Turn 5 -- 1375 BC
Shanghai produces Spearman, I order up Settler.
Hence my comment about allowing it to grow. Is that a misprint? No, I see from the pic that you really do have it on settler. That's not the best plan for Shangahi. You did mention a granary plan earlier... I suppose since we'd waste shields if we swapped back to a spear, we could switch it to granary now. However, the reason for the early focus on granary in Sirian's PROD game is because there are no bonus tiles around, so he has no cities with a good growth curve. In our case, we have lots of cities around capable of a good growth curve building settlers and workers already; what we don't have is defense. The "if we don't need it yet, then we shouldn't be building it yet" rule does come into consideration here -- just how much defense do we need right now? Certainly enough for barbs, though probably not too much more than that just yet -- and there are barbs out there, there's even one on the map right now. A couple more spears before the granary would have done the trick and would have helped us stay strong in the eyes of the AI, though the Iros aren't that aggressive to begin with. It's important not to appear too weak, though, or the AI will try to snag some of our resources/lux away from us. A granary is not a bad plan, so long as we get back to building a number of spears quickly... but a settler is definately not the way to go.
We do have an alternative, though; we could build the Pyramids. The Pyramids are by far the best ancient wonder for the kind of map we appear to be on, and will help our overall growth enormously. If you're concerned about coming to rely on wonders as some kind of crutch, don't be. The only time wonders become problematic is if you're playing at the hardest difficulty levels, and I'm not going to try to teach you how to play on Emperor or Deity in a Regent-level game; if I wanted to do that I'd start an Emperor-level game.

Whoever's up next can decide if they want to go for a granary now and spears later, or more spears now and start Pyramids a bit later. I'd vote for the latter.
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Beijing is building a settler, when it's only size 3 and set to grow in 5? Probably not the best plan; we want Beijing to keep a reasonable pop base going so it can build stuff in good time. Beijing has enough good food-producing tiles available that it can grow all the way to size 6 and still maintain that healthy growth rate, so we should take advantage of that! Bigger cities = more income and faster production; we just need to keep an eye on micromanaging its citizens since we don't want them working that forest and taking growth away from the city. We should probably hold off on that settler for the moment; again, though, we'll be wasting shields if we swap to something cheap. We could build a temple since we're almost halfway there and since we're already starting to fall behind on culture -- if we slip too much we'll have lots of trouble with our cities flipping to other nations. Alternatively, we could build a sword and restart the settler right away. Having one sword around is good for AI intimidation -- the AI considers the number of units you have as well as the best unit you have when calculating relative strength.
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Canton: A barracks is a reasonable idea, it will give us a chance to build more vet spears in between our settlers and workers.
Nanking: Not sure how corrupt we are here, probably moderately so. A worker is a reasonable idea, but we probably don't want to build more than one since food is a bit scarce up there, so I'd say military after the worker is a good bet.
Tuscany Bay: A temple here will help extend the good lands not only here but at Blue dot and Shanghai for access to more bonus grassland. It will also ensure that we don't lose city squares to Niagra Falls, unless he builds a temple first. So, temple has my vote as the first build item.
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Blue dot city: Remember, anything that can wait, should wait? Blue dot can wait. Of course the settler's there now, so it should go ahead and found the city, but the location was perfectly safe from incursion by the Iros until mapmaking, so there would have been no danger in letting it sit vacant a while longer. If we're going to stake a claim to any of that jungle, we need to start getting some (preferably escorted) settlers up there SOON before the AI starts making inroads into it. It looks like Japan already has a couple cities up there -- we need to start establishing our "borders" a couple city lengths away from there (and by the Iroquois) so we can mark off that territory as ours. It also wouldn't hurt to grab those lux up there so we can eventually connect them into our road net. We do NOT want to send workers up there just yet, though, at least not until we pick a spot for and found an FP city.
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Workers: a bit harder to tell what's going on here since you could have some stacked, but I'll assume not. What happened to the worker at Dockonda Bay? Dockonda still needs more mined grassland tiles in radius, as it is still short on good production tiles. Same goes for Beijing, there is a bonus grassland in range that is begging to be worked. We don't need more than one worker improving Canton right now -- it's still only size 1 and can only use that wheat tile! The worker at Shanghai should be concentrating on improving tiles that are in the city's radius NOW, not that will be in range someday. I see we already have a couple workers out by Nanking and Tuskany Bay, probably there to connect up our Iron and start improving those cities. One or two out there (plus whatever they build on their own) are probably enough, we should NOT send any more out there when there are still lots of improvements needed at our core cities. Remember the cities closest to the capital should get the best of everything -- the best city placement, the most attention from workers, and the best lands to work -- because they are the least corrupt cities.
BTW, one option to consider when you have a single source of a resource like Iron that can deplete, is leaving it unconnected until you need it. An unconnected resource never depletes, but a connected resource can deplete even if you aren't using it. One thing we might want to do once we have a horse connected up and inside our borders is to pillage that iron square until we get Chivalry -- we'd prefer to build horses to swordsmen anyway, since horses can be upgraded to Riders.

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Code of Laws vs. Philosophy -- the price will be proportionally lowered for both when we discover more civs, ASSUMING they already have researched them, which they probably haven't, since this is Regent. If we're the first civ to research it, contact won't help us research any faster; nobody can tell us anything about something they don't know themselves! Getting Philosophy done sooner doesn't help unless we are looking to trade it away (which we probably aren't) as we can't do anything with it. Courthouses, OTOH, were already very useful in 1.17, and are even more useful now.
We're getting to the point where we soon are going to want to start considering whether we want to turn down science and save up cash, buying in at latter-civ rates, or go for a tech lead. We need to make contact with more civs before we make that decision, though. More cash in a Republic means more ability to rush-build, more ability to upgrade (e.g. horses to Riders...), more ability to deal for maps/tech/lux/etc., so it's very handy. The problem is, on Regent, the AI still doesn't research stuff all that fast, so we may be stuck in ancient times a while yet. We don't need to make any decisions yet, but my guess is we want to stay on a high-science track until at least Republic, and we'll see after that. Probably we'll want to drop to min-science or no-science for a while so we can get some really respectable income coming in.
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Diplomacy: Contacting AI civs vs. exploring to find them -- this is a judgement call based on how likely you are to be able to contact them. Can you get around Japan to the civs on the other side(s) without violating their borders? If so, then it's worth a shot. Otherwise, getting it over and done with is a good plan -- the savings in beakers on already researched tech might well be worth the cost. Plus, we can now establish embassies to get a rough idea of where they are, and soon we ought to be able to start swapping maps around.
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Can someone please post a zoomed out map of the northern jungle lands so we can get an idea of what a likely FP placement plan would be, and where we need to found some cities to establish borders? (If someone discovers mapmaking, trade territory maps with everyone, so we can get that information for consideration too. Territory maps are cheap relative to world maps -- and we might even be able to turn a profit since we have so many cities.)