Bell Curves
3d6: All Combinations
| Rolls |
Totals |
| 1-1-1 |
2-1-1 |
3-1-1 |
4-1-1 |
5-1-1 |
6-1-1 |
| 1-1-2 |
2-1-2 |
3-1-2 |
4-1-2 |
5-1-2 |
6-1-2 |
| 1-1-3 |
2-1-3 |
3-1-3 |
4-1-3 |
5-1-3 |
6-1-3 |
| 1-1-4 |
2-1-4 |
3-1-4 |
4-1-4 |
5-1-4 |
6-1-4 |
| 1-1-5 |
2-1-5 |
3-1-5 |
4-1-5 |
5-1-5 |
6-1-5 |
| 1-1-6 |
2-1-6 |
3-1-6 |
4-1-6 |
5-1-6 |
6-1-6 |
| 1-2-1 |
2-2-1 |
3-2-1 |
4-2-1 |
5-2-1 |
6-2-1 |
| 1-2-2 |
2-2-2 |
3-2-2 |
4-2-2 |
5-2-2 |
6-2-2 |
| 1-2-3 |
2-2-3 |
3-2-3 |
4-2-3 |
5-2-3 |
6-2-3 |
| 1-2-4 |
2-2-4 |
3-2-4 |
4-2-4 |
5-2-4 |
6-2-4 |
| 1-2-5 |
2-2-5 |
3-2-5 |
4-2-5 |
5-2-5 |
6-2-5 |
| 1-2-6 |
2-2-6 |
3-2-6 |
4-2-6 |
5-2-6 |
6-2-6 |
| 1-3-1 |
2-3-1 |
3-3-1 |
4-3-1 |
5-3-1 |
6-3-1 |
| 1-3-2 |
2-3-2 |
3-3-2 |
4-3-2 |
5-3-2 |
6-3-2 |
| 1-3-3 |
2-3-3 |
3-3-3 |
4-3-3 |
5-3-3 |
6-3-3 |
| 1-3-4 |
2-3-4 |
3-3-4 |
4-3-4 |
5-3-4 |
6-3-4 |
| 1-3-5 |
2-3-5 |
3-3-5 |
4-3-5 |
5-3-5 |
6-3-5 |
| 1-3-6 |
2-3-6 |
3-3-6 |
4-3-6 |
5-3-6 |
6-3-6 |
| 1-4-1 |
2-4-1 |
3-4-1 |
4-4-1 |
5-4-1 |
6-4-1 |
| 1-4-2 |
2-4-2 |
3-4-2 |
4-4-2 |
5-4-2 |
6-4-2 |
| 1-4-3 |
2-4-3 |
3-4-3 |
4-4-3 |
5-4-3 |
6-4-3 |
| 1-4-4 |
2-4-4 |
3-4-4 |
4-4-4 |
5-4-4 |
6-4-4 |
| 1-4-5 |
2-4-5 |
3-4-5 |
4-4-5 |
5-4-5 |
6-4-5 |
| 1-4-6 |
2-4-6 |
3-4-6 |
4-4-6 |
5-4-6 |
6-4-6 |
| 1-5-1 |
2-5-1 |
3-5-1 |
4-5-1 |
5-5-1 |
6-5-1 |
| 1-5-2 |
2-5-2 |
3-5-2 |
4-5-2 |
5-5-2 |
6-5-2 |
| 1-5-3 |
2-5-3 |
3-5-3 |
4-5-3 |
5-5-3 |
6-5-3 |
| 1-5-4 |
2-5-4 |
3-5-4 |
4-5-4 |
5-5-4 |
6-5-4 |
| 1-5-5 |
2-5-5 |
3-5-5 |
4-5-5 |
5-5-5 |
6-5-5 |
| 1-5-6 |
2-5-6 |
3-5-6 |
4-5-6 |
5-5-6 |
6-5-6 |
| 1-6-1 |
2-6-1 |
3-6-1 |
4-6-1 |
5-6-1 |
6-6-1 |
| 1-6-2 |
2-6-2 |
3-6-2 |
4-6-2 |
5-6-2 |
6-6-2 |
| 1-6-3 |
2-6-3 |
3-6-3 |
4-6-3 |
5-6-3 |
6-6-3 |
| 1-6-4 |
2-6-4 |
3-6-4 |
4-6-4 |
5-6-4 |
6-6-4 |
| 1-6-5 |
2-6-5 |
3-6-5 |
4-6-5 |
5-6-5 |
6-6-5 |
| 1-6-6 |
2-6-6 |
3-6-6 |
4-6-6 |
5-6-6 |
6-6-6 |
|
| 3 |
4 |
5 |
6 |
7 |
8 |
| 4 |
5 |
6 |
7 |
8 |
9 |
| 5 |
6 |
7 |
8 |
9 |
10 |
| 6 |
7 |
8 |
9 |
10 |
11 |
| 7 |
8 |
9 |
10 |
11 |
12 |
| 8 |
9 |
10 |
11 |
12 |
13 |
| 4 |
5 |
6 |
7 |
8 |
9 |
| 5 |
6 |
7 |
8 |
9 |
10 |
| 6 |
7 |
8 |
9 |
10 |
11 |
| 7 |
