Dice

Dice (die, singular) include but are not limited to modern six-sided cubes with a separate number of dots on each side. Dice are used in games as a sort of Random Number Generators (RNG's) to bring an element of “chance or luck” (depending one’s deterministic view of the world) into a game by the creation of an event with multiple predictable and describable outcomes. Their true history is no doubt embedded in the religion and rituals of primal cultures for the use of divining rituals with which one could determine a future course of action. Divining by dice, or cleromancy, is a practice common in ancient cultures nearly worldwide and is still present in modern Western culture with the practice of flipping coins, e.g. to determine the kicking or receiving team at the start of a game of American football.

Note that the number of sides a die has may be represented by putting it in number form after the letter "d". For example, a six-sided die could be called a d6.

The simplest kind of die is dual, or binary, in the probability of its outcomes, a d2. For most Westerners, a typical coin is the most familiar form of a binary die. It can be tossed to land with a maximum of two possible outcomes: "heads or tails" as we say today in the USA. The coin tossing tradition to settle all manner of problems was used in ancient Rome where the possible outcomes were navia aut caput (ship or head). The "coin" used for the toss need not be an item of currency, any disc-shaped object will suffice so long as it is marked differently on different sides.

Probably even more ancient, but still common today is the use of round stick of wood or other object split in half lengthwise. This type of die will here be referred to as a half-cylinder and is binary in its outcome upon being tossed. Here again, a toss insures one of two possible and (ideally) equally likely outcomes: a rounded side up or a flat side up. These half-cylinder dice have been and are still used for games such as Nyout, Puluc, Tab, Tablan, Senet and Tau. This half-cylinder probably gradually evolved into sticks that were simply flat on both sides with different markings on opposite sides. The use of these types of divining sticks or counting sticks is well-documented among Native Americans by Stewart Culin in his book Games of the North American Indians.

A number of materials, most naturally occurring, have been used from ancient to modern times for binary dice including coins, flat discs, teeth (beaver teeth marked on both sides were used by Native Americans of Puget Sound area, Washington), bones (some carved and some naturally binary), sea shells (esp. cowries, clams or mussels), corn (sometimes fire-blackened on one side), seeds (esp. plum seeds), nuts (walnut shells work well), and broken pottery (a toss resulting in convex side up, concave side up, or more thoroughly broken pottery.). Although simple, binary lots should not be thought of as primitive. Tossing multiple binary dice can achieve anything that can be achieved with a single die with more sides. Any number of binary dice can be tossed to give a total of possible outcomes one greater than the number of dice thrown. The simplicity of binary language is the reason it is utilized as code for computer processors.

A somewhat more complex binary die is found along with the ancient Royal Game of Ur. It is tetrahedral or pyramidal in shape with two of the four tips specially marked with an inlay. Despite the use of this shape today for quaternary dice (four outcomes), the pyramidal dice of Ur were binary and could either result in a tip with an inlay up or one without. It is curious why the ancient people of Ur made dice of relatively complicated manufacture for binary RNG's.

Various sorts of objects used for binary dice

Astragali

Value (Ancient Rome)

Name

Tetrahedral binary dice used in the Royal Game of Ur

Trias (3)

Supinum

(concave)

Tetras (4)

Pronum

(convex)

Monas (1)

Planum

(flat)

Hexas (6)

Tortuoform

(sinuous)

Ancient dice could not be discussed without mentioning Astragali (Astragalus, singular; also known as knucklebones). These are the rear ankle bones of quadruped animals utilized as dice. They are d4 dice and there are four sides that may show up when tossed, but two sides are smaller and less likely to show up (about 20-30% of throws show one of the two smaller sides). The wide variety of animals that they are derived from attests to their previously widespread use in many parts of the world: goat, sheep, deer, cow, bison and camel. A bison Astragalus was used for a gambling game known as Tanwan by the Papago Indians of Arizona and astragali are known to be used for games up to modern times in parts of Asia, but it is ancient Rome where most discussions of Astragali will concentrate. The Romans probably inherited astragali from the ancient Greeks and they from ancient Egyptians. The Romans also started to fashion them from all sorts of other materials including ivory, gold, silver, onyx, brass or glass. Some from this time period are elaborately painted or decorated and were probably not tossed for games. Astragali were certainly used for divination in ancient times, and probably still are in places. The word astragalomancy, also known is astragyromancy, is sometimes used in place of or variously equated with cleromancy. Astragali are ancestral to the children's playground game of Jacks, which is still sometimes called Knucklebones, although the use of bones has largely been supplanted by by pieces of plastic or metal manufacture in modern times.

Another type of die is the long die or rolling log which may have a square, triangle, pentagon, hexagon, octagon or another polygon for a cross-section. Just like most dice, a throw (or roll) of a long die insures an equal probability of any side or edge landing face up as an outcome (other than the two ends), so long as all sides of the polygon are equal.

