 For other uses, see either Die or
Dice .
Two standard sixsided pipped dice
with rounded corners.
A
die or
dice (
plural dice, from
Old French dé, from
Latin datum "something given or played"
AskOxford: die^{2}) is a small
polyhedral object, usually cubic, 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 cubical
or other
polyhedral 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.
Ordinary dice
Common dice are small
cubes 1 to
3 cm along an edge (16 mm being the standard), whose
faces are numbered from one to six (usually by patterns of dots
called
pips). It is traditional to combine pairs of
numbers that total seven to opposite faces (it has been since at
least
classical antiquity) ;
this implies that at one
vertex
the faces 1, 2 and 3 intersect. It leaves one other 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
"right handed"; if they run clockwise it is called "left handed".
Standard modern Western dice are righthanded, whereas Chinese dice
are often lefthanded.
The pips on traditional European dice are arranged in specific
circular patterns. The face with two usually has the dots in
opposite corners, with the third face containing one between these
two. The fourth face has one in each corner, and the fifth adds one
in the center, forming a
quincunx. The
final face has two rows of three pips along opposite edges of the
face. Pips on Asianstyle dice are in a similar pattern, but are
typically closer to the centre of the die; the "one" pip is larger
than the others; and the "one" and "four" pips are coloured red. It
is suggested 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.
Several legends 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. 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. The bias is reduced somewhat in
the Japanese die with its oversized single pip (pictured). Casino
dice have markings that are flush, offering the assurance that this
brings them very close to providing true uniformly distributed
random numbers.
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 dice
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 are used, all stamped with a matching serial
number to prevent a cheat 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 somewhat smaller. Their
corners and edges are rounded to allow greater movement inside the
dice cup and prevent chaotic rolls from damaging the playing
surface.
Computer generated dice
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. Some sites which show examples of computer generated
random dice are
GoTinker and
random.org
History
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.
Excavations from ancient tombs in the
Harappan civilization, seem to
further indicate a
South Asian origin.
Dicing is mentioned as an
Indian
game in the
Rig Veda,
Atharva Veda and
Buddha games list.
It is also mentioned
in the great Hindu epic, the Mahabharata, where Yudhisthira plays a game of dice against the
Kauravas for the northern kingdom of
Hastinapura. 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.
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
[920].
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.
Terms
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"; the others are the numbers 2–6 in old French.(The dice game
marketed as
Kismet uses
ace,
deuce, and
trey.)
Notation
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
"Crooked dice" refers to dice that have been altered in some way to
change the distribution of their outcome.
Loaded dice
A
loaded or
gaffed or
cogged 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.
Plastic dice can be biased to roll a certain number by heating them
(for example in an oven) with the desired face upward, so that the
plastic will soften slightly and "pool" at the opposite (bottom)
side of the die without showing much, if any, visible
distortion.
Transparent
acetate dice, used in all
reputable
casinos, are harder to tamper
with.
Cheat dice
Cheat dice (see below) are often sold as loaded dice but usually
are not technically loaded.
Shaved dice
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.
Iced Dice
Iced dice have lead in them, making them land on the 6 side more
often. The "ice" refers to the lead in the dice.
Variants
Dice with faces other than digit sequences
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:
 color dice (e.g., with the colors of the playing pieces used in
a game)
