>I just don't believe in the implementation of this idea
The "idea" is no different from what Chessmaster does; the analysis mechanism has been described many times in various sources.

I'm still talking about the technical part :D

>And seeks to obtain it
That's already the strategic map; I don't think we'll be dealing with that.

Without competent play on the strategic map, the AI will still be in the toilet.
First of all, chains. With chains, the player will gain a huge advantage by devouring everything more.
Secondly, the imba spell mass slow — under it, everything turns into mere meat.
Perhaps the game will boil down to "got slow and smashed to splinters".

I imagined it at the "rumor" level — some neutrals telling others that Galtran is running around here frying everyone with chain lightning. The implementation would again be at the level of a table, where after each battle we record the spell and level used by the player.

Yeah, I'd be interested in playing against an AI that sees the entire map, knows my whole army, and the spells in my spellbook. Sort of a "cheater" level. But not everyone would be into that :D

But the box of Homm3 said "strategic game".

Many are so used to such an AI that they don't even entertain the thought of improving it — like, what, the exploit with one dragonfly and a hundred zombies won't work anymore?
The offline players have achieved a special art. It truly is an art (of exploitation). I vaguely remember there was some tournament; someone found a sequence where the computer had an army many times stronger and just sat in the castle doing nothing :D Yeah, just sat there watching itself get killed.
Offline players are the best testers :D

The game's difficulty level will be determined by the depth of analysis of that n.

And ideally, the calculations should be done on all cores, not just one. Have an eight-core processor? — then let all 8 work at 100%. Like in distributed computing.