For what purpose? To manically chop down all forests so we have no way to rush LH? I thought the whole idea was to get new sources of resources? Delaying getting a third city puts us further "behind".
On a less sea-oriented game we would probably already have more workers due to more land improvements, need for roads to connect cities, etc. Even there though, 1 worker by the time we get 3 cities feels insufficient. There's a balance between settling new cities and improving tiles in existing cities that they can work as they grow. If we're going Hunting-AH next there is a fur camp that can be built, a pig mine to convert to pasture, and of course that pig in city 3. In the meantime we can build more mines (not the greatest tiles but better than an unimproved one if the city grows to use them), or we can "pre-chop" the forests in preparation for GLH wonder later.
One thing with workers too is that sometimes there is burst of work, like to improve a new city or to rush a wonder, and then there are lulls. It's good to have enough workers ready for the burst (like how
@sampsa is getting 2 workers to finish that pasture 2 turns earlier for city 3, since pigs is such a good growth tile). During the lulls the pre-chopping mentioned above in an option... just to be clear, by that we mean that you start chopping a forest but tell the worker to stop on the 2nd turn of chopping, not let it chop it on the 3rd turn. BUG-BULL mod does it automatically which is nice, it always stops your workers so you can decide if you want the chop now or not.
Third island city should build monument anyway. Only way that city is going to be able to access the fish is via getting to level 2 culure and we want that done Asap. And as you say earlier city on island means sooner increase in trade. Thus it can be much sooner. Though I don't think you do need the capitals culture to grow a second time to get access to that pig. You get access to it earlier with the culture fusion. But again we don't need the pig or the fish to make a third city useful.
The monument takes 10 turn to expand borders, so it would need to be built by turn 39 to get the pigs before the capital border gets them, which means the city needs to be settled a few turns earlier (even if you're helping the monument with a chop). It's not impossible if you prioritize it enough, but definitely needs to be very rushed, and then need to figure out what else is left behind in that rush.
Also it's a fine thing to talk about fog busting when you all seem to have decided building a warrior at first is no good. I think I should build a warrior first, I tried it not building a warrior at first for better comparison but I think it's needed. Along with a scout a bit latter to take huts
In a less sea-focused game, usually after the worker you let your city grow by building 1 or more warriors. Here we were growing while building boats. On the other hand more sea means less land tiles to fogbust.
Are you asking why I'm suddenly suggesting fogbusting units as a priority if they weren't earlier? Part of it is because it feels like we got the early game priorities done (working those good seafood tiles, settling a 2nd city, getting a good economic start with those seafood tiles and trade routes). But it's also partly about the time when barbarians become a threat, mostly when they can enter your culture. That happens when the average number of cities by player reaches 3 (
https://forums.civfanatics.com/threads/when-do-barbarian-units-enter-cultural-borders.299483/). On deity the AI start with a 2nd settler, and that point is reached very fast, usually around turn 40. On immortal, if the player can get 3 cities before T50, the AI probably won't be any faster. Of course, you need your perimeter to be secured earlier than that turn where they become dangerous, so I am considering it at 32 (Again if it were more a sea map we would have more warriors earlier.)
(One thing though is that it's always good to fogbust the location of your planned next city, even the 2nd one, because you don't want a barbarian unit or worst a barbarian city to spawn there. So here I parked my initial warrior south of capital to cover that area. I could have scouted a little bit more but I want to come back to that location not too late.)
Fogbusting also doesn't guarantee the units won't come for your cities. They can kill you fogbusting unit or sometimes walk past it. I see
@sampsa teched Archery after Hunting-AH. I assume that's because he saw there was no horse nor copper, and that there was no AI nearby (which could have fogbusted or killed barbarians spawning between us), in which case having archers available to be whipped/chopped in a hurry provides greater safety.
---
Re: getting warriors and scouts earlier for the huts. We're getting back to the initial subject of the thread. Since you tried the way without them, you could try now with warrior-scout earlier. (I'm suggesting you try since you appear to have experience on that playstyle and presumably can get the most of a map with huts.) You can see how many extra huts you get. Then however you would have to consider the probability of each thing that a hut could give to compare with the other scenario. What I mean is that if you get just a map from the hut, well you had 16% chance of getting a tech (with scout), so the comparison should take into account different outcomes and not just the particular dice roll you got.