373:
275:
416:
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1376:
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142:
501:
1839:
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1822:
554:
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1807:
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404:
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40:
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392:
1998:
1045:
854:
3715:
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2018:
1397:
1118:
1335:
1077:
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978:
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48:
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1213:. 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
2207:
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, a sphere with an octahedral cavity and a small internal weight will settle with one of the 6 points of the cavity
937:
Normally, the faces on a die will be placed so opposite faces will add up to one more than 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
861:
Various shapes such as two-sided or four-sided dice are documented in archaeological findings; for example, from
Ancient Egypt and 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
835:
A loaded, weighted, cheat, or crooked die is one that has been tampered with so that it will land with 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
2298:
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 the outcome of events. Games typically determine results either as a total on one or more dice above or below a
983:
Each face has three numbers, arranged such that the upright number, placed either near the vertex or near the opposite edge, is the same on all three visible faces. The upright numbers represent the value of the roll. This die does not roll well and thus it is usually thrown into the air instead.
933:
does not have a side that faces upward when it is at rest on a surface, so it must be read in 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.
546:
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
911:, 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.
50:
2299:
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,
55:
53:
49:
1318:
A long die intended to be rolled lengthwise. 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 up-facing edge are read as the result of the die roll.
54:
616:
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 the dice cup and stop forceful rolls from damaging the playing surface.
1106:. Icosahedra have been found dating to Roman/Ptolemaic times, but it is not known if they were used as gaming dice. Modern dice with 20 sides are sometimes numbered 0–9 twice as an alternative to 10-sided dice. The sum of the numbers on opposite faces is 21 if numbered 1–20.
52:
2281:
Typical role-playing dice, showing a variety of colors and styles. Note the older hand-inked green 12-sided die (showing an 11), manufactured before pre-inked dice were common. Many players collect or acquire a large number of mixed and unmatching
542:
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 is called "left-handed". Western dice are normally right-handed, and
Chinese dice are normally left-handed.
1054:. 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
2136:
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
187:
and up to the 2nd century CE) was played with flat two-sided throwsticks which indicated the number of squares a player could move, and thus functioned as a form of dice. Perhaps the oldest known dice were excavated as part of a
611:
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
1170:, an infinite set of tetrahedra made from congruent non-regular triangles: 4 sides. This is a less symmetric tetrahedron than the Platonic tetrahedron but still sufficiently symmetrical to be face-transitive. Similarly,
1362:
A prism 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.
2233:, have inverted this system by making the lower values more potent. In 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
589:. 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.
415:
372:
2094:
A sphere containing another sphere with 100 facets flattened into it. Note that this design is not isohedral; it does not function as a uniform fair die as some results are more likely than others.
903:. 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 is the 10-sided die, a
1961:
A truncated sphere with thirty-six landing positions. Rows of spots are present above and below each number 1 through 36 so that this die can be used to roll two six-sided dice simultaneously.
51:
607:
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 a paint of the same
2175:
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
604:
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.
2167:
Dice may have numbers that do not form 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
553:
3276:
570:
2466:. If the result of a modified dice roll is negative, it is often taken to be zero or one; for instance, when the dice roll determines the amount of damage to a creature.
2227:
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
2345:
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.
167:
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
2359:
In many gaming contexts, especially tabletop role-playing games, shorthand notations representing different dice rolls are used. A very common notation, considered a
857:
A typical set of polyhedral dice in various colors. They consist of the five
Platonic solids, along with a ten-sided die that is also used for generating percentages.
3109:
1381:
Five-faced long die for the Korean Game of
Dignitaries; notches indicating values are cut into the edges, since in an odd-faced long die these land uppermost.
672:
are generally obsolete, with the names of the numbers preferred, they are still used by some professional gamblers to designate different sides of the dice.
2274:
as dice. They referred to such dice as "the dice of the gods" and they sought to understand the universe through an understanding of geometry in polyhedra.
2251:), different sides of the dice can offer completely different abilities. Several sides often give resources while others grant the player useful actions.
473:, 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
945:
are arranged such that adjacent integers appear on adjacent faces, allowing the user to easily find the next lower number. They are commonly used with
941:
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
2817:
3040:
2434:
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
2306:
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
3595:
881:. Dice using both the numerals 6 and 9, which are reciprocally symmetric through rotation, typically distinguish them with a dot or underline.
934:
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.
3646:
274:
3735:
592:
The coloring for numbering is achieved by submerging the die entirely in paint, which is allowed to dry. The die is then polished via a
403:
3022:
2239:, 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
3392:
3283:
523:, most often 1.6 cm (0.63 in) across, whose faces are numbered from one to six, usually by patterns of round dots called
241:
3730:
3331:
3487:
The
Pythagorean sourcebook and library: an anthology of ancient writings which relate to Pythagoras and Pythagorean philosophy
2148:
354:
3494:
3259:
2983:
2958:
2859:
2626:
2597:
824:
129:
of the dice instead of marked on it. Loaded dice are specifically designed or modified to favor some results over others for
3309:
216:
dice dating to 2500–1900 BCE, including at least one die whose opposite sides all add up to seven, as in modern dice.
1125:"Uniform fair dice" are dice where all faces have an equal probability of outcome due to the symmetry of the die as it is
3207:
2782:
2216:
1209:
can, in principle, be made with any number of faces, including odd numbers. Long dice are based on the infinite set of
302:
were smaller dice with sides numbered from one to six. Twenty-sided dice date back to the 2nd century CE and from
3135:
316:
originated in China as developments from dice. The transition from dice to playing cards occurred in China around the
3679:
3579:
3252:
Playing at the World: A History of
Simulating Wars, People and Fantastic Adventures, from Chess to Role-Playing Games
1062:
ones at the other. The sum of the numbers on opposite faces is usually 9 (if numbered 0–9) or 11 (if numbered 1–10).
