It the end, it is just a question of math, but it has quite a lot of variables which I exact numbers I doesnt know right now.
But let's have some simplified example. For simplification reasons let's assume your new city has an average 5
during the time for building both the shrine and monument and no other boni from growth, culture, production or gold. All at standard speed.
I took the 5
for simple reasons, first we will have for our little calculations natural numbers, second, it is quite realistic to have an average of 5
during 26 turns, if you consider, that you might have 2 to 3 policies unlocked, settled on hill, forest tiles and population growth.
A shrine and monument are together (2*65
=) 130
. With 5
per turn it takes 26 turns for both buildings to be built.
You have a 2 case situation:
Case A:
City Founded -> 13 turns for Shrine first -> 13 turns for Monument second
You will have after 26 turns
13*2*
= 26
Case B:
City Founded -> 13 turns for Monument first -> 13 turns for Shrine second
That part is more tricky, because it depends on the time needed for the borderblob.
If I remember correctly the first border blob at standard speed is after 30 culture.
A monument with Expanse produces during the shrine build time
13*2*1.5
= 39
towards the border blob. But we need just 30
for the blob, giving you 20
and 10
You reach your border blob after
30
/ (2*1.5
) = 10
That means after 23 turns you get your blob, giving you the bonus.
That shrinks the time for the shrine by two turns.
So in total you will have
20
+ 2*2
= 24
I hope I didnt maken a major mistake here.
If you look at that simplified example, shrine first gives you 2
more, but your city will only contribute 2*2
towards your social policies.
Monument first gives less faith, but 22
towards your social policy.
If you want to even out the example a bit more and add the first border blob for case A you will have
[(13+10)*2 + 20]*
= 66
and 20
In case B you will have after the same time just 20
extra, total 44
, but 42
. Looks less, but you are closer to the next border blob. But sadly I dont have the culture cost formula for bordergrowth at hand now, so its hard to tell which is better in the long run, but your deadline is anyway to get to 800
for the prophet.
But that only works in that simple case. Normally the production time for the first building is longer then the one for the second one. 5
for the first one might be a bit much, for the second one a bit to few.
It highly depends on your city location, the potential help of a worker, your chosen policies and your potential civs boni.
In general you can say, the higher your production, the better is to go for monument first, the lesser, it is shrine first.
