Liberty start : libraries or monuments first ?

going liberty, I might build a monument first in the first two cities, then a library first in the third city. the idea is to get the NC up fast, so ideally you would be buying that third library if possible. I find 4 cities before the NC is too slow, found the 4th city after NC.

I agree with this strategy. You should be buying that third library if at all possible. But my answer to monuments vs. library is GRANARY. You'll never have enough food to quickly build a library unless you have a Granary to support your existing population and grow you some new ones.
 
I sometimes chop out libraries in my expansion cities and build monuments second. Anything to speed up NC is good, saves 400g for other things, like upgrading archers, and really I'm not going to need that chop for anything else unless I build a wonder in an expo, which is rare. So naturally I favor expo spots with first-ring forests. Plus you can pre-chop. So you're only delaying monuments by a few turns. But usually I go monuments first and chop out the monuments. Speeding up the rate of tile acquisition is highly useful. Lots of ways to skin this cat.


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