3113:
2262:. A pair of common dice is usual, though other forms of polyhedra can be used. Tibetan Buddhists sometimes use this
559:
Typical facets showing the more compact pip arrangement of an Asian-style die (top) vs. a
Western-style die (bottom)
2130:
459:
435:
Dice are thrown onto a surface either from the hand or from a container designed for this (such as a cup, tray, or
78:) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating
3764:
263:, indicating that dicing (or a related activity) was commonplace when the psalm was composed. Knucklebones was a
17:
2334:
2203:
A die can be constructed in the shape of a sphere, with the addition of an internal cavity in the shape of the
508:
895:
Dice are often sold in sets, matching in color, of six different shapes. Five of the dice are shaped like the
919:
869:
of polyhedral dice started around the end of the 1960s when non-cubical dice became popular among players of
1402:
Two six-faced long dice are used to simulate the activity of scoring runs and taking wickets in the game of
1297:. Some coins with 1 marked on one side and 2 on the other are available, but most simply use a common coin.
458:
by uncertainty in minor factors such as tiny movements in the thrower's hand; they are thus a crude form of
3708: – analysis of dice probabilities, also featuring Uspenski's work on rolling multiple dice
2900:
2875:
2506:
1182:
Two other types of polyhedra are technically not face-transitive but are still fair dice due to symmetry:
477:, where they are often used to decide the distance through which a piece will move along the board (as in
3544:
1832:
697:
534:
Opposite sides of a modern die traditionally add up to seven, requiring the 1, 2, and 3 faces to share a
3471:
3044:
2292:(D&D) is largely credited with popularizing dice in such games. Some games use only one type, like
2045:
1800:
121:
or irregular shapes, may have faces marked with numerals or symbols instead of pips and may have their
2565:
2102:
2011:
586:
209:
2717:
1154:, with kite faces: any even number not divisible by 4 (so that a face will face up), starting from 6
3007:
The
Opposite Pairs of Numbers on a Die. The numbers on a die run so: six one, five two, three four.
2143:
1575:
1038:
915:
904:
220:
1581:
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1044:
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3642:
2756:
1888:
287:
156:
3610:
3225:
1969:
1431:
117:
from one to six on its upper surface, with each value being equally likely. Dice may also have
79:
2614:
922:
of random percentages, and summing the values of multiple dice will produce approximations to
2948:
2851:
2844:
2288:
2028:
1919:
946:
878:
811:
characters, the faces can be shown in text using the range U+2680 to U+2685 or using decimal
601:
33:
2195:
1704:
Eighteen faces are squares. The eight triangular faces are rounded and cannot be landed on.
1340:
A long die intended to be rolled lengthwise. It cannot stand on end as the ends are capped.
3657:, 96(4):337–339, 1989 (Discussion of dice that are fair "by symmetry" and "by continuity".)
3417:
3162:
1596:
1533:
1447:
1103:
1070:
1059:
1055:
320:(618–907 CE), and coincides with the technological transition from rolls of manuscripts to
271:; a derivative form had the four sides of bones receive different values like modern dice.
3026:
8:
3757:
3385:
2235:
2062:
1918:
A truncated sphere with thirty-two landing positions. The design is similar to that of a
1783:
1692:
1653:
1441:
1277:
1090:
1082:
Each face is a regular pentagon. The sum of the numbers on opposite faces is usually 13.
923:
447:
446:
The result of a die roll is determined by the way it is thrown, according to the laws of
141:
391:
3866:
3821:
3589:
3445:
2694:
2669:
2529: – Pattern of five points, four in a square or rectangle and a fifth at its center
2514:
2286:
Polyhedral dice are commonly used in role-playing games. The fantasy role-playing game
1838:
1766:
1164:, with triangle faces: any multiple of 4 (so that a face will face up), starting from 8
500:
466:
443:) of the die that is uppermost when it comes to rest provides the value of the throw.
321:
87:
3000:
2051:
3693:
3675:
3575:
3500:
3490:
3338:
3255:
3058:
2979:
2954:
2922:
2855:
2699:
2681:
2670:"The Burnt City and the Evolution of the Concept of "Probability" In the Human Brain"
2622:
2593:
2520:
2315:
2311:
2184:
1141:
874:
837:
582:
535:
439:). The face (or corner, in cases such as tetrahedral dice, or edge, for odd-numbered
383:
303:
95:
3178:
2642:
1821:
1076:
2689:
2538:
2482:
2229:
2179:, where a narrower range of numbers is required. Other numbered variations include
1982:
1418:
1350:
1306:
1281:
1210:
1195:
1161:
1126:
890:
593:
1096:
977:
3845:
3650:
3005:. Translated by Paton, W.R. New York: G.P. Putnam's and Sons. 1918. Book 14, §8.
2271:
2263:
2204:
2172:
2034:
1806:
1588:
1137:
1051:
966:
908:
900:
528:
483:
249:
113:) from one to six. When thrown or rolled, the die comes to rest showing a random
2523: – Game variations and descriptions of intransitive die and their behaviour
1265:
1244:
1018:
630:
3861:
3797:
3750:
3638:
3196:
2476:
2180:
2068:
1623:
A truncated sphere with fourteen landing positions. The design is based on the
1451:
1407:
1261:
1025:
930:
896:
692:
597:
524:
268:
160:
110:
99:
1772:
709:, is a roll of six pips on each die. The pair of six pips resembles a pair of
3892:
3886:
3871:
3792:
3726:
3721:
3667:
3504:
2685:
2360:
2354:
2300:
1624:
1459:
1406:. Originally played with labeled six-sided pencils, and often referred to as
1147:
1133:
1033:
914:
Using these dice in various ways, games can closely approximate a variety of
613:
264:
204:, Scotland have been dated to 3100–2400 BCE. Excavations from graves at
176:
83:
714:
639:
3829:
3739:. Vol. 8 (11th ed.). Cambridge University Press. p. 176–177.
3363:
3139:
2703:
2330:
2319:
2307:
2267:
2082:
1930:
1617:
1539:
1507:
A ten-sided die made by truncating two opposite vertices of an octahedron.
