D&D Polyhedral Dice Roller & Probability
Roll virtual polyhedral RPG dice (d4, d6, d8, d10, d12, d20, d100) with modifiers, advantage/disadvantage, and exact probability success distributions.
Dice Pool Builder
Statistical Probability Distribution
About this tool
How to use it
- Select your dice pool quantities for d4, d6, d8, d10, d12, d20, and d100, or choose a preset attack chip (e.g. 1d20 Check, 2d6 Greatsword, 8d6 Fireball).
- Enter any flat modifier (+ or -) and select your roll mode (Normal, Advantage, or Disadvantage).
- Set your target Armor Class (AC) or Difficulty Class (DC) threshold.
- Click 'Roll Dice' or observe the live probability matrix showing exact mathematical success odds, expected average, standard deviation, and critical hit percentage.
Why it matters
Tabletop RPG gameplay hinges on probability management. Understanding whether an attack or saving throw has a 65% versus 30% chance of success helps Dungeon Masters balance encounters and players make optimal tactical decisions during combat. This tool combines cryptographically secure random number generation with exact polynomial probability distribution calculations.
When to use it
Use during D&D 5e, Pathfinder, or Call of Cthulhu tabletop sessions when playing remotely, when physical dice are unavailable, or when evaluating character builds and spell damage curves.
Good to know
Probabilities for complex multi-die pools are computed using exact discrete probability mass function (PMF) convolutions rather than rough Monte Carlo approximations.
Common questions
How does Advantage and Disadvantage mathematically affect a d20 roll?
Rolling with Advantage (taking the higher of 2d20) shifts the expected average roll from 10.5 up to 13.825 (equivalent to roughly a +3.32 bonus) and nearly doubles your critical hit chance from 5.0% to 9.75%. Rolling with Disadvantage (taking the lower of 2d20) drops the average to 7.175 and reduces critical hit chance to 0.25%.
Is 2d6 better than 1d12 for weapon damage in D&D?
Yes. 2d6 has a higher minimum damage (2 vs 1), a higher average damage (7.0 vs 6.5), and forms a bell-curve distribution centered heavily on 6, 7, and 8 (a 44.4% chance of rolling 7 or higher). A 1d12 has a completely flat 8.33% uniform distribution for every number from 1 to 12.
How are the dice roll outcomes generated?
Rolls use the browser's native window.crypto.getRandomValues API, providing cryptographically secure pseudo-random number generation (CSPRNG) that is substantially more uniform and tamper-resistant than standard pseudo-random generators.
How is the target DC success percentage calculated?
For single-die rolls, it evaluates the exact fraction of faces meeting or exceeding the DC minus the modifier. For multi-die pools (like 8d6), the calculator executes a discrete probability mass function (PMF) polynomial convolution across all dice to determine the exact cumulative probability.
What is the expected average damage of an 8d6 Fireball spell?
An 8d6 Fireball has an expected mean damage of 28.0 (8 × 3.5), with a minimum of 8 and a maximum of 48. The standard deviation is approximately 4.83, meaning roughly 68% of all casts will deal between 23 and 33 fire damage.