What is the optimal strategy for sacrificing faith?
The results of sacrificing faith seem quite complex mathematically. On the one hand, being able to get more faith in the pool for the same points is great, because it increases productivity. On the other hand, you spend days with much less faith than you would have if you hadn't sacrificed it in the first place. I used to be at 30% more efficiency when I sacrificed my pool, and the efficiency loss is quite noticeable. The diminishing returns of sacrificing, and the opportunity cost of not building magnetos, factories etc. earlier (because the materials for them come 30% slower after the sacrifice) make the matter even more complex.
So, is there a clear "winning" strategy? When, or how often, is it good to sacrifice faith?
As a side question, the text says "bonus will carry over through resets", but the sacrifice itself has a label called "reset" and then there is the possibility to reset the whole game. I assume that the faith bonus stays through faith sacrifice resets but not through game resets, is this the case?
Solution 1:
If you still care about your production of other resources, the optimal strategy is probably to sacrifice your faith immediately before resetting the game as a whole, and only then. Sacrificing your faith at any other time (especially if you've sacrificed it before) will give you a large hit to your general production in exchange for a small boost to your total faith generation, which probably isn't worth it.
If you really only care about sacrificing as much faith as possible in the end, then it gets murkier, and as you said, the math is complex. The only thing I'm sure of is that you shouldn't sacrifice your faith if the production bonus from your faith is lower than your faith bonus due to sacrificing, unless you're about to reset the game as a whole. I would probably sacrifice once my faith production bonus is double my faith sacrifice bonus (but again, only if I'm willing to cut most of my other production to speed up faith generation).
Edit: At some point after this answer was written, the faith bonus was nerfed: it now begins to suffer diminishing returns at 750%, and is hard capped at 1000%. If you're able to store enough faith to quickly get your faith bonus over 750% after sacrificing faith, then it makes sense to begin sacrificing faith often. (The Apocrypha bonus has no such diminishing returns.)
Solution 2:
As a side question, the text says "bonus will carry over through resets", but the sacrifice itself has a label called "reset" and then there is the possibility to reset the whole game. I assume that the faith bonus stays through faith sacrifice resets but not through game resets, is this the case?
Every time you reset your faith, you will receive special bonus called faithRatio. Higher faithRatio makes your faith pool grow faster.
This faithRatio stays accumulated forever, regardless of the game resets.