1430:
Similar in constitution to the 5-sided die. Seven-sided dice are used in a
1171:
379:
360:
337:
317:
313:
205:
172:
3696:
3084:
1789:
1698:
998:
2247:
1997:
1190:
1121:
Dice collection: D2–D22, D24, D26, D28, D30, D36, D48, D50, D60 and D100.
971:
236:
230:
3277:"Tumbling Dice & Birthdays: Understanding the Central Limit Theorem"
2901:"Twenty-sided die (icosahedron) with faces inscribed with Greek letters"
298:
were large dice inscribed with one, three, four, and six on four sides.
39:
2560:
2500:
2488:
2399:
means the player should roll six eight-sided dice and sum the results.
2338:
2259:
2255:
2152:
1435:
1214:
1167:
1012:
687:
When rolling two dice, certain combinations have slang names. The term
681:
626:
478:
474:
455:
436:
333:
213:
201:
193:
189:
184:
168:
118:
91:
27:
Throwable objects with marked sides, used for generating random numbers
2619:
Beyond
Babylon: Art, Trade, and Diplomacy in the Second Millennium B.C
200:, estimated to be from between 2800 and 2500 BCE. Bone dice from
3701:
2402:
The notation also allows for adding or subtracting a constant amount
2241:
1294:
1202:
1186:
1178:
are less symmetrical but still face-transitive dodecahedra: 12 sides.
1175:
1157:
1151:
539:
504:
440:
364:
345:
2541: – Objects used for divination in the early Abrahamic religions
2017:
1396:
1264:
die, this is either a sphere with a 1 marked on it or shaped like a
1218:
1028:
attached base-to-base. Usually, the sum of the opposite faces is 9.
2532:
2526:
2342:
2326:
2156:
2125:
1608:
A truncated octahedron. Each face is either a square or a hexagon.
1390:
1369:
1328:
1206:
1129:. In addition to the Platonic solids, these theoretically include:
1117:
422:
325:
309:
260:
130:
126:
109:
with each of its six faces marked with a different number of dots (
3812:
3720:
This article incorporates text from a publication now in the
3662:
Bias and Runs in Dice Throwing and Recording: A Few Million Throws
1334:
918:. For instance, 10-sided dice can be rolled in pairs to produce a
2494:
2462:
instructs the player to subtract four from the result of rolling
2322:, conventionally used to provide answers to yes-or-no questions.
2294:
2176:
1546:
1483:
1403:
870:
853:
808:
608:
454:
is often credited for the results of a roll). A die roll is made
279:
224:
114:
2088:
1602:
1501:
290:
were passionate gamblers who enjoyed dicing, which was known as
2387:
is the number of sides on each die; if only one die is rolled,
2138:
1248:
710:
574:
122:
3043:. Elliott Avedon Museum & Archive of Games. Archived from
938:
opposite faces will add to one less than the number of faces.
840:
dice, as tampering is easier to detect than with opaque dice.
324:
books. In Japan, dice were used to play a popular game called
3773:
1677:
1004:
A common die. The sum of the numbers on opposite faces is 7.
635:
470:
421:
Chinese dice from Late Yuan Dynasty to early Qing Dynasty in
245:
180:
3059:"7 Surprising Facts About How Dice Are Made (With Pictures)"
2318:. A specialized icosahedron die provides the answers of the
1955:
1874:
1856:
1734:
409:
A collection of historical dice from various regions of Asia
3518:
2976:
Japanese Popular Prints: From Votive Slips to Playing Cards
2277:
1975:
1912:
1752:
1716:
1659:
1639:
1561:
1519:
1312:
992:
520:
451:
197:
106:
3310:"What's a spindown dice and are standard d20s any fairer?"
2511: – Musical dice games used to randomly generate music
1465:
1254:
2337:
describes a method by which dice can be used to generate
648:
569:
294:("to play at dice"). There were two sizes of Roman dice.
3742:
1880:
A truncated sphere with twenty-eight landing positions.
701:
traces use of the term as far back as 1919. The US term
2325:
Dice can be used to generate random numbers for use in
2108:
2406:
to the roll. When an amount is added, the notation is
1937:
1894:
1862:
A truncated sphere with twenty-six landing positions.
1758:
A truncated sphere with twenty-two landing positions.
1740:
A truncated sphere with twenty-one landing positions.
1424:
1356:
1287:
1268:. It entirely defies the aforementioned use of a die.
43:
Four traditional dice showing all six different sides.
1683:
A truncated sphere with seventeen landing positions.
1438:. Seven-sided dice are described in the 13th century
1722:
A truncated sphere with nineteen landing positions.
1567:
A truncated sphere with thirteen landing positions.
581:
Non-precision dice are manufactured via the plastic
59:
Dice of different sizes being thrown in slow motion.
1645:A truncated sphere with fifteen landing positions.
2843:
1525:A truncated sphere with eleven landing positions.
1024:Each face is triangular and the die resembles two
531:is occasionally seen, such dice are less common.)
2780:
1471:A truncated sphere with seven landing positions.
3884:
2783:"Rig Veda 10.34.1 [English translation]"
2741:Possehl, Gregory. "Meluhha". In: J. Reade (ed.)
2535: – Spinning lot, generating random outcomes
2497: – Four-sided spinning top used on Hanukkah
1489:A truncated sphere with nine landing positions.
2667:
3164:The Number Concept: Its Origin and Development
2718:"National Museums of Scotland - Two bone dice"
2310:of the Moon, the second die represents the 12
2162:
873:, and since have been employed extensively in
278:Roman wall painting showing two dice-players,
145:Composite image of all sides of a 12 mm (
3758:
3691:
3446:"[TMP] 'What are Average Dice' Topic"
3179:"s | Search Online Etymology Dictionary"
2950:The Shorter Science and Civilisation in China
2668:NASER MOGHADASI, Abdorreza (September 2015).
2517: – Method of review often used in Norway
1439:
680:, meaning "a unit"; the others are 2 to 6 in
3545:"EFF's New Wordlists for Random Passphrases"
3243:
2946:
2754:
2258:and using dice for such a purpose is called
1058:faces converge at one sharp corner, and the
3664:, Psychometrika, vol. 36, no. 1, March 1971
3197:"Dice faces in block Miscellaneous Symbols"
3017:
3015:
2978:. University of Hawaii Press. p. 164.