 Poker dice, with labels reminiscent
of playing cards. Several varieties
exist, but the most common contain the following pattern:
9♣, 10♦, Jack
(blue), Queen (green), King (red), A♠
 dice with letters (e.g. in Boggle)
 average dice (2, 3, 3, 4, 4, 5) (In some war games, units are
identified as regulars or irregulars. Because regulars are more
predictable, the strength of a regular unit is multiplied by an
average die. For this reason, average dice are jocularly called
regular dice.)
 cheat dice, such as:
 one face each with two through five, and two with sixes,
or
 for craps, a pair of dice in which one die
has five on each face, and its mate has a mixture of twos and
sixes, guaranteeing rolls of seven or 11.
 dice with a single sequence of markings repeated multiple
times, for example:
 a cubical die numbered twice from 1 to 3, or thrice from 1 to
2.
 cubical dice numbered twice from 0 to 2. Dice rolls with these
dice have the same expected value as
the number of dice thrown.
 icosahedral dice numbered twice from 1 to 10 (commonly used in
Dungeons &
Dragons before the popularization of tensided dice).
 Fudge dice,
numbered twice from −1 to 1, represented as −, blank, +.
 random direction dice, also known as scatter dice. The dice
have arrows on each side; the outcome of a roll is a random
direction. Scatter dice are used in tabletop wargames such as Warhammer Fantasy Battle to
determine random movements of troops, wind direction or direction
of misfired arms. Note that this is an unusual case where the
majority of the time the die is read not according to which symbol
is shown on its uppermost face, but its compass orientation.
 A doubling cube with the numbers 2, 4, 8, 16, 32, and
64 is used in backgammon and some other
boardgames. This die is not actually rolled; it is used to denote
the current stakes of the game. There is also a doubling octahedron
with 1, 2, 4, 8, 16, 32, 64, and 128.
 Some board games use dice with
positive and negative numbers for use in gain or loss of
something.
 Sicherman dice, a pair having the
same odds of rolling a given sum as a pair of standard sixsided
dice, but with different markings: one die has 1, 3, 4, 5, 6, and
8, and the other has 1, 2, 2, 3, 3, and 4. Sicherman dice are the
only such alternative arrangement if positive whole numbers are
used.
 I Ching dice such as
 Eightsided dice bearing the eight trigrams
 Sixsided dice bearing yin and yang twice each, and old yin and
old yang once each
 "Projector dice" which are clear and marked only on one of each
pair of opposing faces. For a "six"sided die, e.g., a clear
twelvesided shape is used. Rolled on an overhead projector such a die will have
the top or bottom marking equally readable.
Noncubical dice
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.
In more recent times around the early 1950s, they have become
popular among players of
wargames and have
since been used 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
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 a
normal distribution (a "bell
curve"),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 obviously 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.
Standard variations
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 it was used for is not
known. 
Rarer variations
Sides 
Shape 
Notes 
1 
sphere 
Most commonly a joke die , 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. 
The full geometric set of "uniform fair dice" (
facetransitive) are:
 Platonic solids, the five regular
polyhedra: 4, 6, 8, 12, 20 sides
 Catalan solids, the dual of the 13 Archimedean solids: 12, 24, 30, 48, 60,
120 sides
 Bipyramids, the duals of the infinite
set of prism, with triangle faces:
any even number above 4
 Trapezohedrons, the duals of the
infinite set of antiprisms, with kite
faces: any even number above 4
 Disphenoids, an infinite set of
tetrahedra made from congruent nonregular triangles: 4 sides
 "Rollingpin style dice" (also called "rolling logs") are the
only way to make dice with an odd number of flat faces.
They are based on an infinite set of prisms. All the (rectangular) faces they
may actually land on are congruent, so they are equally fair. (The
other 2 sides of the prism are rounded or capped with a pyramid,
designed so that the dice never actually rests on those
faces.)
Probability
Probability distribution for the sum
of two sixsided dice
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 
2

