DnD Dice Roller

D&D polyhedral dice: the seven-die set, NdX notation, and Platonic origins

A standard Dungeons & Dragons dice set contains seven polyhedral dice — the five Platonic solids plus the pentagonal trapezohedron d10 plus a percentile d10. Gary Gygax and Dave Arneson included this assortment when they published the original D&D in 1974, drawing on the mathematical heritage of Plato's Timaeus (c. 360 BCE), which assigned each Platonic solid to a classical element: tetrahedron=fire, cube=earth, octahedron=air, icosahedron=water, dodecahedron=cosmos.

The seven canonical dice

• d4 (tetrahedron, 4 faces) — dagger damage, light weapons; awkward to read because no top face.
• d6 (cube, 6 faces) — shortsword damage and the famous 4d6 drop lowest ability-score roll.
• d8 (octahedron, 8 faces) — longsword damage; 1d8 for the Cleric's Cure Wounds.
• d10 (pentagonal trapezohedron, 10 faces) — percentile skill rolls; not a Platonic solid.
• d12 (dodecahedron, 12 faces) — greataxe damage, the Barbarian's signature die, the rarest in normal play.
• d20 (icosahedron, 20 faces) — attack rolls, saving throws, ability checks; the iconic D&D die.
• d100 (percentile) — rolled as 2d10, one for tens (00, 10, 20…) and one for ones.

NdX+M notation and advantage mechanics

Tabletop notation reads NdX+M: roll N dice with X faces and add modifier M. So 3d6+2 means roll three six-siders and add 2, range 5–20, mean 12.5. In D&D 5e, advantage means roll 2d20 and keep the higher; disadvantage keeps the lower. The expected boost from advantage is roughly +3.3, often quoted as "about +5" at the cliff edges. A natural 20 on an attack is a critical hit (double weapon dice); a natural 1 is an automatic miss.

Probability: uniform vs bell curves

A single d20 is uniform — every result has 5% odds. Multi-dice sums approach a bell curve: 3d6 ranges 3–18 with mean 10.5 and standard deviation 2.96; results 10 and 11 are far more common than 3 or 18. That is why 4d6 drop lowest ability-score rolls produce better characters than 3d6: the expected value jumps from 10.5 to about 12.24.

Materials, fairness, and digital generators

Cheap plastic dice are notoriously unfair — Wyrmwood Gaming's salt-water float tests show many name-brand sets favor specific faces. Premium dice come in machined metal (heavier, more dramatic), semi-precious stone (collector's gemstone sets), and resin/3D-printed boutique pieces. Online platforms like Roll20, Foundry VTT, and Fantasy Grounds use CSPRNGs that easily outperform physical dice on chi-square tests. Critical Role's streaming success popularized "the d20 is sacred" culture, but mathematically a digital roll is at least as fair.

FAQ

Is a digital die or a physical die more fair? A digital die using a quality PRNG (and certainly a CSPRNG) is statistically more uniform than a cheap injection-molded plastic die. Physical precision dice exist but cost an order of magnitude more.

Why use 4d6 drop lowest instead of 3d6 for stats? Dropping the lowest die skews the distribution upward, producing higher average scores (~12.24 vs 10.5) and more "heroic" characters — the de facto standard since AD&D.

Does advantage equal +5? Approximately. The exact bonus depends on the target number: at a DC of 11 advantage adds about +5; at the extremes (DC 2 or DC 20) the effect is smaller.

What is a natural 20? A raw 20 on the d20 before modifiers. On attack rolls it is a critical hit (extra weapon dice). On ability checks and saves, RAW says it is just a 20 — though many tables homerule it as auto-success.

Why is the d12 so rarely used? Only the Barbarian's greataxe and a few spells use d12 by default in 5e. Designers note this as a quirk — the d12 has the smoothest random feel among standard dice but the fewest mechanics tied to it.