, with the desired face upward, the plastic will soften slightly and "pool" at the opposite (bottom) side without showing much, if any, visible distortion.
As noted, the faces of most dice are labeled using an unbroken series of whole numbers, starting at one (rarely zero), expressed with either pips or digits. Common exceptions include:
Doubling cube]]
]] ]] Some dice are polyhedral other than cubical in shape. Both seven– and eightsided dice of modern format are stated in the 13th century Libro de los juegos to have been invented by Alfonso X in order to speed up play in chess variants.^{[11]}^{[12]}
In more recent times around the early 1950s,^{[citation needed]} they have become popular among players of wargames and have since been employed extensively in roleplaying games, Germanstyle board games, and trading card games. Although polyhedral dice are a relative novelty during modern times, some ancient cultures appear to have used them in games (as evidenced by the discovery of two icosahedral dice dating from the days of ancient Rome, currently on display in the British Museum). In modern times, such dice are typically plastic, and have faces bearing numerals rather than patterns of dots. Reciprocally symmetric numerals are distinguished with a dot in the lower right corner (6. vs 9.) or by being underlined (6 vs 9).
The platonic solids are commonly used to make dice of 4, 6, 8, 12, and 20 faces. Other shapes can be found to make dice with other numbers of faces but, other than the 10sided, they are rarely used. (See Zocchihedron.) The 4sided platonic solid is difficult to roll, and a few games like Dayakattai and Daldøs use a 4sided rolling pin instead.
A large number of different probability distributions can be obtained using these dice in various ways. For example, 10sided dice (or 20sided dice labeled with single digits) are often used in pairs to produce a uniform distribution of random percentages; they avoid number base conversions and are more convenient. Summing multiple dice produces approximations to normal distributions ("bell curves"), while eliminating high or low throws can be used to skew the distribution in various ways.
Using these techniques, games can closely approximate the real probability distributions of the events they simulate.
There is some controversy over whether manufacturing processes create genuinely "fair" or "honest" dice (dice that roll with even distributions over their number span). Casino dice are legally required to be fair; those used by others are not subject to legally required standards.
Spherical dice also exist; these function like the plain cubic dice, but have an octahedral internal cavity in which a weight moves which causes them to settle in one of six orientations when rolled. However, these dice are somewhat awkward in use because they require a flat and level surface to roll properly — an uneven surface often causes them to stop partway between two numbers, while a sloped surface will cause the dice to keep rolling.
Cowry shells, Yut sticks or coins may be used as a kind of twosided dice. Because of their lack of symmetry, cowry shells and Yut sticks are not likely to yield a uniform distribution, and the angle and speed of the throw may possibly affect the result.
s set of five dice, (from left) tetrahedron (4 sides), cube (6), octahedron (8), dodecahedron (12), and icosahedron (20).]]
Dice are often sold in sets, matching in color, of five or six different shapes: the five Platonic solids, whose faces are regular polygons, and optionally the pentagonal trapezohedron, whose faces are ten kites, each with two different edge lengths and three different angles; the die's vertices also are of two different kinds.
Normally opposing faces of dice will add up to one more than the number of faces, but in the case of the d4, d5, and standard d10 (among others), this is simply not possible.
Sides  Shape  Notes  

4  tetrahedron  Each face has three numbers: they are arranged such that the upright number (which counts) is the same on all three visible faces. Alternatively, all of the sides have the same number in the lowest edge and no number on the top. This die does not roll well and thus it is usually thrown into the air instead.  
6  cube  A common die. The sum of the numbers on opposite faces is seven.  
8  octahedron  Each face is triangular; looks like two square pyramids attached basetobase. Usually, the sum of the opposite faces is 9.  
10  pentagonal trapezohedron  Each face is a kite. The die has two sharp corners, where five kites meet, and ten blunter corners, where three kites meet. The ten faces usually bear numbers from zero to nine, rather than one to ten (zero being read as "ten" in many applications). Often all odd numbered faces converge at one sharp corner, and the even ones at the other.  
12  dodecahedron  Each face is a regular pentagon.  
20  icosahedron  Faces are equilateral triangles. Typically, opposite faces add to twentyone. A 2nd century AD Roman icosahedron die is in the collection of the British Museum, though the game for which it was used is not known.^{[13]} 
Sides  Shape  Notes 

1  sphere  Most commonly a joke die^{[citation needed]}, this is just a sphere with a 1 marked on it. About spherical dice that may produce more than one result, see the section noncubical dice above. 
2  cylinder  This is nothing more than a coin shape with 1 marked on one side and 2 on the other. While some tasks in roleplaying require flipping a coin, the game rules usually simply call for the use of a coin rather than requiring the use of a twosided die. It is possible, however, to find dice of this sort for purchase, but they are rare, and can typically be found among other joke dice. 
