Re: Stats / Plotted Bell Curve

From: Robert Moon (LegalWriter@msn.com)
Date: 06/02/00


----- 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


     +------------------------------------------------------------+
     | Ensure that you have read the CircleMUD Mailing List FAQ:  |
     |  http://qsilver.queensu.ca/~fletchra/Circle/list-faq.html  |
     +------------------------------------------------------------+



This archive was generated by hypermail 2b30 : 04/10/01 PDT