Going down piety is definitely a good idea if your strategy revolves around religion. Reformation beliefs are INSANELY powerful if you pick the right ones. Lately I've been partial to combining Religious Texts with Unity of the Prophets; AI players will need to burn multiple Great Prophets to root out your religion for more than a few turns. Also, the reduced cost in buying with faith is the difference between your religion only being a personal one affecting your own cities or being a global power.
The major change needed in Piety is the AWFUL policy that gives you the pantheon belief of the second most popular religion. Unless you're at a religious crossroads, this is ALWAYS a worthless policy and, even if you are at one, it may STILL be a worthless policy if a pantheon you don't care about is powerful near you.
I have found the opposite to be true. My strongest religious games are when I avoid Piety until late and take Tradition. The reason for that is that Piety offers nothing you need early on except Faith points, but at the cost of prohibitive Gold. And a civ with a lucky desert start will
still outperform you.
Let's look at what Piety offers you:
50% reduction in build time for shrines and temples.
Surely you're not waiting around for this policy to build your first shrine because to use the Piety tree at all you need a foot in the religious race. So 90% of the time the first point you put in the tree does nothing for you until either your second city or you get to Philosophy.
But wait. Let's say you actually do want to use this ability and build shrines and temples in half the time. Congrats, enjoy -3 gold per city. I hope you took Tithe as your religious ability because you'll need it to break even. (This theme of using your religion just to break even runs strong through Piety. With Liberty or Tradition there is no such tradeoff. What you get is a bonus not a penalty that you then offset just to break even.)
20% reduction in cost of buying units with Faith.
This is not a bad policy overall. Unfortunately its timing makes no sense. You're not going to be buying anything with faith because the entire religious race depends on you saving those points for a prophet. So once again we've got a policy that does nothing for us until later on. Ok, we could try to race for Hagia Sophia and grab a Prophet there and then get to buy stuff early. Except that Tradition players are better wonder builders, likely to have better science, a bigger population, and everything that goes with that. They are better situated to grab the Prophet than the tree allegedly devoted to doing that.
+1 Faith per temple and shrine
Cute but the main implication here early game is that you should build one shrine instead of two because you can't afford more. So while the intent here is good, other than the fact that you can get by with fewer shrines it's not helping you all that much. It's slightly better later on when you can afford all those temples and shrines. But early? You are 80% better off with granaries, water mills, and other buildings that actually benefit the city rather than just allow you to break even (if even that). Moreover, this isn't helping you with steles, it's not boosting Stonehenge, its not boosting Desert Folklore or Aurora, it's not increasing the Celt bonus from forests. So the best ways you would enter and sustain a religious race are not even covered by the policy that supposedly gives a lead in the religious race. Far from doing that, I'd argue, what this policy really is (early on at least) is a Hail Mary bid that is only useful if you've resigned yourself to the fact that you can't possibly win the religious race because of an unlucky start/Ethiopa or the Celts are around and are trying to at least grab the 4th or 5th religion before they are all gone.
10% gold from temples and +3 gold per holy site.
LOL at the holy site until later on. See comments about the entire point of the religious race above.
As for the temples, they are already costing us -2 gold. Someone else did the math and came up with a city needing +20gpt just to break even with this policy. Basically all you are getting here is a tiny discount on the gold cost of temples, and not even one that contributes in any meaningful way until much later in the game.
Religious tolerance.
Not only in this policy terrible, it may actually be the worst policy in the game. Situational doesn't begin to cover it. It's so terrible not just because it is bad in general (which it is), but because it actually runs completely counter to the goals of the Piety tree--building a strong religion and eliminating your opponents'. The implication of this power is that you are a non-Faith player who has resigned to letting the stronger religious civs take you over religiously, but you hope to hold on to part of your pantheon bonus, ie the exact
opposite of what Piety is all about.
Reformation Belief
Ok finally something decent. That you just 4 burned highly questionable policies to get to. And only one and one half of which has in any way, up to this point in the game, likely contributed anything to your empire.
maintenance cost in those 4 cities, even with Organized Religion from Piety. I prefer using pantheons as my foundation and opening Tradition, building just a few shrines and no temples. If not Desert Folklore or Dance of the Aurora, something like Stone Circles or the pantheons for silver/gold or wine/incense will do. Scouts are important too for finding those faith ruins and finding those religious city-states.
from Shrines and/or Temples.
I wound up just saying 10 turns from a calculation similar your second one. I also did one similar to your first calculation but concluded that I don't bother with a religion if I don't have the faith base from something else besides shrines/temples because I won't have the faith to make the most out of it anyway. But even if you want to take 30 turns of extra culture as the baseline, I still contend that +3 culture over the course of hundreds of turns (in particular the first 50 when +3 culture makes the biggest difference) will WAY outshine even 30 turns from piety.
