Larian Studios Forums Baldur's Gate III Baldur's Gate III - Help Tips & Tricks 2-Hander - 1d12 or 2d6 ?

Suppose that my equation is wrong.
We still assume that it's uniformly distributed.

Case 2d6:

Let min=2 and max=12.
Let range=max-min=10
Average of infinite rolls is min+(range/2)=2+5=7
My equation is right for 2d6

Case 1d12:
Let min=1, max =12
Range=max-min=11
Average of infinite rolls is min+(range/2)=1+5.5=6.5
My equation is right for 1d12

Let's take it further.
Case 2d6+1:
Min=3
Max=13
Range=10
min+(range/2)=3+5=8
Average of infinite rolls is 8 (1 more than 2d6)

Now let's assume that it's not uniformly distributed. Id like you to prove that by writing down all rolls for a d6 and d12 made without taking into consideration other modifiers affecting the result (such as proficiency, threatened, etc...). Find the frequency of these rolls and compute the average.