Dice Roller Online

Yes. Each face value is generated by `crypto.getRandomValues()` (W3C Web Cryptography API Recommendation 26 January 2017) and uses rejection sampling so every face has exactly equal probability. The d100 case is the strict test: 100 does not divide 2³² evenly, so naive `r % 100` would give the lower 96 faces about 1 in 4.3 billion more probability than faces 97..100 per roll. Rejection sampling fixes this — the rare retry adds negligible cost (expected fewer than 2 retries per roll regardless of die size). For real wooden dice the story is different: Pearson and Weldon's 1900 dataset (26,306 throws of 12 dice) detected a small but statistically significant bias toward 5 and 6 in the wooden dice of the era because pip carvings remove material from those faces. Modern injection-moulded dice are much closer to fair, but the SVG dice on this page are mathematically exactly fair.

Correct: there is no convex regular polyhedron with 100 faces. The Platonic solids stop at the icosahedron (20 faces); the next regular shape that admits a fair die is the disdyakis triacontahedron (120 faces). In practice d100 is implemented as two d10s (a percentile die plus a unit die), or as a single Zocchihedron (a 100-sided geometric novelty introduced by Lou Zocchi in 1985, mechanically a sphere with 100 flattened faces — not truly fair because its surface has subtle topological constraints). This tool's d100 is purely numerical: it picks 1..100 uniformly using `crypto.getRandomValues()` plus rejection sampling, and renders the result inside the same SVG silhouette as the d10 (a pentagonal trapezohedron) because that is the conventional visual shorthand for "percentile die" in tabletop RPG layouts.

An icosahedron has 20 triangular faces in 3D; on a 2D screen we have to project it. This tool draws a decagonal silhouette (10-sided polygon outline) because the icosahedron's typical visible profile from a tabletop viewing angle is roughly a decagon — the same convention used by online D&D character sheets. The number rendered inside is the rolled face value (1..20). The d4 is rendered as a triangle (tetrahedron projects to triangle), d8 as a square rotated 45° (octahedron's profile at orthographic view is a square diamond), d12 as a hexagon (dodecahedron's profile is hexagonal). The geometric correspondence is approximate by necessity; what matters for the game is the number, which is generated fairly per the previous answer.

For home games and online tabletop sessions, yes — the entropy source (`crypto.getRandomValues()`) is cryptographically secure and the rejection-sampling logic is mathematically exact, which is a property physical dice cannot match (Pearson and Weldon 1900 measured the residual bias in pre-injection-mould wooden dice). For sanctioned tournament play with prize money, organizers typically require physical dice with a defined drop height and a witness — that is procedural fairness, not statistical, and no client-side tool can substitute. For statistics homework demonstrating dice probability (the sum-of-two-dice distribution, modal outcome at 7 for 2d6, the chi-square test against an observed empirical distribution per Pearson 1900), the tool produces clean exact data. The roll history is preserved in the session for audit and re-running a sequence.

Exactly 1 in 20 = 5 % per roll, because the d20 here is uniform on 1..20. "Advantage" (roll twice, take the higher) raises the probability of a natural 20 to 1 − (19/20)² = 1 − 361/400 = 9.75 %; "disadvantage" lowers it to (1/20)² = 0.25 %. These are the same values D&D 5e tabletop play uses; D&D's published probabilities match the math of a uniform d20 exactly (no house-favoring fudge). For two-dice sums (2d6): the modal sum is 7 with probability 6/36 = 16.7 %; sums 2 and 12 are tied for least likely at 1/36 = 2.78 %. Sum distributions for nd6 (n ≥ 3) approach a discrete bell curve per the Central Limit Theorem, centered at 3.5n with variance n × 35/12.