3d6 Bell Curve Probability Distribution (216 Total Combinations)
| Sum Result | Combinations / 216 | Exact Probability | Cumulative (≤ X) |
|---|---|---|---|
| 3 | 1 | 0.46% | 0.46% |
| 4 | 3 | 1.39% | 1.85% |
| 5 | 6 | 2.78% | 4.63% |
| 6 | 10 | 4.63% | 9.26% |
| 7 | 15 | 6.94% | 16.20% |
| 8 | 21 | 9.72% | 25.93% |
| 9 | 25 | 11.57% | 37.50% |
| 10 | 27 | 12.50% | 50.00% |
| 11 | 27 | 12.50% | 62.50% |
| 12 | 25 | 11.57% | 74.07% |
| 13 | 21 | 9.72% | 83.80% |
| 14 | 15 | 6.94% | 90.74% |
| 15 | 10 | 4.63% | 95.37% |
| 16 | 6 | 2.78% | 98.15% |
| 17 | 3 | 1.39% | 99.54% |
| 18 | 1 | 0.46% | 100.0% |
Frequently Asked Questions (Roll 3d6)
What is the average roll of 3d6?
The expected mathematical average (mean) of 3d6 is 3 × 3.5 = 10.5. The sums range from a minimum of 3 (1+1+1) to a maximum of 18 (6+6+6).
What are the most likely results on 3d6?
The most likely outcomes are 10 and 11, each with a 12.50% probability (27 out of 216 combinations). Together, scores between 9 and 12 account for nearly 48.14% of all rolls.
Why do tabletop RPGs like GURPS use 3d6 instead of 1d20?
A 1d20 has a flat, uniform distribution where extreme critical successes and fumbles happen 5% of the time each. In contrast, 3d6 produces a tight normal bell curve where characters consistently perform near their average skill level, making wild swings rare.