----- Original Message -----
From: Axiem <axiem@SWBELL.NET>
> > Of course, this is still based upon the premise that stat values of 9-12
are
> > considered "average" in the D&D world (and are, in fact, the most
commonly
> > rolled bell curve numbers (with equal chance for each) when stats are
> > determined via 3d6.
>
> Actually, I do believe that is wrong. The average of all the possible
> values when rolling 3d6 is 10.5, so 10 and 11 are equally (and together,
> the most) likely to be rolled. And then 9 and 12 are second-most likely.
Technically, you are correct. There are 25 possible combinations in 3d6
that add up to 9 and 12, and there are 27 combinations that add up to 10 and
11. Since I found no previously plotted bell curve graph on the Internet, I
decided to just spend an hour plotting one myself, as set forth below.
NOTE: You must view this with a fixed width font, such as courier.
27 | x x
26 |
25 | x x
24 |
23 |
22 |
21 | x x
20 |
19 |
18 |
17 |
16 |
15 | x x
14 |
13 |
12 |
11 |
10 | x x
9 |
8 |
7 |
6 | x x
5 |
4 |
3 | x x
2 |
1 | x x
|_________________________________________________________________
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
The row represents the possible numbers generated by rolling 3 six-sided
dice. The column represents the number of combinations that add up to a
particular number.
possibilities for a result of
3 4 5 6 7 8
-------------------------------------------------------------------
1, 1, 1 1, 1, 2 1, 1, 3 1, 1, 4 1, 1, 5 1, 1, 6
1, 2, 1 1, 3, 1 1, 4, 1 1, 5, 1 1, 6, 1
2, 1, 1 3, 1, 1 4, 1, 1 5, 1, 1 6, 1, 1
1, 2, 2 1, 2, 3 1, 2, 4 1, 2, 5
2, 1, 2 1, 3, 2 1, 4, 2 1, 5, 2
2, 2, 1 2, 1, 3 2, 1, 4 2, 1, 5
2, 3, 1 2, 4, 1 2, 5, 1
3, 1, 2 4, 1, 2 5, 1, 2
3, 2, 1 4, 2, 1 5, 2, 1
2, 2, 2 1, 3, 3 1, 3, 4
3, 1, 3 1, 4, 3
3, 3, 1 3, 1, 4
2, 2, 3 3, 4, 1
2, 3, 2 4, 1, 3
3, 2, 2 4, 3, 1
2, 2, 4
2, 4, 2
4, 2, 2
2, 3, 3
3, 3, 2
3, 2, 3
possibilities for a result of
9 10 11 12
----------------------------------------------------
1, 2, 6 1, 3, 6 1, 4, 6 1, 5, 6
1, 6, 2 1, 6, 3 1, 6, 4 1, 6, 5
2, 1, 6 3, 1, 6 4, 1, 6 5, 1, 6
2, 6, 1 3, 6, 1 4, 6, 1 5, 6, 1
6, 1, 2 6, 1, 3 6, 1, 4 6, 1, 5
6, 2, 1 6, 3, 1 6, 4, 1 6, 5, 1
1, 3, 5 1, 4, 5 1, 5, 5 2, 4, 6
1, 5, 3 1, 5, 4 5, 1, 5 2, 6, 4
3, 1, 5 4, 1, 5 5, 5, 1 4, 2, 6
3, 5, 1 4, 5, 1 2, 3, 6 4, 6, 2
5, 1, 3 5, 1, 4 2, 6, 3 6, 2, 4
5, 3, 1 5, 4, 1 3, 2, 6 6, 4, 2
1, 4, 4 2, 2, 6 3, 6, 2 2, 5, 5
4, 1, 4 2, 6, 2 6, 2, 3 5, 2, 5
4, 4, 1 6, 2, 2 6, 3, 2 5, 5, 2
2, 2, 5 2, 3, 5 2, 4, 5 3, 3, 6
2, 5, 2 2, 5, 3 2, 5, 4 3, 6, 3
5, 2, 2 3, 2, 5 4, 2, 5 6, 3, 3
2, 3, 4 3, 5, 2 4, 5, 2 3, 4, 5
2, 4, 3 5, 2, 3 5, 2, 4 3, 5, 4
3, 2, 4 5, 3, 2 5, 4, 2 4, 3, 5
3, 4, 2 2, 4, 4 3, 3, 5 4, 5, 3
4, 2, 3 4, 2, 4 3, 5, 3 5, 3, 4
4, 3, 2 4, 4, 2 5, 3, 3 5, 4, 3
3, 3, 3 3, 3, 4 3, 4, 4 4, 4, 4
3, 4, 3 4, 3, 4
4, 3, 3 4, 4, 3
+------------------------------------------------------------+
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