Long dice with the square for a cross-section have been used for well over a thousand years in India and probably the most common sort of long dice used today as they are used for the game of Chaupar. These quaternary dice are tossed or rolled to land and show one of four sides up. Depending of the game being played, a four-sided long die could have different markings and different totals on each of the four sides. Chaupar long dice have sides of 1-3-4-6 or 1-2-5-6. The Scandinavian game Daldøs also uses a four sided "rolling pin"-shaped long die and its sides are 1-2-3-4.

A traditional English game, formerly popular at Christmas time, uses a four-sided long die called a Lang Larence or Long Lawrence. Each of the four sides had a different set of cross-hatch like markings. It was played in a very similar fashion to a gambling game called Put & Take which grew to great popularity around 1920. The Lang Larence is also known to be made as an eight-sided long die. This one only had four differently marked sides as the markings on each of four sides were just repeated twice. The reason for the manufacture with eight sides was probably so that the die would roll more easily.

Six-sided or hexagonal long dice made of bone are known to have been used for gambling and gaming by the ancient Romans.

Three-sided long dice are used for the German board games Die 3 Magier andSchleckermaul and five-sided or pentagonal long dice are known from the Korean game transliterated as Dignitaries.

Long die with odd numbers of sides are usually marked at the edges, as instead of one face always coming up when cast they will always show one edge.

A seven-sided die was used in medieval times for a gambling game known variously as The Arabic Astronomy Game, Los Escaques ("Chess", from the Alfonso Manuscript of 1283), al-Falakiya (Arabic), or Kawakib (Iranian, "Stars").

Today, the most familiar form of die is cubical, or hexahedral, with the numbers 1-6 printed on each side. The invention of these dice is accredited to the ancient Lydians in what is today the country of Turkey. The ancient Greeks spawned the tradition of having the values of opposite sides of the die total seven, which is retained in virtually all cubical dice manufactured today. Modern dice, however, are chiral and there is not, as of yet, a standard for left-handed versus right-handed dice. A right-handed die has the numbers the 1, 2, and 3 in a clockwise fashion when viewed from their common corner, whereas they read counterclockwise in a left-handed die. The traditional English names of the six sides are ace, deuce, trey, quarter, cinc, and sice, although these are rare today. Different types of cubical dice are also utilized in the game of Crown & Anchor and as the doubling cube in Backgammon.

Lang Larence

Three and Five-sided Long Dice

Quaternary long dice called Pas or Pasaka have been used for thousands of years in India and continue to be used for the game of Chaupar. Here, shown are some makeshift replicas of the author's own fashion.

Ancient Roman Hexagonal Bone Die from Kornbluth Photography

http://www.kornbluthphoto.com/HistoricalBone.html

Common 6-sided, or hexahedral, dice

Other games have utilized the five Platonic Solids[2] of which the cube is just one along with the Tetrahedron, Octahedron, Dodecahedron, and Icosahedron as dice. The most common game I know of which uses these dice is the role-playing fantasy game, Dungeons & Dragons.

Also in modern or relatively modern manufacture are dice with sides totaling two, three, five, seven, ten, fourteen, sixteen, twenty-four, twenty-six, thirty, thirty-two, thirty-four, fifty, or one hundred. And we can be sure there are others I am currently unaware of. As a hint to board game inventors looking for a creative edge, I should add that these dice have rarely made their way into positional board games.

The five perfect solids utilized as dice. Left to right they are the tetrahedron or pyramid d4, hexahedron or cube d6, octahedron d8, dodecahedron d12, and icosahedron d20.

Also notable are eighteen-sided dice from ancient Chinese archaeology. They have been found with game sets used to play the enigmatic game known as Liubo, but may have been used for an unrelated drinking or gambling game.

Various unusual dice of modern manufacture: they are clockwise from top left: the d24, d30, d16, d14, d10, d5 and d3.

Eighteen-sided dice used for the ancient Chinese game Liubo

Teetotum

Also mentionable and related to dice are teetotums. A teetotum is like a spinning top with typically eight enumerated sides, although any even number of sides greater than four will also work. They date back as far as the ancient Greeks and Roman Empire and were used with a variety of race and gambling games published in the 18th through 20th centuries. Teetotums are the ancestors of the Jewish children's game of Dreidel. Another type of random number generator is the spinner. The spinner is a (typically) horizontally turned rotating circle or wheel with any number of equal sectors enumerated, painted or otherwise marked differently. Typically, a directional arrow or hand is fixed at center and theoretically has an equal chance of stopping at any marked sector of the circle. An exception to this is the gambling game of Roulette which utilizes a large spinner die and a ball dropped onto it while in motion. The simplest spinners are hand held instruments that often accompany children’s games. Enormous mechanical spinners are utilized in the television game shows The Price is Right, and Wheel of Fortune. All sorts of closely related mechanical devices have been used to randomly generate numbers including contraptions used to play Bingo, Lottery, Raffles, or just about any other game of chance.