Calculating which Player Level to bind your demon

This may be a moot exercise, because the answer remains: highest P-level you can, but I wanted to see at what point do the monsters reach the level caps for each player level, using blunderbores and lancers as the targets (hint: superuniques generally hit the

Cap at P1 and thereafter gain only the P-level

Cap bonus).

First, I had to figure out what the actual Hp of the

Terror zone monsters might be. Further, to be extra sure, I only looked at the minimum Hp per monster. Start with the

Blunderbore family to see if we can identify how much Hp they gain per level (if there is a trend):
We can see that their minimum and maximum health go up by a fixed amount per level, except for the case of the Act 5 blunderbores and maulers, which get an extra boost to Hp. We cannot tell if their Hp increases thereafter by a different amount (unless that happens to be in the game files that I haven't looked at in detail nor have time to decipher).

Lancers are simpler: They all seem to go up by a set amount per level.

Now, we can use these values to estimate what their terrorized Hp will be for non-uniques, champions and uniques. Now we can calculate what the Hp will be after using

Bind Demon, which has a monster-specific health

Cap and a monster-specific player level

Cap bonus: What this basically means is that you are guaranteed to reach the player-level health

Cap very quickly with blunderbores, which start out with high minimum Hp near the

Cap at P1. For Lancers, you need to be at P2 or P3 to get to the caps. NOTE: this is minumum Hp, so in all likelihood, you are close to the caps for most of the monsters you come across by P1-P2.

That said, there are obvious benefits to getting as high player count as possible to get that extra Hp bonus (680 and 660 Hp per add'l player, respectively). The differences are substantial (up to 4,760 add'l Hp for blunderbores and 4,620 Hp for Lancers), so it is still beneficial to aim for the highest player count possible.

However, we can't always find a public P7 game to jump into, so I think this exercise leaves a bit of consolation for those who are only finding P4+ Tzs that still have monsters in them, in that they won't be missing out on the primary health

Cap like they would in a private P1 game (for Lancers, at least). Even so, leaving some Hp on the table for a lower player count is, in my opinion, mitigated by finding the right demon with the right affixes (e.g., Cursed + Stone Skin + _____). As an example, Lancers have 33% physical resists. If a monster does 1,000 damage, then they are receiving 330 less damage, meaning 770 per hit = 24 hits till dead (assuming no regen/leech) for a P8 non-unique or non-Stone skin unique (both 17,820 Hp). Add Stone skin (+50% phys res = 83%) on a P1 lancer (8936 Hp) and that = only 170 per hit = 53 hits until dead on P1 bound Lancer.

Note: even a P1 Lister or Heph is going to have more Hp than any P8 non-super-unique, so if you aren't aiming for a

Blunderbore or Lancer, you can just head right into your own private game and terrorize at will till you find a roll that you like.

Conclusion: Get a Stone Skin demon, preferably with other good resistances/immunities. Higher player count is a bonus.