Why dice come in so many shapes
The 6-sided die is the most familiar, but other shapes exist to cover different probability distributions. Each is used in tabletop RPGs and simulations where the count of possible outcomes matters: a D4 has fewer extremes, a D20 allows fine gradation between catastrophic failure and critical success.
Anatomy of each die
- D4 (tetrahedron): 4 triangular faces. Lands point-up; the number is read at the bottom edge. Average: 2.5.
- D6 (cube): the Monopoly/Yahtzee classic. Average: 3.5.
- D8 (octahedron): two pyramids glued together. Average: 4.5.
- D10 (trapezohedron): 10 pentagonal faces. Average: 5.5. Often numbered 0-9 or 1-10.
- D12 (dodecahedron): 12 pentagonal faces. Average: 6.5.
- D20 (icosahedron): 20 triangular faces. The king of D&D. Average: 10.5. A "natural 20" is critical success, "natural 1" critical fail.
- D100 (percentile): two D10 (one for tens, one for units) giving 1-100. For detailed loot tables.
4d6 drop lowest: the standard D&D ability score
When you create a Dungeons & Dragons 5e character, the default rule for each ability score (Strength, Dexterity, Constitution, etc.) is to roll 4 six-sided dice and sum the highest 3. The average jumps from 10.5 (straight 3d6) to about 12.24, producing more capable characters without guaranteeing high numbers. Probability of a natural 18: about 1.6%.
Other useful notations
- 2d20kh1 (advantage): roll 2 D20 and keep the higher. The "advantage" mechanic in D&D 5e.
- 2d20kl1 (disadvantage): 2 D20, keep the lower. "Disadvantage".
- 1d20+5: roll one D20 and add 5. Character modifiers.
- 1d8r1 (reroll): roll a D8, reroll if it's a 1. For magic weapons that avoid low rolls.
Use cases beyond games
- Deciding what to eat: 6 options, one D6, done.
- Random presentation order: N people, each rolls a D20, sort by result.
- Education: demonstrate uniform distribution and the sum of random variables (2D6 sum is NOT uniform — 7 is the mode).
- Tie-breaking with granularity: when a coin isn't enough, a D6 or D20 gives more resolution.
The 2D6 distribution is not flat
Fun fact: a single D6 has 1/6 chance per face. Sum two D6 and the result ranges 2 to 12 with a triangular distribution: 7 is the most probable (6 combinations), 2 and 12 the rarest (1 each). This is the basis of Catan, where 7 activates the robber and 2 or 12 almost never produce resources.
Why a virtual die is fairer than a physical one
Physical dice can have manufacturing defects that bias results: uneven density, worn corners, faces with less paint than others (high-pip faces are lighter on painted dice). Studies with thousands of rolls show 1-3% bias in standard branded dice. Virtual dice don't have this problem.