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DiceRoller.fun
Independent Probability Tool
3 Dice • Range 3 - 18

3D6 Roller

Rolling 3D6 produces a total between 3 and 18 with an expected average of 10.5. Totals 10 and 11 are tied for the highest probability at 12.50% each.

Dice Tray
3d6
Click button or press Space to roll
Total Result
-- Ready
Roll Breakdown
Roll the dice to see outcome
Select Die Type Standard Polyhedral Set
Roll Configuration Quantity & Modifiers
1 – 100
2 – 1000
± bonus
âš™ Advanced Expression (NdM±K) â–¼
Shortcuts:
âš¡ Quick Dice Rolls 1-Click instant roll

Saved Presets

Roll History

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Exact Mathematical Probability

Combinatorial Engine

Calculates discrete binomial distributions, probability density, and cumulative odds for the active dice expression.

Range (Min - Max) --
Theoretical Average --
Most Likely (Mode) --
Total Permutations --
Query Target Probability
Exactly ( = X ) --%
At Least ( ≥ X ) --%
At Most ( ≤ X ) --%
Probability Density Distribution Hover / tap bar to view odds
View Full Probability Table & Combinations â–¼
Total Ways Exact % ≥ At Least ≤ At Most

Roll N Times (Multi-Trial Simulation)

Execute up to 10,000 repeated trials to calculate empirical distributions and statistics.

Trials --
Mean (Avg) --
Median --
Mode --
Min --
Max --
Sum --

Empirical Frequency Table

Roll Total Hits (Count) Frequency Bar Percentage
Click "Run Trials" to simulate rolls and generate frequency data.

Probability Curve & Mathematical Mechanics

The 3D6 roll produces a genuine bell curve approximation. Standard in classic tabletop stat rolls and systems like GURPS, rolling three dice creates an organic distribution where moderate results (9 through 12) occur almost 50% of the time, while extremes (3 or 18) are rare miracles.

There are 6 × 6 × 6 = 216 total permutations. A 10 or 11 each have 27 combinations (12.5% each). A perfect 18 or minimum 3 each have only 1 combination (1 in 216, or 0.46%).

Prominent Tabletop Games Using 3D6

  • • GURPS core skill and combat resolution system (roll under skill rating)
  • • Classic "3d6 down the line" RPG ability score generation (Strength, Dex, Con, Int, Wis, Cha)
  • • Fudge / Fate conversion comparisons
  • • Hero System action checks

3D6 Distribution Overview

Min Total 3
Max Total 18
Average 10.5
Most Likely 10 and 11 (12.50% probability each)
Total Sum Permutations Exact Probability
3 1/216 0.46%
6 10/216 4.63%
9 25/216 11.57%
10 27/216 12.50%
11 27/216 12.50%
12 25/216 11.57%
15 10/216 4.63%
18 1/216 0.46%

Explore Related Dice Systems

2D6 Roller → 4D6 Roller → D20 Roller →

Frequently Asked Questions About 3D6

What is the chance of rolling an 18 on 3D6?
Exactly 1 in 216, which is approximately 0.463%.
What is the average of 3D6?
The mathematical expected average is 3 × 3.5 = 10.5.
Why do games like GURPS prefer 3D6 over 1D20?
1D20 has a flat 5% chance for every number, making high and low extremes equally likely. 3D6 has strong central clustering around 10–11, giving players reliable, predictable skill checks with reduced chaotic variance.