I just have question or two?
How many improved tiles are we going to use anyways?
We can improve 1 hill and a pig. How often are you using your pig? The two improvements will deny us of 3F1H1C.
How many FHC does an earlier second city give us?
Good questions, it is very good to make me defend the rationale I have used, as it leads to me uncovering my mistakes or incorrect assumptions.
How many improved tiles are we going to use?
Not an easy question to answer, it depends I guess, but what the saves do illustrate is what a worker could do in the time. We don't know what we will find outside our immediate BFC other than the direction we started in. In my test the worker has built 1 Pasture, 1 mine, 1 farm, 1 cottage & 5 roads.
We can improve 1 hill and a pig. How often are you using your pig?
Every turn except for 4 when we starve Caput Mundi to get GW 1 turn earlier. 6F1C is a super tile! Even with Imperialist trait, it is the best tile we have to help build settlers or workers.
The two improvements will deny us of 3F1H1C. per turn!
How many FHC does an earlier second city give us?
Comparing the 2 fastest city scenarios:
If we go WB->GW->Settler we do get a settler 3 turns earlier (the city itself gets 2C, but 2 maintenance, Caput Mundi gets extra 1 commerce, but extra 1 maintenance, so net sum is nothing) but the city must fend for itself with no worker. The first worker we get doesn't come for another 3t after the city, and assuming it Pastures and Mines Caput Mundi first, it won't get to city 2 until 12-13 turns after city is settled (in other words city 2 would advised to build its own worker).
If we go WB->Worker->GW->Settler the worker is farming a tile for city 2 the turn it is founded, with Caput Mundi arguably already over-improved.
.... Tests until city 3 (assuming we build it before BW)
I have attached a few more saves from each strategy, this time making the save once we have 3 cities. In all 3 scenarios I have built Archers as they will be useful after we get BW. I think the results speak for themselves. (though I admit I messed up in the WB-GW-Settler-Worker test, I should have built a worker instead of a warrior for city 2, but it wouldn't be finished anyway)