Trying out Prince

I always find that Stonehenge is good to build. It gives you lots of faith, which can potentially get you to a religion first. I do play fairly religiously but if you do get it first, you get first cracks at converting cities, and if you build up enough pressure, new religions that get founded can be crushed and limited from expanding.

Stonehenge is iffy on higher difficulties. Emperor, you can get it pretty easily if you beeline it. Immortal, you need a few forests. Deity, good luck. Also, even with it on Deity, there's no guarantee you get a religion with it. Thus, it is a lower level wonder, being utterly fantastic there.
 
The AIs seeking religion in G&K are flavor driven. Those with low religion flavor will never build Shrines.

Playing with random civs; its an extremely rare game in which you won't evenually found a religion if you make Shrine your first building.
(The same AIs that found it quick will enhance quickly and at that point strictly limit the number of new pantheons down to only what the remaining spots will be after all existing pantheons form full religions. Eventually your one Shrine will cause you to reach 200 faith points.)
Now it may be questionable how much good founding a religion is if an AI is already in the Industrial era by the time you found it.
 
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