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Before things get too confusing, let's talk about "mount A4:0", because there actually is a possible E4 site in the mountains (The Factory).

Sorry Max, "mount A4:0" means not only are there no unique A4 sites in the mountains, there are no non-unique A4 sites either. So you can searched manually with an Eagle King to A3 in the mountains, and not bother looking for A4. (unless the province is both 'mountains' and 'plains').

"mount E4:1" means there is exactly one unique site that's possible in the mountains. And no non-unique E4 sites either. So if you found "The Factory" in a different province already, then you don't need to bother searching the mountains (or any province actually) to E4.

Of course, it may be more efficient to spell site search to find the E3's, depending on what stage the game's in etc.

My numbers are about optimizing searching because it's likely that in the early game at least, you've run around with a mage manually searching some sites, but probably not to level 4 in many paths.

This is especially true in the water. It's a waste to go casting Dark Knowledge everywhere if you've already peeked around with a D2, because there's nothing higher.