Medium dice, sometimes referred to as d6 dice, are six-sided dice used in many tabletop roleplaying games, wargames, and other games involving dice rolls. The “medium” refers to their size – they are larger than typical cubic dice with sides around 0.25″, but smaller than the large, ~0.5″ d10s and percentile dice used in some games.

With their six sides, medium dice have a uniform distribution, meaning each side has an equal 1-in-6 probability of landing face up. This makes them useful as randomizers and for basic probability games and simulations. Their six sides also allow them to generate a suitable range of random numbers for game mechanics that require more granularity than a simple coin flip, but less than the wide ranges of larger polyhedral dice.

## Origins

Dice made of bone, wood, and other materials date back thousands of years, with cubic dice appearing in ancient Mesopotamia and Egypt. These early dice came in a range of shapes, though many civilizations favored cubic dice due to their ease of manufacture and fair rolls.

Six-sided dice emerged in ancient Greece and Rome, often made of hard materials like bronze, marble, or dense ebony wood. Sophisticated lathe techniques enabled the creation of precisely cubed dice with rounded corners and edges for fair rolls. High quality cubic dice were common in the Roman empire for gambling and divination purposes.

The modern numbered arrangement of medium dice – with sides ranging from 1 to 6 – first appeared in medieval Europe. Before then, some 6-sided dice were numbered with only 1, 3, 4, and 6, skipping 2 and 5. The 1-6 numbering established today gained dominance by the middle ages and gave players a convenient range of distinct values from a single roll.

Medieval Europeans crafted medium dice from materials like bone, antler, ivory, and wood. As board games like backgammon grew in popularity, quality hand-crafted dice were in high demand, often turned on lathes or carved by hand. Discovering loaded or biased dice could lead to high stakes disputes, making precision craftsmanship a must.

## Use in Tabletop Games

Medium six-sided dice became a staple of classic strategy and war games developed in 18th and 19th century Europe. In these early wargames simulating ancient battles, individual dice rolls determined the outcomes of combat, morale, and other game mechanics. Prussian army officer Georg von Reiswitz’s influential 1812 kriegsspiel manual was among the first to formally adopt medium dice – a convention carried on by later war and strategy games.

The twentieth century saw an explosion in the popularity of tabletop roleplaying games, spearheaded by titles like Dungeons & Dragons. In D&D’s mechanics, different medium dice were designated for generating ability scores, determining combat damage, and simulating countless other random outcomes. The act of rolling dice to resolve fuzzy real-world scenarios became central to RPGs.

Today, medium six-sided dice remain a ubiquitous tool for introducing chance outcomes in tabletop games. Plastic dice have largely replaced hand crafted materials, but their six-sided form factor and 1-6 numbering have endured as a standard. The simple and convenient probability range of a d6 throw still forms the foundation for game mechanics across every genre.

## Probability and Statistics

Medium dice have long served as useful tools for studying probability and statistics. Their uniform distribution – with each of the 6 values having equal 1/6 odds – makes them ideal for modeling basic experiments like coin flips, sampling populations, and simulating random walks. Introductory statistics and data analysis courses will often use multiple medium dice rolls to demonstrate fundamental concepts like the law of large numbers and central limit theorem.

Simulating medium dice rolls is also helpful for illustrating computational concepts like generating pseudorandom numbers and random sampling. The simplicity of coding a digital d6 roll makes it a staple example programming exercise.

Data scientists working with stochastic models, Monte Carlo simulations, or other probabilistic methods also find virtue in the simplicity of the 6-sided die. The uniform distribution is easy to analyze mathematically and simulate computationally, so digital d6 rolls are often used where randomness is required.

## Game Design and Balance

Game designers think carefully about the probability curves of different dice when creating game mechanics and content. The flat distribution of a 6-sided die creates different gameplay than the bell curve results of a 12-sided die roll. The probabilities enable different styles of risk, reward, progression and balance.