2621:. Metropolitan Museum of Art. p. 151.
3765:
3751:
3594:: CS1 maint: location missing publisher (
3274:
2953:. Cambridge University Press. p. 55.
836:gambling halls frequently use transparent
547:sides. Red fours may be of Indian origin.
219:Games involving dice are mentioned in the
3660:Iverson, G. R.; Longcour, W. H.; et al.;
2745:. London: Kegan Paul Intl. 1996a, 133–208
2693:
2155:, and instructions for sexual acts using
720:
196:, an archeological site in south-eastern
171:of hoofed animals, colloquially known as
3725:
3307:
3249:
3223:
3012:
2755:Ashmolean Museum, University of Oxford.
2276:
2215:
2194:
2124:
1116:
852:
568:
499:
273:
140:
46:
38:
3572:Dungeons & Dragons Rules Compendium
3484:
2974:Salter, Rebecca (2006). "Board Games".
2895:
2893:
2850:. Greenwood Publishing Group. pp.
2592:. SAGE Publications. pp. 171–173.
2590:Encyclopedia of Play in Today's Society
14:
3885:
3608:
3440:
3438:
3275:Paret, Michelle; Martz, Eston (2009).
3160:
3154:
2973:
2947:Ronan, Colin; Needham, Joseph (1986).
2612:
1198:: the basis of long dice and teetotums
643:"something which is given or played".
620:
306:as early as the 2nd century BCE.
3746:
3692:
3112:. Oxford Dictionaries. Archived from
2587:
825:Miscellaneous Symbols and Pictographs
67:
3472:"Making better use of dice in games"
3254:. Unreason Press. pp. 315–318.
3224:Horridge, Kevin (27 November 2017).
3171:
2890:
2841:
2781:www.wisdomlib.org (27 August 2021).
2581:
2391:is normally not shown. For example,
2074:Each face is an isosceles triangle.
2057:Each face is an irregular pentagon.
2040:Each face is an isosceles triangle.
1844:Each face is an irregular pentagon.
1795:Each face is an isosceles triangle.
1778:Each face is an isosceles triangle.
1665:Each face is an isosceles triangle.
884:
713:on a freight train. Many rolls have
286:Although gambling was illegal, many
3569:
3435:
3410:
2822:Johns Hopkins Archaeological Museum
2643:"8 Oldest Board Games in the World"
2606:
2223:by Master Jean de Mauléon (c. 1520)
2120:
1160:, the duals of the infinite set of
1150:, the duals of the infinite set of
1112:
538:. The faces of a die may be placed
328:. There are two types of sugoroku.
253:
24:
3609:Mearls, Mike; et al. (2016).
3489:. Grand Rapids, MI: Phanes Press.
3308:Girdwood, Andrew (30 March 2019).
2923:"domino | game piece | Britannica"
1817:Pseudo-deltoidal icositetrahedron
848:
25:
3909:
3685:
3655:The American Mathematical Monthly
3398:from the original on 2 March 2011
3329:
3226:"6 Ways Casinos Stop Dice Cheats"
3213:from the original on 3 June 2001.
2383:is the number of dice rolled and
2190:
2114:Each face is a scalene triangle.
819:, and the emoji using U+1F3B2 or
3811:
3713:
3674:, Elliot Right Way Books, 1999,
3519:"EFF Dice-Generated Passphrases"
2846:Daily Life of the Ancient Romans
2815:
2674:Iranian Journal of Public Health
2491: – Role-playing game system
2107:
2087:
2067:
2050:
2033:
2016:
1996:
1974:
1954:
1936:
1911:
1893:
1873:
1855:
1837:
1820:
1805:
1788:
1771:
1751:
1733:
1715:
1697:
1676:
1658:
1638:
1616:
1601:
1580:
1560:
1538:
1518:
1500:
1482:
1464:
1423:
1395:
1374:
1355:
1333:
1311:
1286:
1253:
1095:
1075:
1043:
1017:
997:
976:
564:
552:
460:hardware random number generator
414:
402:
390:
371:
353:
3632:
3611:"System Reference Document 5.1"
3602:
3563:
3537:
3511:
3478:
3464:
3378:
3356:
3323:
3301:
3268:
3217:
3189:
3128:
3102:
3077:
3051:
3033:
2992:
2967:
2940:
2915:
2868:
2835:
2809:
2800:
2314:, and the third represents the
2266:. It is highly likely that the
2211:
1144:: 12, 24, 30, 48, 60, 120 sides
490:
3574:. Renton, WA USA. p. 17.
3549:Electronic Frontier Foundation
3523:Electronic Frontier Foundation
2774:
2748:
2735:
2710:
2661:
2635:
2553:
2335:Electronic Frontier Foundation
2208:held downwards by the weight.
1993:Icosipentagonal trapezohedron
865:The modern tradition of using
830:
587:polymethyl methacrylate (PMMA)
495:
248:references to "casting lots" (
13:
1:
3672:Dice Games Properly Explained
3161:Conant, Levi Leonard (1896).
2806:2.3, 4.38, 6.118, 7.52, 7.109
2743:The Indian Ocean in Antiquity
2546:
2503: – Automobile decoration
1450:in order to speed up play in
540:clockwise or counterclockwise
507:of dice. Faces may be placed
2395:denotes one four-sided die;
931:four-sided (tetrahedral) die
929:Unlike other common dice, a
7:
3250:Peterson, Jon (July 2012).
3138:. AskOxford. Archived from
2469:
2363:, expresses a dice roll as
2348:
2163:Alternatively-numbered dice
2151:, playing card symbols for
1833:Pentagonal icositetrahedron
1446:as having been invented by
843:
698:Online Etymology Dictionary
10:
3914:
3366:. games.rengeekcentral.com
3364:"games.rengeekcentral.com"
2761:jameelcentre.ashmolean.org
2479: – Form of divination
2352:
2046:Pentagonal hexecontahedron
1801:Deltoidal icositetrahedron
888:
715:names in the game of craps
136:
31:
3854:
3838:
3820:
3809:
3780:
3772:
3641:; and Keller, Joseph B.;
3485:Guthrie, Kenneth (1988).