3

4

5

6

7

8

9

10

11

12

Probability 
^{1}⁄_{36}

^{2}⁄_{36}

^{3}⁄_{36}

^{4}⁄_{36}

^{5}⁄_{36}

^{6}⁄_{36}

^{5}⁄_{36}

^{4}⁄_{36}

^{3}⁄_{36}

^{2}⁄_{36}

^{1}⁄_{36}

Probability (simplified) 
^{1}⁄_{36}

^{1}⁄_{18}

^{1}⁄_{12}

^{1}⁄_{9}

^{5}⁄_{36}

^{1}⁄_{6}

^{5}⁄_{36}

^{1}⁄_{9}

^{1}⁄_{12}

^{1}⁄_{18}

^{1}⁄_{36}

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.
 F_{s,n}(k) = \sum_{i=1}^{kn+1} {F_{s,1}(i) F_{s,n1}(k  i)}
\,
where F_{s,1}(k) = \frac{1}{s} for all 1\leq k \leq s and 0
otherwise.
A fastest algorithm would adapt the
exponentiation by squaring
algorithm, using F_{s,x+y}(k) = \sum_i {F_{s,x}(i) F_{s,y}(k  i)}
\,.
For example, in the triangular curve described above,
 { border="0" cellpadding="0" cellspacing="0"
Equivalently, one can calculate the probability using
combinations:
 F_{s,n}(k)=\frac{1}{s^n}\sum_{i=0}^{\left \lfloor \frac{kn}{s}
\right \rfloor} (1)^i {n \choose i} {ksi1 \choose n1}
The probability of rolling any exact sequence of numbers is simply
\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 \frac{1}{6^3}, or
\frac{1}{216}.
The article
Sampling
equiprobably with dicedescribes the probabilities of sampling
with dice from any range.
Application in roleplaying games
While polyhedral dice had previously been used in teaching basic
arithmetic, the
fantasyroleplaying gameDungeons & Dragonsis largely
credited with popularizing their use in roleplaying games. Some
games use only one type, such as
Exaltedwhich 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.
Typical roleplaying dice, showing a
variety of colors and styles.
Note the older handinked green 12sided die (showing an 11),
manufactured before preinked dice were common.
Many players collect or acquire a large number of mixed and
unmatching dice.
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 masterfiat, 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 & Dragonsthird 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 Darknessseries). 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 & Dragonsand some other roleplaying games
which use more than one kind of die,
dice
notationis 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 generally 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, sets of percentile
dice exist where one is marked in tens (00, 10, 20... up to 90) and
the other from 0 to 9.
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.
Use of dice for divination
Some people believe that 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
Pythagoreansused
the "
Platonic Solids" as dice, but
it is highly likely. They referred to these perfect geometries as
"The Dice of the Gods". Julia E. Diggins, writer of
String,
Straightedge, and Shadow(Viking Press, New York, 1965) writes
how the Pythagorean Brotherhood sought to understand the mysteries
of the Universe through an understanding of geometry in polyhedra.
It is recorded that the dodecahedron (12sided platonic solid) was
discovered by Pythagoras. (Guthrie: The Pythagorean
Sourcebook)
Astrological dice are a specialized set of three 12sided dice for
divination, using the concepts of
astrologyand containing astrological symbols for
the
planets, the
zodiacsigns 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
runesprinted 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.
See also
Notes
 Standard Dice from diceplay
 Chinese Dice from the Elliott Avedon Museum
& Archive of Games
 Gotinker.com, Project site
 Random.org  True Random Number Service,
Random.org Random number generation

http://www.presstv.ir/detail.aspx?id=5668§ionid=351020108
 Possehl, Gregory. "Meluhha". In: J. Reade (ed.) The Indian
Ocean in Antiquity. London: Kegan Paul Intl. 1996a,
133–208
 2.3, 4.38, 6.118, 7.52, 7.109
 AskOxford: ace

http://www.fullbooks.com/TheArtofIuglingorLegerdemaine.html
 http://games.rengeekcentral.com/tc4.html
 http://wwmat.mat.fc.ul.pt/~jnsilva/HJT2k9/AlfonsoX.pdf
 The International Bone Rollers' Guild
 Properties of Dice
References
 Persi Diaconis and Joseph B. Keller. "Fair Dice". The
American Mathematical Monthly, 96(4):337339, 1989.
(Discussion of dice that are fair "by symmetry" and "by
continuity".)
 Bias and Runs in Dice Throwing and Recording: A Few Million
Throws. G. R. Iverson. W. H. Longcour, et al. Psychometrika, Vol.
36, No. 1, March 1971
 Knizia, Reiner (1999). Dice Games
Properly Explained. Elliot Right Way Books. ISBN
0716021129.
External links
 Analysis of dice probabilities, also features Uspenski's work
on rolling multiple dice.
 mathematically "Fair Dice"

F_{6,2}(6)\, 
=\sum_n {F_{6,1}(n) F_{6,1}(6  n)}\, 


=F_{6,1}(1) F_{6,1}(5) + F_{6,1}(2) F_{6,1}(4) + \ldots +
F_{6,1}(5) F_{6,1}(1)\, 


=5\cdot\frac{1}{6}\cdot\frac{1}{6}=\frac{5}{36}\approx0.14\, 