Roll 3d6
Three six-sided dice tighten the curve that two dice start. The extremes need all three dice to agree, which almost never happens, so results bunch near the centre much harder than a pair does. GURPS built an entire system on how reliable that centre is.
Press Roll to throw the dice.
Press Space to roll again. Type notation like 2d6+3 or 4d6dl1 straight into the box.
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Rolling 3d6 gives totals from 3 to 18 out of 216 equally likely outcomes. The most likely total is 10 and 11 at 12.5%. The lowest total comes up 0.46% of the time and the highest 0.46%. The average roll is 10.5.
- Minimum
- 3
- Maximum
- 18
- Mean
- 10.5
- Median
- 10.5
- Std deviation
- 2.96
- Most likely
- 10 and 11
- Its odds
- 12.5%
3d6 probability distribution
The extremes each need every die to agree, which is why 3 and 18 are rare. Middle totals can be built several different ways, so they dominate the table below.
| Total | Ways | Probability | This or lower |
|---|---|---|---|
| 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% | 16.2% |
| 8 | 21 | 9.72% | 25.93% |
| 9 | 25 | 11.57% | 37.5% |
| 10 | 27 | 12.5% | 50% |
| 11 | 27 | 12.5% | 62.5% |
| 12 | 25 | 11.57% | 74.07% |
| 13 | 21 | 9.72% | 83.8% |
| 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% |
When you'd roll 3d6
Use 3d6 when you want a roll that behaves itself. GURPS asks you to roll at or under a skill rating, and because the curve is steep, a single point of skill matters a great deal near the middle and almost nothing at the edges. The oldest D&D ability score method uses the same dice: roll three, write the total down, move to the next stat, and live with whatever the dice gave you.
Where this roll shows up
- GURPS, where you roll 3d6 and try to come in at or under a skill number
- Classic Dungeons & Dragons ability scores, rolled 3d6 straight down the list
- Random tables that want a strong centre and rare extremes
3d6 questions
Why does GURPS use 3d6 instead of a d20?
Because the curve makes skill ratings meaningful. On a flat d20 every point of skill is worth the same. On 3d6 the middle of the range is crowded, so a point gained near a typical difficulty changes your odds much more than a point gained at the extremes.
Is rolling 3d6 for ability scores harsh?
Compared with modern methods, yes. The totals cluster near the middle of the range, so genuinely high scores are rare and you cannot reroll away a bad one. Later editions introduced 4d6 drop lowest and point buy partly because 3d6 straight down produced a lot of unremarkable characters.
What is 3d6 straight down?
You roll 3d6 six times and assign the totals to your ability scores in the printed order, no swapping. It is the original D&D method and it produces characters you did not plan, which some tables consider the point.
How is 3d6 different from 1d18?
Both top out at eighteen, but a flat eighteen-sided roll gives every score the same chance. Three dice make the middle scores common and the top and bottom scores rare, which is why an eighteen rolled on 3d6 is worth bragging about.