🎲 Dice Roller
Roll D4, D6, D8, D10, D12, D20, or D100. Add a modifier. Perfect for D&D and tabletop RPGs.
Popular dice types: D4 (pyramid), D6 (classic cube), D8 (octahedron), D10 (percentile/ten-sided), D12 (dodecahedron), D20 (icosahedron, standard for D&D), D100 (percentile roll using two D10s). Modifiers are added to the total after rolling.
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Tabletop RPG Dice: Probabilities and Strategy
Understanding the probability distributions behind different dice helps you make better strategic decisions in D&D, Pathfinder, and other tabletop RPGs. Each die type produces a different shape of probability distribution, and the number of dice you roll dramatically changes the odds.
Single Die vs. Multiple Dice Distributions
A single die produces a flat uniform distribution — every result is equally likely. Roll 1d6: each number from 1–6 has a 16.7% chance. But roll 2d6 and the distribution becomes bell-shaped: 7 is the most likely result (16.7% chance) because six combinations produce it (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), while 2 and 12 have only a 2.8% chance each (one combination each).
Standard RPG Dice Probabilities
- d20 hitting AC 15 (needing 15+): 30% (6 out of 20 numbers)
- d20 with advantage hitting AC 15: 51% (1 − 0.70² = 51%)
- 3d6 rolling 18: 0.46% (1 in 216)
- 4d6 drop lowest, rolling 16+: about 19%
The advantage mechanic in D&D 5e is mathematically equivalent to adding approximately +3.325 to your roll on average — a significant boost that can determine combat outcomes.
Understanding Dice Probability
Each die roll is an independent event with equal probability for each face. For a standard d6 (6-sided die), each number has a 1-in-6 (16.67%) probability. When rolling multiple dice, probabilities multiply. Rolling two d6s and getting a specific result like (6,6) has a probability of 1/6 × 1/6 = 1/36 (2.78%). The possible sums from two d6s range from 2 to 12, but they're not equally likely — the sum 7 is most probable (6 ways to get it: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1) while 2 and 12 each have only 1 way. This is why craps (which uses two d6s) places the most favorable bets around the number 7. The expected (average) result for a die with n sides is (n+1)/2 — a d20 averages 10.5, a d6 averages 3.5.
Common Dice Types in Tabletop Games
Tabletop RPGs like Dungeons & Dragons use a standard set of polyhedral dice: d4 (4 sides, tetrahedron): used for small damage like daggers. d6 (6 sides, cube): most common die, used for damage, attributes, and board games. d8 (8 sides, octahedron): used for longer weapons and hit dice for some character classes. d10 (10 sides, pentagonal trapezohedron): used alone for percentile rolls paired as d% and d10, or with a d10 for 1–100 rolls. d12 (12 sides, dodecahedron): the rarest in standard use; barbarian hit dice and great axe damage. d20 (20 sides, icosahedron): the central die in D&D — all attack rolls, skill checks, and saving throws. d100 / percentile dice: two d10s, one representing tens, giving results from 01 to 100.
Dice Probability for Advantage and Disadvantage
D&D's "advantage" mechanic (roll two dice, take the higher) and "disadvantage" (roll two, take the lower) significantly shift the probability distribution. With advantage on a d20, the probability of rolling a natural 20 rises from 5% (1/20) to 9.75% (1 − (19/20)²). The probability of rolling a natural 1 (critical failure) drops from 5% to 0.25% with advantage. The average roll on a d20 is 10.5; with advantage it rises to about 13.8; with disadvantage it falls to about 7.2. This is why advantage/disadvantage are powerful mechanics — advantage is roughly equivalent to a permanent +3 to +5 bonus on most rolls, and is far more impactful than the +1 or +2 bonuses from most equipment. For probability analysis of complex dice expressions, the online dice probability calculator tools are invaluable for game design.
