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Maybe I can figure something out for the update 2 Saturdays from now
Mana:
Base game gives you an average of 3 mana from king + 3 for free. Your changes give the player an average of 4 mana from king + 7 for free. This means you get TWICE the mana, at any time. That's too much.
You should probably add 1 base mana but go for a 0-4 range for kings and starting leaders of republics at 3/0/0 instead of 4/1/1.
Same mana average, lower spread.
Combat:
You should probably not tinker with days for stackwipe and things complicated that way.
The easiest way to keep the balance is to go from 0-9 and add 1 to the bottom roll whenever you remove 1 from the top roll. So 2-7, 3-6 etc.
The complicated way is to remove from the top roll, and for every 2 you remove from the top roll, you have to add 1 to the fire, shock and morale ATTACK pips of every unit, of every unit type, at all tech levels, for all tech types, without ignoring natives. (It's just the first option with extra steps, Morty).
Those two possibilities get you the same average casualties as base game, but the min-max casualties range is shorter.
On the combat side of things, I definitely agree with you that I would prefer not to alter stackwipe days, but it was a compromise. Like you mentioned about dice rolls, I actually wanted to change dice rolls from 0-9 to 3-7, however I looked at the code available to me and it seems I can only alter the maximum value of the dice roll, not the minimum. You also mentioned pips on units, and that is a way I could do it, I even talked about it with siu while we were first discussing the dice roll issue, however we agreed that if we altered unit pips that it would look ugly and just confuse people, since most people probably don't understand the details of how pips affect combat.
If you know of a mod that alters the minimum dice roll value, I would appreciate it if you could point me to one so I could get in touch with the developer, but so far the best thing I can do is ask for paradox to add that as another value in the defines file.
I probably read somewhere "increased by 4" or misread in the game the base as 7 instead of 4 (I just checked and it is, indeed, 4).
So my bad, you're right, it is an increase of 1+1 on average.
A thought just came to me, if the pips are the problem, what about adding a +2 bonus from terrain to the attacker?
The old fort system (pre-1.12) was way better than what we currently have and the way CK2 does sieges should be the basis.
Suggestions:
Either: speed up all sieging speed by 25-50%
or: Lower fort defense on actual forts by 50-75%, increase flat fort defense by some 25% (to reflect on the old fort system)
Another option is to increase the dice roll effects so early game sieges don't last 5 years.
If you think Republican Governments are OP, I would ask that you provide an explanation of why you think they are OP.
I'm talking more MP wise, that's why I said republic gov is OP comparing to monarchy.