[QuiDortDine]

It is for sure just a funny hobby project, but your statement had me intrigued:

> Suppose in D&D I am told to roll 20 d6, but instead of rolling that many dice I want to roll just two (larger) dice and add a constant. Which standard D&D dice might give the closest variance and what is the constant?

Interestingly, ChatGPT 4o tells me to use 2d19 + 51, even after correcting it and asking for larger dice. Impressive math for sure but not worth much if it doesn't respect constraints. I guess I could try again until it stumbles upon the right answer, but it's all to say it's not quite there yet.

[zug_zug]

To be fair, I didn't hand-check the answer it gave (and I didn't retype the whole prompt exactly here) - but here's what it gave me [4o model]:

... (lots of calculations)

Final Comparison

    Variance of 20d6: 58.33458.334
    Variance of 1d20+1d12+53: 45.166745.1667

The variance of 1d20+1d12+53 is closer to 58.334 than previous combinations and represents a reasonable approximation for both mean and variance.

[Edit: Just checked it in google sheets, this looks right to me]

[QuiDortDine]

Yes, it's technically correct, but you said a larger dice, which a d12 is not :)

I would be curious to know if the larger dice version is impossible, but then I would also expect it to tell me.

[zug_zug]

I'm confused. I consider a d12 a larger die than a d6. Perhaps you're making a pun about physical size of the dice?

[QuiDortDine]

Oh wow I actually misread the comment, thought it was 6d20. Ok scratch everything!