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Depending on the circunstance it's totally worth, but if you don't need a unit ASAP and could use a pagoda, buy the pagoda...
/edit: And of course you can't upgrade your units with faith + they still cost maintenance. It only saves you a bunch of hammers.
It really depends on your start, pantheon choice, and what civ you are playing as to how useful holy warriors can be...
Looks TERRIBLE on paper...Using precious Faith that can be used to buy GPs for a few garbage warriors, losing a precious follower belief to do it and early game faith is often difficult to accumulate any decent amount.
It is never useful, ever. If you are generating so much faith you can pay x4 the cost for military units your faith would always, always be better spent picking "to the glory of god" so you can pick whatever great person you want.
It is there so that if everything else better has been taken, you can get 'something' just like how some pathenon & religious beliefs are poor but that makes the race to be 1st in religion to be meaningful.
But as the anti-Holy Warrior brigade very rightly points out, you shouldn't be making that kind of decision in the first place. To which I say, you know, sometimes it happens no matter your best intentions. When he got out of bed that fateful morning, Lieutenant Gorman didn't once consider he was going to get to hold the luscious PFC Vasquez in his arms, caressing her hands in his, but at the end of the day that's exactly how things worked out for him.
That does of course not mean that you "shouldn't" go for that belief if you have that special strategy that works really good with it, but overall, in a standardised scenario, the belief is just bad, even as a warmonger.
Went a few policies into Piety and then to the Liberty production boost for buildings. Purchased several troops with faith and fulfilled City State quests. Sitting first in army, but I prefer playing nice and my happiness isn't great so gifted a few to City States that requesting units.
With the beliefs I choose, I can purchase units and cheaper missionaries to get science when spread to other religions (and go mosque of djenne for 3 spreads). Seems pretty useful. Can buy a unit on command whenever needed or field a decent army quickly and use my gold for citystates and use production bonus in cities to focus on buidings.
The science boost from missionary spread would be much more useful at a higher difficulty, as the AI are better at spreading their religion around. I'm getting varying amounts of science with each spread. Anyone know how the amount of science through missionary spread is calculated?
Another consideration is if you're invaded and tiles and happiness pillaged and your production and economy suffers, your faith purchasing abilities are unaffected.
http://cloud-3.steampowered.com/ugc/3298070082291565279/6FB05AC1376E85921BC19E9DBAA361A905B3D5B4/
In a 1 city cultural playthough you only have, as the title says, 1 city. So you should have the workshop + ironworks national wonder which is more than enough hammers to get a military unit every 3 turns. You can also take commerce and pick mercenaries if you really need a fast army. The x3 faith cost is always a rip off no matter what unit you are buying and the whole point of a cultural victory is to keep generating culture till you win so once again generating GP is still the better option.
If you are picking and using holy warriors in games, I would love to play against you online and see how it works out for you because I assure you, 1 city is not going to generate enough faith to reliably get out an army on a dime if you are in trouble and need it.
Not saying "you are wrong" but it is certainly not the most efficient use of faith.