3282:. Minitab. Archived from
3167:. Macmillan. p. 124.
2569:. Oxford University Press
2508:Musikalisches Würfelspiel
2103:Disdyakis triacontahedron
2012:Deltoidal hexecontahedron
2007:
1762:
1571:
1414:
1344:
957:
916:probability distributions
907:die, whose faces are ten
465:One typical contemporary
210:Indus Valley civilization
183:(played before 3000
3649:21 February 2008 at the
2144:Warhammer Fantasy Battle
1900:Each face is a rhombus.
1576:Heptagonal trapezohedron
1039:Pentagonal trapezohedron
905:pentagonal trapezohedron
625:The word die comes from
3736:Encyclopædia Britannica
2613:Finkel, Irving (2008).
1889:Rhombic triacontahedron
585:process, often made of
509:counterclockwise (top)
105:A traditional die is a
2289:Dungeons & Dragons
2283:
2224:
2200:
2171:, which have the same
2133:
1970:Disdyakis dodecahedron
1440:
1122:
947:collectible card games
858:
721:Unicode representation
578:
519:Common dice are small
516:
430:
283:
212:settlement, unearthed
192:-like game set at the
164:
82:, commonly as part of
60:
44:
2280:
2254:Dice can be used for
2245:(and its descendant,
2219:
2198:
2128:
2029:Pentakis dodecahedron
2023:Each face is a kite.
2003:Each face is a kite.
1943:Each face is a kite.
1920:truncated icosahedron
1827:Each face is a kite.
1812:Each face is a kite.
1120:
1104:equilateral triangles
889:Further information:
856:
572:
503:
340:(794–1185 CE), while
277:
144:
58:
42:
34:Dice (disambiguation)
3386:"wwmat.mat.fc.ul.pt"
3332:"Properties of Dice"
3204:The Unicode standard
3142:on 29 September 2007
2842:Matz, David (2002).
2303:is frequently used.
2264:method of divination
1597:Truncated octahedron
1534:Rhombic dodecahedron
1432:seven-player variant
924:normal distributions
920:uniform distribution
573:Western, Asian, and
527:. (While the use of
244:. There are several
125:carved out from the
32:For other uses, see
3570:Sim, Chris (2007).
3450:The Miniatures Page
3116:on 14 February 2015
3002:The Greek anthology
2588:Laird, Jay (2009).
2236:Castles of Burgundy
2063:Triakis icosahedron
1784:Tetrakis hexahedron
1693:rhombicuboctahedron
1654:Octagonal bipyramid
1442:Libro de los juegos
621:Etymology and terms
596:process similar to
448:classical mechanics
242:Buddhist games list
3867:Jerry L. Patterson
3694:Weisstein, Eric W.
3452:. 20 November 2009
3289:on 1 November 2013
3183:www.etymonline.com
2927:www.britannica.com
2649:. 29 November 2017
2515:Die throw (review)
2333:applications. The
2284:
2225:
2201:
2134:
1767:Triakis octahedron
1142:Archimedean solids
1123:
899:, whose faces are
879:trading card games
875:role-playing games
862:and Roman times.
859:
676:is from the Latin
579:
517:
284:
165:
133:or entertainment.
96:role-playing games
61:
45:
3880:
3879:
3496:978-0-933999-50-3
3474:. 2 October 2014.
3261:978-0-615-64204-8
3089:www.dice-play.com
2985:978-0-8248-3083-0
2960:978-0-521-31560-9
2861:978-0-313-30326-5
2816:Good, Alexandra.
2787:www.wisdomlib.org
2757:"Terracotta Dice"
2628:978-1-58839-295-4
2599:978-1-4522-6610-7
2521:Intransitive dice
2485: – Dice game
2230:Axis & Allies
2185:intransitive dice
2141:, directions for
2118:
2117:
1951:Truncated sphere
1908:Truncated sphere
1870:Truncated sphere
1852:Truncated sphere
1748:Truncated sphere
1730:Truncated sphere
1712:Truncated sphere
1673:Truncated sphere
1635:Truncated sphere
1613:Truncated sphere
1557:Truncated sphere
1515:Truncated sphere
1479:Truncated sphere
1110:
1109:
885:Common variations
838:cellulose acetate
805:
804:
695:on each die. The
691:is a roll of one
583:injection molding
336:and dates to the
56:
16:(Redirected from
3905:
3815:
3767:
3760:
3753:
3744:
3743:
3740:
3719:
3717:
3716:
3707:
3706:
3626:
3625:
3623:
3621:
3615:
3606:
3600:
3599:
3593:
3585:
3567:
3561:
3560:
3558:
3556:
3541:
3535:
3534:
3532:
3530:
3515:
3509:
3508:
3482:
3476:
3475:
3468:
3462:
3461:
3459:
3457:
3442:
3433:
3432:
3430:
3428:
3414:
3408:
3407:
3405:
3403:
3397:
3390:
3382:
3376:
3375:
3373:
3371:
3360:
3354:
3353:
3351:
3349:
3343:
3337:. Archived from
3336:
3327:
3321:
3320:
3318:
3316:
3305:
3299:
3298:
3296:
3294:
3288:
3281:
3272:
3266:
3265:
3247:
3241:
3240:
3238:
3236:
3221:
3215:
3214:
3212:
3201:
3193:
3187:
3186:
3175:
3169:
3168:
3158:
3152:
3151:
3149:
3147:
3132:
3126:
3125:
3123:
3121:
3106:
3100:
3099:
3097:
3095:
3081:
3075:
3074:
3072:
3070:
3065:. 19 August 2019
3055:
3049:
3048:
3037:
3031:
3030:
3029:on 30 July 2013.
