Who knew adding/subtracting dice does not change the probability profile (well not me I guess)

UPDATE – Reddit said this better:

“I think more precisely, flipping the sign of a die doesn’t change the distribution, just the offset”

I have to admit my brain did not intuitively grasp the below when I recently stumbled across this (mathematicians wince much!!):  

https://anydice.com/program/30be1 

That is, 2D6+D6 (i.e. 3D6) and 2D6-D6 have the same probability shape (just shunted along). Likewise D6-2D6 and -3D6 (<– this last one I get at least).

So, that is from a design POV add/subtracting dice does not change the shape of the probability curve, just shunts it around a bit. 

Here’s and example using using a total of 6 x D6 (i.e. 6D6 and 4D6-2D6):

https://anydice.com/program/30c97 

Can’t think how to use this yet, but I will remember it as part of my dice tool kit …

Shooting from the hip here – maybe in big dice pools once you exceed a certain number start using negative dice to reset the range a 1 e.g. 7D6-D6 (range 1 to 40) rather than 8D6 (range 8 to 48). 

https://anydice.com/program/30c23 

Or maybe any system where you want a curve but with + AND – numbers – maybe in a weather system when you want + and – temperatures?

So, maybe in a tundra landscape:
Summer temperatures: 3D6
Spring temperatures: 2D6-D6
Autumn temperatures: D6-2D6 
Winter temperatures: -3D6 

Maybe not the best example, but an example at least!