"HW rulez" mod (add-on) for HoMM3.

Not all guessing games are the same; it's one thing when there are three Castles with GM5, and it's unknown if even one of them has control. It's another thing when you know 100% that at least one of these cities has control—that makes it a different kind of guessing game. Is it really not clear to you, despite all your intelligence and experience, that you are forcing me to break this down for you step by step?

You say the phrase "different guessing game" with such breathlessness, as if it were some kind of sodomy with geese. Yes, different, so what? It differs from the original only by a slightly higher probability of building control. The fewer Castles with GM5 on the map, the greater that probability is. With an average number of them, there's practically no difference; it only manifests when there are few (1-3).

As for "cyclic running being unlikely," there is a real example—perhaps not exactly on this topic, but it illustrates it: the final of CIS-13, specifically on a mirror map. Alex significantly outpaced Bayazet in troops and leveling, but Bayazet managed to find a Dragon Utopia with a blue cap in a dark corner (Alex thought a Dragon Utopia wouldn't fit there, but it was compactly pressed against the rocks), and this happened to be the only control on the map. On day 131, Alex took Bayazet's capital, and Bayazet began "playing for a draw"—jumping all over the map and seizing Castles, sometimes with his main army, and sometimes with one-hit wonders bought out in the towns. Alex resisted for several days but then realized it was useless; he locked himself in his own capital and spent 3-4 days simply rebuilding the tower until he built Dimension Door, then returned and caught Bayazet.

It's just that people haven't fully tasted all the nuances of mirror maps yet, and the motivation to resist in fun games or during the group stage is low, but in serious Tournaments, they will squeeze every possibility out of mirror maps, including this kind of running "for a draw."