3025:. Archived from
3019:
3010:
3009:
2996:
2990:
2989:
2971:
2965:
2964:
2944:
2938:
2937:
2935:
2933:
2919:
2913:
2912:
2910:
2908:
2897:
2888:
2887:
2885:
2883:
2872:
2866:
2865:
2849:
2839:
2833:
2832:
2830:
2828:
2813:
2807:
2804:
2798:
2797:
2795:
2793:
2778:
2772:
2771:
2769:
2767:
2752:
2746:
2739:
2733:
2732:
2730:
2728:
2714:
2708:
2707:
2697:
2680:(9): 1306–1307.
2665:
2659:
2658:
2656:
2654:
2639:
2633:
2632:
2610:
2604:
2603:
2585:
2579:
2578:
2576:
2574:
2557:
2539:Urim and Thummim
2483:Crown and Anchor
2465:
2461:
2433:
2398:
2394:
2170:
2169:2, 3, 3, 4, 4, 5
2121:Non-numeric dice
2111:
2091:
2071:
2054:
2037:
2020:
2000:
1983:scalene triangle
1978:
1958:
1940:
1915:
1897:
1877:
1859:
1841:
1824:
1809:
1792:
1775:
1755:
1737:
1719:
1701:
1680:
1662:
1642:
1620:
1605:
1584:
1564:
1542:
1522:
1504:
1486:
1468:
1460:Truncated sphere
1445:
1427:
1419:Pentagonal prism
1399:
1378:
1359:
1351:Triangular prism
1337:
1315:
1307:triangular prism
1290:
1260:Most commonly a
1257:
1224:
1223:
1113:Rarer variations
1099:
1079:
1047:
1021:
1001:
980:
952:
951:
901:regular polygons
822:
818:
814:
725:
724:
705:, also known as
646:While the terms
594:tumble finishing
556:
418:
406:
394:
375:
357:
255:
154:
153:
149:
69:
57:
21:
3913:
3912:
3908:
3907:
3906:
3904:
3903:
3902:
3883:
3882:
3881:
3876:
3850:
3846:Craps principle
3834:
3816:
3807:
3776:
3771:
3729:, ed. (1911). "
3714:
3712:
3688:
3651:Wayback Machine
3639:Diaconis, Persi
3635:
3630:
3629:
3619:
3617:
3613:
3607:
3603:
3587:
3586:
3582:
3568:
3564:
3554:
3552:
3543:
3542:
3538:
3528:
3526:
3517:
3516:
3512:
3497:
3483:
3479:
3470:
3469:
3465:
3455:
3453:
3444:
3443:
3436:
3426:
3424:
3418:"Specialist D6"
3416:
3415:
3411:
3401:
3399:
3395:
3388:
3384:
3383:
3379:
3369:
3367:
3362:
3361:
3357:
3347:
3345:
3341:
3334:
3328:
3324:
3314:
3312:
3306:
3302:
3292:
3290:
3286:
3279:
3273:
3269:
3262:
3248:
3244:
3234:
3232:
3222:
3218:
3210:
3199:
3195:
3194:
3190:
3177:
3176:
3172:
3159:
3155:
3145:
3143:
3134:
3133:
3129:
3119:
3117:
3108:
3107:
3103:
3093:
3091:
3083:
3082:
3078:
3068:
3066:
3057:
3056:
3052:
3039:
3038:
3034:
3023:"Standard Dice"
3021:
3020:
3013:
2999:
2997:
2993:
2986:
2972:
2968:
2961:
2945:
2941:
2931:
2929:
2921:
2920:
2916:
2906:
2904:
2903:. metmuseum.org
2899:
2898:
2891:
2881:
2879:
2878:. christies.com
2876:"christies.com"
2874:
2873:
2869:
2862:
2840:
2836:
2826:
2824:
2814:
2810:
2805:
2801:
2791:
2789:
2779:
2775:
2765:
2763:
2753:
2749:
2740:
2736:
2726:
2724:
2722:nms.scran.ac.uk
2716:
2715:
2711:
2666:
2662:
2652:
2650:
2641:
2640:
2636:
2629:
2611:
2607:
2600:
2586:
2582:
2572:
2570:
2559:
2558:
2554:
2549:
2544:
2472:
2463:
2459:
2431:
2430:; for example,
2396:
2392:
2357:
2351:
2272:Platonic solids
2214:
2205:dual polyhedron
2199:A spherical die
2193:
2173:arithmetic mean
2168:
2165:
2123:
1981:Each face is a
1587:Each face is a
1545:Each face is a
1389:Capped 6-sided
1368:Capped 5-sided
1327:Capped 4-sided
1189:: the basis of
1127:face-transitive
1115:
1050:Each face is a
1026:square pyramids
897:Platonic solids
893:
887:
851:
849:Polyhedral dice
846:
833:
820:
816:
812:
723:
623:
567:
560:
557:
529:Arabic numerals
498:
493:
433:
426:
419:
410:
407:
398:
395:
386:
384:Ptolemaic Egypt
376:
367:
358:
304:Ptolemaic Egypt
151:
147:
146:
139:
100:games of chance
47:
37:
28:
23:
22:
18:Polyhedral dice
15:
12:
11:
5:
3911:
3901:
3900:
3898:Gaming devices
3895:
3878:
3877:
3875:
3874:
3869:
3864:
3862:Frank Scoblete
3858:
3856:
3852:
3851:
3849:
3848:
3842:
3840:
3836:
3835:
3833:
3832:
3826:
3824:
3822:Advantage play
3818:
3817:
3810:
3808:
3806:
3805:
3800:
3798:Floating craps
3795:
3790:
3784:
3782:
3778:
3777:
3770:
3769:
3762:
3755:
3747:
3727:Chisholm, Hugh
3710:
3709:
3687:
3686:External links
3684:
3683:
3682:
3668:Knizia, Reiner
3665:
3658:
3634:
3631:
3628:
3627:
3601:
3580:
3562:
3551:. 19 July 2016
3536:
3510:
3495:
3477:
3463:
3434:
3409:
3377:
3355:
3344:on 28 May 2012
3322:
3300:
3267:
3260:
3242:
3216:
3188:
3170:
3153:
3127:
3101:
3076:
3050:
3047:on 1 May 2008.
