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I had a case where, on a map, the capital was Lich, and there were many Liches. And they didn't want to join, even with a diplomat. And I was playing as Necropolis, and, as you can imagine, I really needed those guys. And as soon as I replaced my army's POWERFUL LICHES with ORDINARY ones, that is, I approached the guys with their direct relatives, they immediately changed their minds. All in the same game day!!!
I didn't quote a lot of smart words because there are many of them (and I'm too lazy to look for them in the tomes). But the fact that the presence of the same creatures affects the probability of joining (if upgraded creatures are on the map, you need to have upgraded ones, and vice versa) - this has also been repeatedly tested by me personally (this is also written in the research of other Heroes players, and even the increase in the probability of joining is expressed as a percentage). Therefore, I fully support what you wrote. But when replaying a scenario, each monster can be assigned a certain status, under which they will never join, no matter how much money and skills you have. After restarting the map, the status changes.