3  Roundedoff triangular prism  This is a roundedoff triangular prism, intended to be rolled like a rollingpin style die. The die is roundedoff at the edges to make it impossible for it to somehow land on the triangular sides, which makes it look a bit like a jewel. When the die is rolled, one edge (rather than a side) appears facing upwards. On either side of each edge the same number is printed (from 1 to 3). The numbers on either side of the upfacing edge are read as the result of the die roll. Another possible shape is the "American Football" or "Rugby ball" shape, where the ends are pointed (with rounded points) rather than just rounded. A third variety features faces that resemble warped squares. 
5  Triangular prism  This is a prism that is thin enough to land either on its "edge" or "face". When landing on an edge, the result is displayed by digits (2–4) close to the prism's top edge. The triangular faces are labeled with the digits 1 and 5. 
7  Pentagonal prism  Similar in constitution to the 5sided die. When landing on an edge, the topmost edge has pips for 1–5. The pentagonal faces are labeled with the digits 6 and 7. This kind of die is particularly odd since it has pips for five of its results and digits for two of them. Sevensided dice are used in a sevenplayer variant of backgammon. Some variants have heptagonal ends and rectangular faces. 
12  rhombic dodecahedron  Each face is a rhombus. 
14  heptagonal trapezohedron  Each face is a kite. 
16  octagonal dipyramid  Each face is an isosceles triangle. 
24  tetrakis hexahedron  Each face is an isosceles triangle. 
24  deltoidal icositetrahedron  Each face is a kite. 
30  rhombic triacontahedron  Each face is a rhombus. Although not included in most dice kits, it can be found in most hobby and game stores. 
34  heptadecagonal trapezohedron  Each face is a kite. 
50  icosakaipentagonal trapezohedron  Similar to the 14 and 16sided dice, the faces of the 50sided die are kites, although very narrow. 
100  Zocchihedron  100sided dice can be found in hobby and game stores, and such a die is used in some narrative roleplaying games such as Dungeons & Dragons. They are not, however, a true polyhedron. A 100sided die is made by flattening 100 facets on a sphere. The name Zocchihedron was taken from its creator, Lou Zocchi. A typical d100 will be hollow and filled with small plastic objects to dampen the die's momentum when rolled (lest it take off like a golf ball). A 100sided die is equivalent to a pair of tensided dice, and so, even in roleplaying games, the Zocchihedron is rarely seen and is generally more of a novelty item. 
The full geometric set of "uniform fair dice" (facetransitive) are:
For a single roll of a fair ssided die, the probability of rolling each value, 1 through s, is exactly ^{1}/_{s}. This is an example of a discrete uniform distribution. For a double roll, however, the total of both rolls is not evenly distributed, but is distributed in a triangular curve. For two sixsided dice, for example, the probability distribution is as follows:
Sum            

Probability            
Probability (simplified)            
For three or more die rolls, the curve becomes more bellshaped with each additional die (according to the central limit theorem). The exact probability distribution $F\_\{s,n\}$ of a sum of n ssided dice can be calculated as the repeated convolution of the singledie probability distribution with itself.
where $F\_\{s,1\}(k)\; =\; \backslash frac\{1\}\{s\}$ for all $1\backslash leq\; k\; \backslash leq\; s$ and $0$ otherwise.
A fastest algorithm would adapt the exponentiation by squaring algorithm, using $F\_\{s,x+y\}(k)\; =\; \backslash sum\_i\; \{F\_\{s,x\}(i)\; F\_\{s,y\}(k\; \; i)\}\; \backslash ,$.
For example, in the triangular curve described above,
$F\_\{6,2\}(6)\backslash ,$  $=\backslash sum\_n\; \{F\_\{6,1\}(n)\; F\_\{6,1\}(6\; \; n)\}\backslash ,$ 
$=F\_\{6,1\}(1)\; F\_\{6,1\}(5)\; +\; F\_\{6,1\}(2)\; F\_\{6,1\}(4)\; +\; \backslash ldots\; +\; F\_\{6,1\}(5)\; F\_\{6,1\}(1)\backslash ,$  
$=5\backslash cdot\backslash frac\{1\}\{6\}\backslash cdot\backslash frac\{1\}\{6\}=\backslash frac\{5\}\{36\}\backslash approx0.14\backslash ,$ 
Equivalently, one can calculate the probability using combinations:
The probability of rolling any exact sequence of numbers is simply $\backslash frac\{1\}\{s^n\}$ . For example, the chance of rolling 1, 2, and 3 in that order with three rolls of a sixsided die is $\backslash frac\{1\}\{6^3\}$, or $\backslash frac\{1\}\{216\}$.
The article Sampling equiprobably with dice describes the probabilities of sampling with dice from any range.
s: a d4, d6, d8, d12, d20, and two d10s for percentile: ones and tens.]] While polyhedral dice had previously been used in teaching basic arithmetic, the fantasy roleplaying game Dungeons & Dragons is largely credited with popularizing their use in roleplaying games. Some games use only one type, such as Exalted which uses only tensided dice, while others use numerous types for different game purposes, such as Dungeons & Dragons, which make use of 20, 12, 10, 8 and 4sided dice in addition to the traditional 6sided die. Unlike the common sixsided die, these dice often have the numbers engraved on them rather than a series of dots.
