I am planning on running an epic-level campaign with a party of indeterminate size. The idea is they will be fighting Asmodeus with a custom stat block who will be approximately CR 40. They will have Tiamat, a CR 30 god fighting on their side (stats from Rise of Tiamat). How many players/NPCs of level 20 will be necessary to make this an encounter of Hard or Deadly difficulty (for a well-balanced party)?
CR 40 would effectively entail more/more powerful attacks, more legendary actions allowed, higher AC, and higher raw scores.
Actually, I found a work-up of Asmodeus that is close but not quite what I want. I will make some minor edits to that, but it is almost what I want. Perhaps a bit higher AC, play around with his legendaries, etc. (with rolling-for-initiative's rules except for Pledge of Tiamat or with a caveat that makes that useless).
Best Answer
For this question I'll be assuming a 4 character party, so you can adjust the number of players necessary. When figuring out encounter difficulty, there are a few things that are mentioned but not expanded on in the DMG, which I will talk about here:
Here's what you need to consider:
All in all, my conclusion is the following: given a party of four who is also accompanied by a CR 30 Tiamat, not only do you not need to add anyone to the party, you can probably give a small buff to Asmodeus. If the party has weaker gear, such as no legendary items or artifacts, you can add one party member.
You can also simply take Asmodeus as he is now, and add one or two level 20 NPCs on his side if the party is particularly strong (i.e. Moon Druid, Divination Wizard, Warlock 2/Sorcerer 18, and Rogue/Bard) Good luck!