I usually send a worker from the capitol. Never did a numeric analysis on this however. The intuition tells me:
- Building Worker stops growth. Its a big problem.
- Its ok when you just settle, as You dont want to work uniproved tiles. So in capital there is basicly no other choice.
(Note that IF you have the choice - like Seafood - you would often rather Build WBoat first, so capital can grow, while building/improving)
- While Building the Worker in your new City will delay growth for 15 turns, your Capital probaly can do it much faster. Also your capital might actually be at the Happy cap already, so delaying growth there is not a big issue. Even if not at happy cap - the capital is working improved tiles, so it builds the worker more efficient, than the new city would.
- Also sending the Worker with the settler reduces the amount of time, the new city has to work unimproved tiles, those speeding up growth there.
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What i usually do is: use my first (or first two - if i plan to chop a lot) workers to improve a couple of tiles tiles near capital (maybe 6 - depends on whats there), then i send one worker away with the settler. The capital is working those "pre-improved" tiles, while i build a new worker in the the capital, who - again - improve a couple of tiles near capital and then goes off to the next new city.