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## Bell Curves

### 3d6: How Often A Number Occurs

Total Occurs Percent
3 1 0.46%
4 3 1.39%
5 6 2.78%
6 10 4.63%
7 15 6.94%
8 21 9.72%
9 25 11.57%
10 27 12.50%
11 27 12.50%
12 25 11.57%
13 21 9.72%
14 15 6.94%
15 10 4.63%
16 6 2.78%
17 3 1.39%
18 1 0.46%

This table shows how often any single total occurs when 3d6 are thrown.

The lowest total you can roll on 3d6 is a 3. A 3 appears only once, on a roll of 1-1-1. The highest total is a 18 and appears only once as well, a roll of 6-6-6. Each of the other totals occur more than once. The two most common totals are 10 and 11, which appear twenty-seven times each. You can verify this on the previous page.

In the table, the first column shows the total. The second column shows the number of times each total appears in the 216 possible results. The last column shows the percentage chance of any specific total appearing on any single roll. The total number of times a specific total occurs, divided by the total number of occurances gives the percentage chance for any number to show up.

A total of 3 shows up only once, and there are 216 possible results, so the chance of rolling a 3 is 1/216, or less than 0.5%.

A total of 18 shows up only once as well, so the chance of rolling a 18 is the same as rolling a 3: less than 0.5%.

However, each of the other rolls show up more frequently in the table on the previous page. A total of 10 shows up twenty-seven times, so the chance of rolling 10 is 27/216 or 12.5%.

If you did a graph of these numbers you would see that the curve was vaguely bell-shaped: pointy on the ends and bulgy in the middle.

Last updated: 2001 Nov 29