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.
Frequently Asked Questions
Q: What does 2d6 mean?
It means roll two 6-sided dice and add the results.
Q: What does 4d6dl1 mean?
It means roll four 6-sided dice and drop the lowest one.
Q: What is advantage?
Advantage means rolling twice and keeping the higher result. Disadvantage means rolling twice and keeping the lower result.
Q: Why does 2d6 cluster around 7?
Because there are more combinations that make 7 than combinations that make 2 or 12.
Q: What does simulation mode show?
Simulation mode shows the distribution of outcomes after many repeated rolls, along with useful statistics.
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