Dice Roller & Probability Simulator

Roll one die or many dice, use RPG notation like 2d6 + 3, test advantage / disadvantage, drop high or low dice, simulate thousands of rolls, view histograms, check mean, median, and standard deviation, and even run a simple multi-player game mode.

Background

A dice roller can be more than a randomizer. It can help students explore probability distributions, expected value, and how repeated trials create patterns. That makes this tool useful for games, statistics, and probability lessons.

How to use this calculator

Choose a mode: Basic, Formula / RPG, Simulation, or Game.
Enter your dice settings or notation, then click Roll / Calculate.
Use the stats, histogram, roll history, and math explanation to understand the results.

How this calculator works

Basic mode: rolls a chosen number of standard dice and applies optional modifiers and keep/drop rules.
Formula / RPG mode: parses formulas like 2d6+3, 1d20+2d6, 4d6dl1, and 1d20adv+5.
Simulation mode: repeats the same roll many times and summarizes the distribution.
Game mode: simulates repeated rounds for multiple players and declares a winner.

Supported notation

Standard: NdS such as 2d6 or 1d20

Flat modifier: 2d6+3, 1d20-1

Mixed dice: 1d20+2d6, 2d8+1d4+2

Drop / keep: 4d6dl1, 5d10kh3

Advantage / disadvantage: 1d20adv+5, 1d20dis

Exploding dice: 3d6!, 3d6!+1d4

Example Problem & Step-by-Step Solution

Example 1 — rolling 2d6

Roll two 6-sided dice.
Add the two faces together.
The smallest total is 2 and the largest total is 12.
The average expected total is 7.

Example 2 — 4d6 drop lowest

Roll four 6-sided dice.
Find the smallest die.
Drop that die.
Add the remaining three dice to get the final score.

Example 3 — simulation intuition

Simulate 2d6 thousands of times.
Count how often each total appears.
You will usually see middle totals like 6, 7, and 8 more often than edge totals like 2 or 12.