Skills for an Inferno hero.

I haven't fully figured it out myself yet, and that's because of the strange way the set works, which gives percentage bonuses to everything except the racial skill itself, although it somehow takes it into account when a gate is successfully opened.
But in general, if you're interested in this topic, I can recommend a good video about opening gates:
https://www.youtube.com/watch?v=V2Ifu9ZEfzA

I haven't watched the video yet, but here's the table I promised, with some comments.
The table is in a notepad format because it looks awkward if you just copy the numbers into the post. The numbers mean so many creatures out of a thousand, i.e., 525 means 525 out of 1000 summoned, or 52.5 percent, which is more accurate.

Conclusions.

1. I've figured out for myself that Wide Gates of Hell only double the percentage of the upgraded racial skill, without additional bonuses from castles or artifacts.
That is, with a standard 1 castle and skillful gating, it will be (40*2)+10 = 90 percent, and not (40+10)*2 = 100. Similarly, with 4 castles, for example, it will be (40*2)+40 = 120, and not (40+40)*2 = 160.
Thus, the static bonus from the Gate Lord in Leadership looks more convincing; all stacks will guarantee summoning 40+10+20 = 70 percent, which is better than 5 stacks of 50, 2 stacks of 90 percent.
The amulet works the same way, i.e., it will be (45*2)+10 = 100 percent.

2. Nimue's specialization adds a percentage per level, so at level 20, he is as if he has a Gate Lord or 3 castles instead of 1. It's a good bonus, but only against half of the factions. I haven't decided whether to give him Wide Gates or Gate Lord; building 2 branches is risky – defense is needed. Here, perhaps, as an exception, Wide Gates, because it will guarantee 70 for everyone, plus a chance of 110 percent for 1-3 stacks. Moreover, luck is built in.

3. It was once again confirmed that the developers have a dismissive attitude towards demons. I'm talking about the "Will of Urgash" set. The description says that it adds 25 percent. Logically, it should be 40+10+25 = 75. In reality, we have 40+10+2.5 = 52.5 percent. And then it linearly adds 2.5 percent, i.e., even with 6 castles, the bonus will be 15 percent, and it will only reach its promised effect of 25 percent with 10 castles, which will never happen.
There are other nuances in other variations (I'm not a mathematician; I can't derive an exact formula), but in any case, the percentage is negligible.
It's doubly frustrating, considering that the developers' favorites, the Dark Elves, have a set that works as it should, with a strange name, "Power of Runes," which quite nicely doubles the damage from chains, and no one is screaming about imbalance.
After testing, I put the demon set in last-to-last place (I don't like that the barbarian set reduces initiative); there's more benefit from 5 attack than from gating.

4. Considering the fact that all the perks for gating efficiency (except for quick gating) are in the second tier (after gathering troops, soldier's luck), I'm less and less striving for them and taking them. I limit myself to soldier and magesight, which is more useful. And in leadership, I often take the speed aura first.

That's it, it might be useful for beginners and those interested in the hellish army.