D&D General Custom Dice Curve

[Harzel]

How would I go about generating a bell curve such that the range is 1-12 and the high point is 5?

Obviously, 2d6 come close. I was also thinking about 2d4 + 1d6 -2.

By "high point" do you mean the mean value (average) or the most likely single result? Those are not the same thing.

 

[jgsugden]

You have results oriented questions, but we only know a bit about your goals. Do you want the 2 and 12 to have equal probability? Should the total of the probability to the left of the 5 equal the total of the probability to the right of it?

The last time I tried to shift the probability curve around, I determined that my best approach was to change dice based upon training and talent levels. A weak PC with no training trying to do something would roll 2d4 while a strong PC with a lot of pysical training might be rolling 2d12. I added an exploding die mechanic (if a die hit the maximum value, you added a die and subtracted 1 from the result) and a few other tweaks and ended up with exactly what I needed.

 

[Bohandas]

Roll 1d20, reassigning the numbers above 12 as follows:

13=1
14=2
15=2
16=3
17=3
18=3
19=4
20=4

EDIT:
The following may be better as it has actual fives in it:

13=1
14=1
15=1
16=2
17=3
18=4
19=5
20=5

In any case the reassigned numbers need to add up to 22 and the total of all the numbers needs to add up to 100
EDIT:
If you want 5 to be the most likely number, you could also roll d% and replace the numbers above 12 with seventy-five "5"s, eight "4"s, and five "3"s