Medium dice occupy a useful middle ground for many games. They provide more nuance than a d2 coin flip or simple high/low card draw, enabling mechanics with a gentle curve. But their range isn’t too wide like larger dice – they allow some uncertainty while keeping outcomes reined in.

In RPGs for instance, d6 rolls are used in moderation for damage, skill checks, and resource generation. The 1-6 range gives a measurable spread between high and low rolls, but won’t swing wildly like a d20. For game balance, d6 rolls produce just enough variability while preventing severe spikes.

## Manufacturing

Mass manufacturing enabled the low cost production of precision medium dice. Injection molded plastic dice took off in the 20th century, replacing hand crafted dice assets.

Today, precision manufactured medium d6 remain inexpensive to produce. An uninked monochromatic die can be injection molded for well under a penny per unit. For colored dice, tampon printing or pad printing can add insignia for just cents more per die.

Plastic medium dice are manufactured from polymers like ABS or polypropylene plastic, chosen for durability, friction, and density. Precisely balanced construction ensures fair randomness in rolls, with spots located opposite each other, rounded edges, and flush face symmetry.

## Probability Curves

The uniform probability distribution of a 6-sided die roll leads to a distinct probability curve. On a graph plotting outcome value versus probability:

Value | Probability |

1 | 1/6 |

2 | 1/6 |

3 | 1/6 |

4 | 1/6 |

5 | 1/6 |

6 | 1/6 |

Each outcome has equal probability, forming a flat horizontal line. This contrasts with dice like D10s and D20s which have bell curve distributions, with peak probability in the middle values.

The uniform curve of a D6 has a couple useful properties. The most probable result is no more likely than the least probable. The values exhibit maximum entropy, with the widest spread of outcomes. D6 rolls also have a convenient range – not too narrow with high certainty like coins, but not too wide with highly variable results.

## Uses Beyond Gaming

The randomness and uniform distribution of medium dice have proven useful for many purposes beyond games and statistics:

– **Decision making** – Medium dice can provide an unbiased, random element for making choices, whether for major questions or simple daily selections. The limited range prevents extreme results.

– **Raffle drawings** – A single medium die can select a “winner” from a small pool of entrants. Using multiple dice enables larger raffle pools.

– **Random sampling** – Rolling medium dice is an easy way to select random items from a small population for inspection, testing, or extraction.

– **Simulations** – Their probabilities make d6 useful for simulating anything from molecule behavior to call center traffic. Dice rolls introduce entropy into computational models.

– **Gambling** – Some casual dice games use medium dice as their primary randomizer. Though d6 alone enable only simple games of change compared to multifaceted dice.

– **Divination** – Medieval Europeans sometimes used sets of dice to cast fortunes, believing rolling dice could reveal occult insights. Modern mystics occasionally still use dice pools for divination.

The simplicity and universality of the 6-sided shape contributes to its widespread utility. Aside from games, medium dice are handy tools whenever an easy and fair random element is needed.

## Notable Medium Dice

Some medium dice have become historically notable either for their materials, craftsmanship, or lore:

– **Knucklebones** – Ancient dice originally made from the ankle bones of hoofed animals. Also called astragali.

– **Medieval european dice** – Intricately crafted from materials like bone, antler, ivory, or wood. Signified social status.

– **Royal Game of Ur** – One of the earliest board games, played in ancient Mesopotamia using pyramidal dice.

– **Etruscan divination dice** – Made of bronze, gold, or silver. Used by fortune tellers in ancient Italy.

– **Dungeons & Dragons dice** – Transformed d6 and polyhedrals into gaming staples. Sets still made today.

– **Neolithic carved dice** – Found carved from stone or antler. Show some of the earliest dice craft.

– **Las Vegas casino dice** – Manufactured to extremely high standards to prevent tampering and ensure fair odds.

## Conclusion

Medium six-sided dice hold an important place in the history of games, statistics, and randomness. Their six faces provide a uniform probability curve with maximum entropy, proving useful for countless purposes over millennia. Medium dice continue to enable random elements and range in everything from roleplaying adventures to computational models. Both physically and mathematically, the simple form factor contains endless possibility.