City Location
Doesn't the fact that we know Bill mean we will know where his capital is located?
It's easy to have a player and an AI meet without revealing any info... the AI can be given a Lion next to our starting area and then the Lion can be deleted, and we won't see any of that AI's territory. Or, we can have a Lion created near the AI, deleted, and then the revealed squares can be hidden via the World Builder.
We can figure out where our capital is located by going to F1 -> City Info in the drop-down menu at the bottom left, and looking for X and Y, but I don't have any trick for figuring out where the AI's capital is located.
Early Writing
BTW, it is too early to see if we want Alpha so soon.
True. Alpha will be of less use to us if it's only us and Willem within contact of each other. Of course, BtS AIs send out Work Boats early, and we can do so too, thus even if we're the only 2 players on the same continent as each other, we can probably meet other AIs reasonably early on.
We are Creative and Philosophical, so our Civ SCREAMS for us to get Writing reasonably early and working on an early Great Scientist. If it weren't for the Gems being under Forests, I'd go for Writing before Bronze Working, but we need Bronze Working before Writing due to the Gems squares being so strong to work.
Alphabet?
There is a good chance that AI will have it learned not too long after we learn writing on Immortal level.
Perhaps in a typical game, but with the strong Gems Mines and hiring Scientists (because we will not stand a chance of hitting the podium if we don't get at least 1 early Great Scientist, given our Traits), we end up being far ahead of the AIs in the test game in terms of research. Writing is still tradeable when Alphabet comes in on Turn 60 or earlier in the test game.
With Alphabet being only 1 step away from Writing and us being able to delay Animal Husbandry, we can be all-but-guaranteed to get Animal Husbandry in trade... as soon as Willem researches it (which he will PROBABLY do before he even thinks about researching Alphabet), since Animal Husbandry is a non-monopoly tech and you can trade for it when an AI knows know other AIs in the game.
If we can get Animal Husbandry, Sailing, and Masonry in trade, Alphabet will have pretty much paid for itself, except that we'll also have Alphabet in hand, while we wouldn't if we self-teched those techs.
So, if we want The Great Lighthouse, Alphabet is probably a very strong play, assuming that our Work Boats can meet a couple of neighbours.
Given the fact that we'll probably Chop 3 to 5 Forests by learning Math early, I don't see 30 to 50 Hammers from Math making it a better choice than Alphabet, if we are choosing between those 2 techs on the way to Currency. Alphabet lets us build Research, if we choose to go for uber-fast Currency. As much as I like the idea of gifting Workers to Willem and stealing them back, we can probably gift him 1 Worker without warring and can give him some of the smaller Gold gifts without warring, as well.
One thing worth doing, though, is getting a Trade Network connection to Willem... the more turns of trading an AI Resources, the more they seem to offer you in total Gold from their coffers. If gifting him a City gets him to build a Road to us, then we can get such a Trade Network connection... a Trade Network connection could become even more important if he founds a Religion, so that it can auto-spread to us.
At some point, though, we'll want to take Willem's Cities with some Liberating of Cities involved, so that we can take his good Cities and get him up to being Friendly toward us with massive Liberating (probably best accomplished via 2 wars, by getting his capital close to our capital at the end of the first war, to make it easier to Liberate Cities to him--him being Creative helps a lot in terms of being able to get Liberating credit), so even if we go for early Alphabet and follow that up with Currency, doing so doesn't rule out spamming Military Units, gifting some Cities, and capturing + recapturing Cities in an order so as to manipulate where Willem's new capital gets relocated to, and then rinsing and repeating to get him up to Friendly status for better tech trading in the future.
City Settling Order
We can have the second city settled on T24 and on T26 the cities will be connected via the capital culture expansion.
For your info, if we settle City 2 at the location 2N of the G Riv Wheat, we get our first two Cities connected via Trade Routes immediately.
The strength of settling by the Cow for City 2 might be in getting the Crab connected soon, but I see you building Warriors instead of another Work Boat.
If we settle by the Cow for City 3, we should have enough Hammers to get it a Work Boat sooner after the City gets settled than we can get a Work Boat relative to the settling date by settling that location as City 2.
Meanwhile, 2N of the Wheat lets City 2 steal the Wheat when the capital doesn't need it, and allows us to get 2 Gems Mines connected pretty quickly.
I could see City 2 as a Cow City possibly working, but by making it City 3, we won't feel so compelled to share a G Riv Farm with the capital and thus can settle 1E of the Cow, getting what fog-busting makes it look like 2 more GH squares, both for additional production and great visibility of the land to the west (a Hills square within your Cultural Borders will allow you to see 2 squares away from that Hills square).
Anyway, if you want to demonstrate that settling by the Cow beats settling 2N of the Wheat for City #2, I'll be more than happy to see the results!
First Gems Mine
I like the second city a bit early to get the gem mine up sooner.
For getting the first Gems Mine online ASAP, the timing of learning Bronze Working is a more important factor than the timing of settling City 2.
As long as we have settled City 2 such that at least one Gems square will be within our Cultural Borders after we have finished Chopping the Forest, then that's the timing that will matter.
Assuming that we settle adjacent to a Gems Mine, like we can by settling 2N of the Wheat, then we can settle the City as late as T29 + however many Worker turns it takes to Chop the Forest (it depends upon how many Workers we have) and still get the Gems Mine online at the same time as having settled the City earlier.
Actually, I cheated a bit when I did the testing, since I gave ourselves Gold in order to compare the scenarios against one another... in reality, we'll probably get Bronze Working on T30 (needs to be confirmed... it's possible that without using Binary Science, we could still get Bronze Working on T29, which would mean potentially earning +1 turn of working the first Gems Mine, depending upon our Worker turns).
Bronze Working is Flask-dependent, so if we settle City 2 without Trade Routes, and Maintenance costs us 3 Gold per turn, we also have the potential of slowing down when we learn Bronze Working, which would then likely earn us less turns of working the first Gems Mine.
Tested Variants
I suppose I just valued the warrior out before the settler, as I had some horrible barb experiences with the test save.
My point was that we will still have the option to get a Warrior out before the Settler and start the Settler at Size 4 on T18 by working the Unfarmed Corn instead of the Uncamped Deer, and because of the extra F + H + C earned from growing sooner and the extra 3 Food from learning Agriculture 1 turn sooner, we end up surpassing the approach of getting the Work Boat sooner by a net +1 F and +1 C.
In other words, we keep exactly the option that you wanted open, of being able to get that early Warrior out by T18, but we will earn more F + H + C inputs overall.
We won't even have to make that decision until T14.