3041:"Chinese Dice"
3032:
3011:
2991:
2984:
2966:
2959:
2939:
2914:
2889:
2867:
2860:
2834:
2818:"Knucklebones"
2808:
2799:
2773:
2747:
2734:
2709:
2660:
2634:
2627:
2605:
2598:
2580:
2551:
2550:
2548:
2545:
2543:
2542:
2536:
2530:
2524:
2518:
2512:
2504:
2498:
2492:
2486:
2480:
2477:Astragalomancy
2473:
2471:
2468:
2353:Main article:
2350:
2347:
2213:
2210:
2192:
2191:Spherical dice
2189:
2181:Sicherman dice
2164:
2161:
2122:
2119:
2116:
2115:
2112:
2105:
2100:
2096:
2095:
2092:
2085:
2080:
2076:
2075:
2072:
2065:
2059:
2058:
2055:
2048:
2042:
2041:
2038:
2031:
2025:
2024:
2021:
2014:
2009:
2005:
2004:
2001:
1994:
1991:
1987:
1986:
1979:
1972:
1967:
1963:
1962:
1959:
1952:
1949:
1945:
1944:
1941:
1934:
1933:trapezohedron
1931:Heptadecagonal
1928:
1924:
1923:
1916:
1909:
1906:
1902:
1901:
1898:
1891:
1886:
1882:
1881:
1878:
1871:
1868:
1864:
1863:
1860:
1853:
1850:
1846:
1845:
1842:
1835:
1829:
1828:
1825:
1818:
1814:
1813:
1810:
1803:
1797:
1796:
1793:
1786:
1780:
1779:
1776:
1769:
1764:
1760:
1759:
1756:
1749:
1746:
1742:
1741:
1738:
1731:
1728:
1724:
1723:
1720:
1713:
1710:
1706:
1705:
1702:
1695:
1689:
1685:
1684:
1681:
1674:
1671:
1667:
1666:
1663:
1656:
1651:
1647:
1646:
1643:
1636:
1633:
1629:
1628:
1621:
1614:
1610:
1609:
1606:
1599:
1593:
1592:
1585:
1578:
1573:
1569:
1568:
1565:
1558:
1555:
1551:
1550:
1543:
1536:
1531:
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1134:Catalan solids
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801:🎲
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602:abrasive agent
598:rock polishing
566:
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425:Museum, China.
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332:is similar to
269:ancient Greece
221:ancient Indian
161:Leicestershire
159:die, found in
138:
135:
84:tabletop games
26:
9:
6:
4:
3:
2:
3910:
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3723:
3722:public domain
3704:
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3698:
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3690:
3689:
3681:
3680:0-7160-2112-9
3677:
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3581:9780786947256
3577:
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3546:
3540:
3525:. 12 May 2016
3524:
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3423:
3422:em4miniatures
3419:
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3387:
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3365:
3359:
3340:
3333:
3330:Kybos, Alea.
3326:
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3166:
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3141:
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3090:
3086:
3085:"Casino Dice"
3080:
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2615:"Board Games"
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2390:
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2355:Dice notation
2346:
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2340:
2336:
2332:
2328:
2323:
2321:
2317:
2313:
2309:
2304:
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2301:dice notation
2297:
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2269:
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2261:
2257:
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2250:
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2206:
2197:
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2027:
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2019:
2015:
2013:
2010:
2006:
2002:
1999:
1995:
1992:
1989:
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1984:
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1977:
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1630:
1626:
1625:cuboctahedron
1622:
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1398:
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979:
975:
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968:
965:
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954:
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950:
948:
944:
943:spindown dice
939:
935:
932:
927:
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921:
917:
912:
910:
906:
902:
898:
892:
882:
880:
876:
872:
868:
863:
855:
841:
839:
828:
826:
821:🎲
810:
800:
797:
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791:
788:
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782:
779:
778:
774:
771:
768:
765:
762:
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748:
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742:
739:
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730:
727:
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718:
716:
712:
708:
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679:
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667:
663:
659:
655:
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650:
644:
642:
641:
637:
633:
632:
628:
618:
615:
614:serial number
610:
605:
603:
599:
595:
590:
588:
584:
576:
571:
565:Manufacturing
555:
550:
549:
548:
544:
541:
537:
532:
530:
526:
522:
514:
512:
506:
502:
488:
486:
485:
480:
476:
472:
468:
463:
461:
457:
453:
449:
444:
442:
438:
424:
417:
412:
405:
400:
393:
388:
385:
381:
378:Twenty-sided
374:
369:
366:
363:die, made of
362:
356:
351:
350:
349:
347:
343:
339:
335:
331:
