[Fate]

The first gem spent gives you +1 in that path for all purposes, all subsequent gems increase your effective path for fatigue reduction only.

So the first gem moves your 12S mage up to 13S (or 13S up to 14S). The other 3 (or four if your mage is 13S) may only reduce fatigue.

I know the AI likes to spend gems to reduce fatigue if it can, but I am not always sure it will. The only way to know for sure is to try it.

Assuming the AI spends as many gems as it can you have:

8 (for spell) + 1 (path increase) + 3 (fatigue reduction) = 12 (your astral level)

Fatigue = 800 / (1 + effective extra S level) = 800 / (1 + 1 (path increase) + 3 (fatigue reduction) + 4 (normal extra paths)) = 800 / (9) ~= 88.9 or 89

Penetration = 10 + Pen Items + (extra paths / 2) = 10 + 4 + (((4 + 1 (path increase))/2) = 14 + (2.5) = 16.5, just like you have already stated.

As MR easily resists, that is effectively 12.5 penetration (I likewise am not sure which way Dominions will round this, but I believe down to just 12).

And finally, the natural 5 fatigue reduction is unconscious only, so if you have 14 endurance it will put you at 89 - 14 = 75 fatigue.

PotS puts you at 13 S. So you can spend another gem (if the AI wants to).

Fatigue = 800 / (1 + 1 + 4(extra fatigue reduction gem) + 5 (extra path) = 800/11 = 72.27 ~= 72?

Penetration = 10 + 4 + (5 (extra path) + 1 (same gem increase) / 2) = 10 + 4 + 3 = 17

at MR easily that is effectively 13 Penetration. So PotS nets you +1 Penetration and - ~17 fatigue.