8 |
9 |
10 |
11 |
12 |
| 8 |
9 |
10 |
11 |
12 |
13 |
| 9 |
10 |
11 |
12 |
13 |
14 |
| 5 |
6 |
7 |
8 |
9 |
10 |
| 6 |
7 |
8 |
9 |
10 |
11 |
| 7 |
8 |
9 |
10 |
11 |
12 |
| 8 |
9 |
10 |
11 |
12 |
13 |
| 9 |
10 |
11 |
12 |
13 |
14 |
| 10 |
11 |
12 |
13 |
14 |
15 |
| 6 |
7 |
8 |
9 |
10 |
11 |
| 7 |
8 |
9 |
10 |
11 |
12 |
| 8 |
9 |
10 |
11 |
12 |
13 |
| 9 |
10 |
11 |
12 |
13 |
14 |
| 10 |
11 |
12 |
13 |
14 |
15 |
| 11 |
12 |
13 |
14 |
15 |
16 |
| 7 |
8 |
9 |
10 |
11 |
12 |
| 8 |
9 |
10 |
11 |
12 |
13 |
| 9 |
10 |
11 |
12 |
13 |
14 |
| 10 |
11 |
12 |
13 |
14 |
15 |
| 11 |
12 |
13 |
14 |
15 |
16 |
| 12 |
13 |
14 |
15 |
16 |
17 |
| 8 |
9 |
10 |
11 |
12 |
13 |
| 9 |
10 |
11 |
12 |
13 |
14 |
| 10 |
11 |
12 |
13 |
14 |
15 |
| 11 |
12 |
13 |
14 |
15 |
16 |
| 12 |
13 |
14 |
15 |
16 |
17 |
| 13 |
14 |
15 |
16 |
17 |
18 |
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OK. That's a lot of numbers.
Now you see why I decided to sneak up on this all the way from 1d6. :-)
Like the 2d6: All Combinations
page, the table on the left (labeled Rolls) shows all the
possible ways that 3d6 can be rolled.
Feel free to test this for yourself; you'll need 648d6 to do so.
Even if you're a gamer, I doubt you have that many d6 lying around
somewhere, and I don't want to know if you do... :-)
The table on the right (labeled Totals) shows the total
of each roll. Frex, the last row of the Rolls table
co-responds to the last row of the Totals table:
a 3d6 roll that showed a 1, 6, and 6 (1-6-6) would be a total of 13,
a 3d6 roll that showed a 2, 6, and 6 (2-6-6) would be a total of 14,
a 3d6 roll that showed a 3, 6, and 6 (3-6-6) would be a total of 15,
etc.
Note that the total number of possible totals is equal to the number
of faces on each die multiplied together. If we were rolling 2d4, the
total number of combinations would be 4x4 or 16. Rolling 1d4+1d8 would
be 4x8 or 32. The total number of possible totals on 3d6 is 216.
We'll be using that number in our next table.
Copyright © 1999 Bob Simpson. All Rights Reserved.
Last updated: 2001 Nov 29
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