327:
323:
322:block printed
319:
315:
314:playing cards
311:
307:
305:
301:
297:
293:
289:
282:, 1st century
281:
276:
272:
270:
266:
265:game of skill
262:
258:
257:yappîlū ḡōrāl
251:
247:
243:
239:
238:
234:
232:
227:
226:
222:
217:
215:
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207:
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178:
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162:
158:
143:
134:
132:
128:
124:
120:
116:
112:
108:
103:
101:
97:
93:
89:
85:
81:
80:random values
77:
73:
65:
41:
35:
30:
19:
3830:Dice control
3787:
3734:
3711:
3700:
3671:
3661:
3654:
3633:Bibliography
3620:12 September
3618:. Retrieved
3616:. p. 96
3604:
3571:
3565:
3553:. Retrieved
3548:
3539:
3527:. Retrieved
3522:
3513:
3486:
3480:
3466:
3454:. Retrieved
3449:
3425:. Retrieved
3421:
3412:
3400:. Retrieved
3380:
3368:. Retrieved
3358:
3346:. Retrieved
3339:the original
3325:
3313:. Retrieved
3303:
3293:29 September
3291:. Retrieved
3284:the original
3270:
3251:
3245:
3233:. Retrieved
3229:
3219:
3203:
3191:
3182:
3173:
3163:
3156:
3144:. Retrieved
3140:the original
3130:
3118:. Retrieved
3114:the original
3104:
3092:. Retrieved
3088:
3079:
3067:. Retrieved
3062:
3053:
3045:the original
3035:
3027:the original
3006:
3001:
2994:
2975:
2969:
2949:
2942:
2930:. Retrieved
2926:
2917:
2905:. Retrieved
2880:. Retrieved
2870:
2845:
2837:
2825:. Retrieved
2821:
2811:
2802:
2790:. Retrieved
2786:
2776:
2764:. Retrieved
2760:
2750:
2742:
2737:
2725:. Retrieved
2721:
2712:
2677:
2673:
2663:
2651:. Retrieved
2646:
2637:
2618:
2608:
2589:
2583:
2571:. Retrieved
2564:
2555:
2507:
2455:
2451:
2447:
2443:
2439:
2435:
2427:
2423:
2419:
2415:
2411:
2407:
2403:
2401:
2388:
2384:
2380:
2376:
2372:
2368:
2364:
2358:
2331:cryptography
2324:
2320:Magic 8 Ball
2312:zodiac signs
2305:
2293:
2287:
2285:
2268:Pythagoreans
2253:
2246:
2240:
2234:
2228:
2226:
2221:Playing Dice
2220:
2212:Applications
2202:
2166:
2142:
2135:
2083:Zocchihedron
1305:Rounded-off
1266:Möbius strip
1245:Möbius strip
1227:Faces/sides
1201:
1181:
1148:Trapezohedra
1124:
1071:Dodecahedron
1056:odd numbered
955:Faces/sides
942:
940:
936:
928:
913:
894:
866:
864:
860:
834:
806:
798:⚅
795:⚄
792:⚃
789:⚂
786:⚁
783:⚀
706:
702:
696:
688:
686:
677:
673:
669:
665:
661:
657:
653:
647:
645:
638:
629:
624:
606:
591:
580:
545:
533:
518:
510:
491:Construction
482:
464:
445:
434:
380:serpentinite
361:Knucklebones
341:
338:Heian period
330:Ban-sugoroku
329:
318:Tang dynasty
308:
299:
295:
292:aleam ludere
291:
285:
256:
235:
229:
223:
218:
206:Mohenjo-daro
173:knucklebones
166:
104:
86:, including
75:
71:
63:
62:
29:
3839:Mathematics
3803:Terminology
3643:"Fair Dice"
3529:16 November
3120:14 February
2932:20 November
2339:passphrases
2248:Dicemasters
1497:Decahedron
1191:barrel dice
1172:pyritohedra
1168:Disphenoids
1091:Icosahedron
972:Tetrahedron
831:Loaded dice
817:⚅
813:⚀
496:Arrangement
475:board games
346:racing game
237:Mahabharata
231:Atharvaveda
92:board games
3887:Categories
3555:4 December
3235:11 October
3230:Casino.org
3063:gmdice.com
2647:Oldest.org
2573:1 December
2566:OED Online
2561:"die, n.1"
2547:References
2501:Fuzzy dice
2489:d20 System
2260:cleromancy
2256:divination
2153:poker dice
2149:Fudge dice
2131:Fudge dice
1436:backgammon
1215:dayakattai
1187:antiprisms
1176:tetartoids
1158:Bipyramids
1152:antiprisms
1140:of the 13
1102:Faces are
1013:Octahedron
689:snake eyes
682:Old French
627:Old French
479:backgammon
450:(although
342:e-sugoroku
334:backgammon
267:played in
254:יפילו גורל
214:terracotta
202:Skara Brae
194:Burnt City
190:backgammon
155: in)
119:polyhedral
88:dice games
3702:MathWorld
3590:cite book
3505:255212063
3456:18 August
3427:18 August
3348:7 October
3069:20 August
2686:2251-6085
2327:passwords
2316:12 houses
2270:used the
2242:Quarriors
2129:A set of
1448:Alfonso X
1295:coin flip
1207:teetotums
1203:Long dice
891:Isohedron
823:from the
513:clockwise
505:Chirality
467:dice game
441:long dice
397:Roman die
382:die from
365:soapstone
259:), as in
163:, England
3647:Archived
3393:Archived
3208:Archived
2907:28 March
2827:16 April
2766:19 March
2704:26587512
2653:12 March
2533:Teetotum
2527:Quincunx
2470:See also
2379:, where
2361:standard
2349:Notation
2343:Diceware
2177:wargames
2157:sex dice
1691:Rounded
1391:long die
1370:long die
1329:long die
1280:or Flat
1278:Cylinder
871:wargames
844:Variants
780:Decimal
775:U+1F3B2
754:Unicode
707:midnight
484:Monopoly
423:Jiangyin
326:sugoroku
310:Dominoes
300:Tesserae
261:Psalm 22
246:biblical
179:game of
177:Egyptian
131:cheating
127:material
3781:History
3724::
3402:18 June
3370:18 June
3146:18 June
2882:18 June
2792:28 July
2695:4645795
2495:Dreidel
2295:Exalted
1547:rhombus
1404:cricket
827:block.
809:Unicode
772:U+2685
769:U+2684
766:U+2683
763:U+2682
760:U+2681
757:U+2680
728:Symbol
711:boxcars
703:boxcars
634:; from
609:density
280:Pompeii
225:Rigveda
150:⁄
137:History
123:numbers
115:integer
3855:People
3793:Hazard
3718:
3697:"Dice"
3678:
3578:
3503:
3493:
3315:9 July
3258:
3094:1 July
2982:
2957:
2858:
2702:
2692:
2684:
2625:
2596:
2139:Boggle
1249:sphere
1236:Notes
1233:Image
1230:Shape
1219:daldøs
1211:prisms
1196:prisms
1162:prisms
1136:, the
961:Notes
958:Shape
807:Using
666:cinque
600:. The
575:casino
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