Dice: A Fascinating Topic for Gamers and Mathematicians
Dice are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random values, commonly as part of tabletop games, including dice games, board games, role-playing games, and games of chance. A traditional die is a cube with each of its six faces marked with a different number of dots (pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely.
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Dice may seem like simple toys, but they have a rich and fascinating history, a variety of types and designs, and a lot of applications in gaming and mathematics. In this article, we will explore some aspects of dice that you may not know or appreciate.
History of Dice
Dice have been used since before recorded history, and it is uncertain where they originated. It is theorized that dice developed from the practice of fortune-telling with the talus of hoofed animals, colloquially known as knucklebones. The Egyptian game of senet (played before 3000 BCE 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 backgammon-like game set at the Burnt City, an archeological site in south-eastern Iran, estimated to be from between 2800 and 2500 BCE. Bone dice from Skara Brae, Scotland have been dated to 31002400 BCE. Excavations from graves at Mohenjo-daro, an Indus Valley civilization settlement, unearthed terracotta dice dating to 25001900 BCE , including at least one die whose opposite sides all add up to seven, as in modern dice.
Games involving dice are mentioned in the ancient Indian Rigveda, Atharvaveda, Mahabharata and Buddhist games list. There are several biblical references to "casting lots" (Hebrew: יפילו גורל yappîlū ḡōrāl), as in Psalm 22, indicating that dicing (or a related activity) was commonplace when the psalm was composed. Knucklebones was a game of skill played in ancient Greece; a derivative form had the four sides of bones receive different values like modern dice.
Although gambling was illegal, many Romans were passionate gamblers who enjoyed dicing, which was known as aleam ludere ("to play at dice"). There were two sizes of Roman dice. Tali were large dice inscribed with one, three, four, and six on four sides. Tesserae were smaller dice with sides numbered from one to six.
Dice have also been used in various cultures for divination, magic, rituals, and education. Dice have influenced the development of mathematics, statistics, probability theory, cryptography, and game theory.
Types of Dice
The most common form of die is the cube, but there are many other shapes and designs of dice. Some of them are:
Polyhedral dice: These are dice with more than six faces. They are often used in role-playing games such as Dungeons & Dragons. The most common polyhedral dice are four-sided (D4), six-sided (D6), eight-sided (D8), ten-sided (D10), twelve-sided (D12), and twenty-sided (D20). There are also other polyhedral dice with different numbers of faces, such as D30 or D100.
Poker dice: These are six-sided dice that have the symbols 9, 10, J (jack), Q (queen), K (king), and A (ace) instead of pips. They are used to play poker the binomial probability formula, which is: P(X = k) = n C k * p^k * (1 - p)^(n - k) Where: - P(X = k) is the probability of getting exactly k successes in n trials. - n is the number of trials. - k is the number of successes. - p is the probability of success in each trial. - n C k is the binomial coefficient, which is the number of ways to choose k items from n items. For example, if we want to find the probability of rolling exactly three sixes in 10 rolls of a fair six-sided die, we can use the binomial formula as follows: P(X = 3) = 10 C 3 * (1/6)^3 * (5/6)^(10 - 3) P(X = 3) = 120 * 0.00463 * 0.16151 P(X = 3) = 0.0899 This means that there is about an 8.99% chance of rolling exactly three sixes in 10 rolls of a fair die.
Dice probability can also be used to find the expected value, variance, and standard deviation of a binomial distribution. The expected value is the average number of successes in n trials, and it is equal to n times p. The variance is the measure of how much the outcomes vary from the expected value, and it is equal to n times p times (1 - p). The standard deviation is the square root of the variance, and it indicates how much the outcomes deviate from the mean on average.
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For example, if we roll a fair die 10 times, the expected value of the number of sixes is: E(X) = n * p E(X) = 10 * (1/6) E(X) = 1.67 This means that on average, we expect to roll about 1.67 sixes in 10 rolls of a fair die. The variance and standard deviation are: Var(X) = n * p * (1 - p) Var(X) = 10 * (1/6) * (5/6) Var(X) = 1.39 SD(X) = sqrt(Var(X)) SD(X) = sqrt(1.39) SD(X) = 1.18 This means that the number of sixes in 10 rolls of a fair die varies by about 1.39 from the mean, and deviates by about 1.18 on average.
Conclusion
Dice are more than just simple toys; they are fascinating objects that have a lot of history, variety, and applications. Dice have been used for thousands of years for gaming, gambling, divination, magic, rituals, and education. Dice come in many shapes and designs, such as cubes, polyhedra, poker dice, non-transitive dice, and crooked dice. Dice are also useful for studying probability, which is the measure of how likely an event is to occur. Probability can be calculated using formulas and rules based on the number of trials, the number of successes, and the probability of success in each trial.
Here are some fun facts about dice that you may not know:
The word "dice" comes from the Latin word "datum", which means "something given or played".
The singular form of "dice" is "die", but it is rarely used nowadays.
The opposite faces of a standard six-sided die always add up to seven.
The world's largest collection of dice belongs to Kevin Cook, who has over 20,000 dice of different types and designs.
The world record for the most dice balanced on one finger is 42, set by Tai Star Valianti in 2017.
FAQs
What are dice made of?
Dice can be made of various materials, such as bone, ivory, wood, metal, plastic, resin, or glass. Some dice are also made of edible materials, such as sugar or chocolate.
How do you roll dice online?
There are many websites and apps that allow you to roll dice online. You can choose the number and type of dice you want to roll, and click a button or shake your device to generate random results. Some examples are [Random.org](^1^), [Roll Dice Online](^2^), and [Dice Roller](^3^).
How do you make your own dice?
There are many ways to make your own dice at home. You can use cardboard or paper to cut out and glue together different shapes of dice. You can use clay, polymer, or resin to mold and bake different shapes of dice. You can use a drill or a knife to carve out holes or grooves on wooden or metal dice. You can use paint, markers, stickers, or decals to decorate and mark your dice. You can also use recycled materials, such as bottle caps, nuts, or beads, to make dice. Be creative and have fun!
How do you cheat with dice?
Cheating with dice is not recommended, as it is dishonest and unfair. However, there are some ways that people try to cheat with dice, such as:
Using crooked dice, which are not fair and have a higher probability of landing on certain faces.
Switching dice, which involves secretly replacing the dice with different ones that have a desired outcome.
Palming dice, which involves hiding one or more dice in the hand and dropping them when needed.
Sliding dice, which involves throwing the dice in a way that they do not roll but slide on the surface.
Controlling dice, which involves throwing the dice in a way that they land on a specific face or combination.
What are some interesting facts about dice?
Some interesting facts about dice are:
The word "dice" comes from the Latin word "datum", which means "something given or played".
The singular form of "dice" is "die", but it is rarely used nowadays.
The opposite faces of a standard six-sided die always add up to seven.
The world's largest collection of dice belongs to Kevin Cook, who has over 20,000 dice of different types and designs.
The world record for the most dice balanced on one finger is 42, set by Tai Star Valianti in 2017.
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