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I once came across a video in one of the Reddit threads about reproducibility/changing outcomes with different restarts, where the author described approximate patterns. Using the "Rubi and Crom" campaign as an example.
Previously, walkthroughs could be found on ag.ru in the "Heroes" section, but now that section no longer exists. In general, it was directly stated at the beginning of different campaigns that you could achieve combinations of secondary skills by restarting. Essentially, the sets of these combinations were static, meaning that several options would appear. Moreover, after one of the restarts, they could cycle up to two times. After that, you had to restart the game. The same thing happens with the starting artifacts; you can try to generate something decent, but sometimes the restarts fall into a cycle and never produce anything worthwhile. ))
But battles are a different matter; you can skip a turn or perform some action to influence the randomness. For example, you can sit and count the turns of the enemy unit and notice that its morale drops on the 5th turn. To prevent this from happening, you need to somehow change the situation, for example, by moving your unit or, conversely, skipping a turn. Otherwise, the morale will drop again on the 5th turn. This is what I'm talking about. This always works for me, but the reasons for this behavior are unclear to me.
I haven't played Heroes of Might and Magic 3.