Roleplaying games generally use dice to determine the outcome of events, such as the success or failure of actions which are difficult to perform. A player may have to roll dice for combat, skill use, or magic use, amongst other things, generally referred to as a "check". This is generally considered fairer than decision by game master fiat, since success and failure are decided randomly based on a flat probability. Games typically determine success as either a total on one or more dice above (Dungeons & Dragons third edition) or below (Call of Cthulhu) a target number, or a certain number of rolls above a certain number (such as 8 or higher on a d10) on one or more dice (White Wolf's World of Darkness series). The player may gain a bonus or penalty due to circumstances or character skill, usually either by a number added to or subtracted from the final result, or by having the player roll extra or fewer dice. For example, a character trying to climb a sheer wall may subtract from their dice roll (known as a penalty) if the wall is slippery, which simulates the increased difficulty of climbing a slickened surface, while a character using a rope may add to the roll (known as a bonus) to simulate that the rope makes the act of climbing easier.
Dice can also be used by a game master for other purposes, such as to randomly generate game content or to make arbitrary decisions. Some games use dice to determine what attributes the player's character has when created, such as how strong he or she is.
In Dungeons & Dragons and some other roleplaying games which use more than one kind of die, dice notation is used for clarity and conciseness. For example, a sixsided die is referred to as a d6
, and the notation for rolling two such dice is 2d6
. A constant bias may be added or subtracted by ordinary arithmetic: for example, 2d6+4
adds a 4 point bonus, while 2d62
subtracts a 2 point penalty. Games which use only one type of dice rarely require complex dice notation.
A common special case is percentile rolls, referred to in dice notation as 1d100
or 1d%
. Since actual hundredsided dice are large, almost spherical, and difficult to read, percentile rolls are usually handled by rolling two tensided dice together, using one as the "tens" and the other as the "units". A roll of ten or zero on either die is taken as a zero, unless both are zeros or tens, in which case this is 100 (rather than zero). To avoid this confusion, some sets of percentile dice exist where one is marked in tens (00, 10, 20... up to 90) and the other from 0 to 9. White and black percentile dice are also used, and are commonly found in colorcoded dice sets, or sold separately.
Dice for roleplaying games are usually made of plastic, though infrequently metal, wood, and semiprecious stone dice can be found. Early polyhedral dice from the 1970s and 1980s were made of a soft plastic that would easily wear as the die was used. Typical wear and tear would gradually round the corners and edges of the die until it was unusable. Many early dice were unmarked and players took great care in painting their sets of dice. Some twentysided dice of this era were numbered zero through nine twice; half of the numbers had to be painted a contrasting color to signify the "high" faces. Such a die could also double as a tensided die by ignoring the distinguishing coloring.
Dice can be used for divination. Using dice for such a purpose is called cleromancy. A pair of standard 6sided dice is usual though other forms of polyhedra can be used. Tibetan Buddhists sometimes use this method of divination.
It is uncertain if the Pythagoreans used the platonic solids as dice, but it is highly likely.^{[citation needed]} They referred to these perfect geometries as "the dice of the gods". Julia E. Diggins writes that the Pythagorean Brotherhood sought to understand the mysteries of the Universe through an understanding of geometry in polyhedra. (Guthrie: The Pythagorean Sourcebook)
Astrological dice are a specialized set of three 12sided dice for divination, using the concepts of astrology and containing astrological symbols for the planets, the zodiac signs and the astrological houses. The first die represents planets, the Sun, the Moon, and two nodes (North Node and South Node). The second die represents the 12 zodiac signs, and the third represents the 12 houses. In simplified terms, the planets, etc. could represent the 'actor'; the zodiac signs could represent the 'role' being played by the actor; and the house could represent the 'scene' in which the actor plays.
Rune dice are a specialized set of dice for divination (runecasting), using the symbols of the runes printed on the dice.
An icosahedron is used to provide the answers of a Magic 8Ball, which is conventionally used to provide advice on yesorno questions.

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This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed (1911). Encyclopædia Britannica (Eleventh ed.). Cambridge University Press.
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[[File:thumbright250pxDifferent types of dice]] Dice are objects used in games when something random needs to be done, such as moving a piece a random number of places on a board. Most dice are cubes that have the numbers 1, 2, 3, 4, 5 and 6 on the faces. Dice are sometimes made in other shapes than cubes, but the 6sided die (die is the single of dice) is the most common. A die is usually rolled by the player’s hand.
Some games are played with two dice and some use only one. Some games that use dice are Monopoly, Yahtzee, Risk, Dungeons and Dragons, and many more. Dice with different numbers of sides are called polyhedral dice.
Weights can be put inside a die to make it only land on a certain number once it is rolled.
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