In case you're interested in the correct analytical solution...

[mikeshardmind]

You can find working python code for this here: https://github.com/unified-moderation-network/salamander/blob/main/src/contrib_extensions/dice/dicemath.py#L108-L116

Notably, this does not equal what you conjectured at 24:56 of the associated video

And you are welcome to use this in any follow-up.

[dmoody256]

I had a feeling his conjecture was wrong, although I don't have the knowledge or experience to prove it, simply taking his code and running it more than a million times, rather running it 100's of millions of times, shows a mean slightly below his conjecture, for example the 2 d20 tended towards a mean of 13.825, not 13.8333 like his conjecture proposed.