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Welcome back. Last time you might remember that we left on a bit of a cliffhanger, following Kublai's stack east, away from our border. We were also about to revolt and swap civics, but we're going to be doing that next turn. Why?
Because we're about to get a Great Scientist in Antium. (I'll be moving a citizen from the farm to be another Scientist next turn, by the way, I just wanted to regrow faster.) It'll take him 2 turns to walk to Rome because I didn't finish a road there, just using the river for my network; so I'll revolt that turn and he can build our Academy simultaneously. That'll also finish Horseback Riding.
His stack moves to the English border, then... into the fog? Wait. 
He's going after Alex, not Victoria! Well, he has fewer cities and hasn't made much headway against the English that I can see, so that makes sense. Well, that may be for the best, that puts his army even further away. That does mean Alex is going to get smashed, since phalanxes are helpless against Mounted units that aren't chariots. Well, not "helpless," but at a disadvantage. I need to train a spy to go to Russia anyway, so after the revolt, I'll train 2, and if either returns From Russia With Love Drama they'll go to England next.
Well, Cathy certainly wasted no time trading for Metal Casting. 
But wait... she didn't use Drama, and it doesn't look like she traded with Bismarck. Looks like maybe... Currency plus some cash to Alex? Huh. Hey, why'd he trade with her and not me?! Anyway, regardless, I'll also trade with Alexander for it. Here's something else you can do with tech trades:
Deliberately give an AI military tech. Horse Archers will let him fight Keshiks and try to do something about those catapults. Feudalism would've worked too, and arguably better; but longbows aren't great against mounted units and he could've used it to trade for stuff he's missing, which will make it harder to trade more with him later. In any case, I'll be getting Kublai off his back soon enough (if indeed that's what's going down). 
OK, enough waiting, it's time. Alea iacta est. Once we're in Theocracy there's no point in infrastructure unless it's something obvious like a Forum in Antium (more Great Scientist points and bolstering its high commerce) or Barracks or whatnot, it's all praetorians, catapults, and the occasional longbow to leave on garrison duty.
Competing offers for Horses. You can see that since Bismarck likes me more, since he offers a better deal (Kublai wanted 20GPT after the marble and dyes, without a 3rd resource). We're going to deal with Kublai: I'd rather part with a happiness resource I don't need than gold, and a deal locks you in for 10 turns, while if I declare on Kublai before that then obviously that cancels the trade early.
First turn queue. Ravenna will be whipping the Courthouse since it's about to grow and will then be getting some catapults for Ning-hsia, and Neapolis just whipped a Library (interestingly, without the Organized Religion bonus, this turned into a 2-pop whip for near max overflow, instead of 1) and will be making catapults as well. It has enough commerce and a need for culture that it made sense to finish the Library first. Mediolanum needs culture to get my copper back, so once the monastery is in optimal whip position, I'll do that and put it on units too.
Cathy! 
Well, now I don't feel bad at all at stealing Drama from you in return! (I couldn't screencap quite in time to show the espionage icon over Rome, but that's why it's centered there.)
A couple turns pass to 520AD, still building up. I decide to overflow Mediolanum into a spy and try to get my revenge (fitting, all this over Drama ) on Cathy, and Boudica shows up wanting to trade Machinery. Intrigued, I see that Alex already has it! That was fast! I had started self-teching it after putting about 800 beakers into Education (I can bulb the rest of it, and I want to get Guilds and Banking knocked out so I can get Economics right after Education for that free Merchant), but fortunately only 1 turn of research had elapsed.
Two obsolete techs for letting me get started on windmills and crossbows? I do agree that's fair!
Next turn, and I chop the last grass forest near Rome to put a farm there, Clams + Cows just isn't quite enough food for all those brown cottages and hills. I decide to make an exception for building buildings and put the chop (and one in 2 turns to finish it, on the riverside plains hill forest 2N of the city) into a Forge. Why? Well, it gives me a chance to talk about Bureaucracy! See, normally in Civ4 multipliers apply individually to the base value and then are added together (instead of multiplying each other). In a Bureaucracy capitol, that's still true of production (if I already had a Forge, a chop would be 52 (30 (x1.5) + (x1.25)) instead of 56 (45 x1.25)), but not commerce. Our base 38 commerce is turned to 57, and then the Academy and Library get factored in. Rome is actually a pretty weak commerce capitol, you can get 200 beakers from just the one city under optimal conditions; but it's still providing 1/3rd of our entire empire's research. That's why I have a monastery in the queue, that 10% doesn't sound like much, but it's another 10 beakers here!
I get a note that Cathy switched to Vassalage, looks like she managed to get a nice trade off of Bismarck (who now is the only other one with Drama). Looks like she's going after Divine Right, a freebie I'd much rather she chase than, say, Liberalism. Still no Apostolic Palace yet, and I don't have Buddhism in any of my cities (and won't as long as I have Theocracy going), so definitely nervous about trading Boudica Theology earlier. 
But she just finished the Mausoleum (and very little failgold to be had, so nobody else must've been) so I doubt she was building it too, she's never been the wonder-crazy type so far as I know. Kublai has 90 gold, so I go ahead and sell him Calendar to wrap up the turn.
Lincoln also revolted to Vassalage this turn, so most of the AIs are getting Feudalism (this is to be expected in the mid-1st millenium at Immortal, it can start happening in the late BCs on Deity). Longbows would obviously be much tougher to kill than regular archers, but Kublai still doesn't have it, and praetorians can still get the job done. Really, regular swordsmen can too, as long as you're not going after someone Protective, you just take more losses and ideally attack with trebuchets instead of catapults. I haven't been able to make any trades for awhile, but that's OK; every turn an AI has a 5% chance of forgetting 1 trade toward the "we fear you are becoming too advanced" threshold, so dry spells have their use. Really, I'm hoping more that AIs get cash instead of techs to trade for; I'll be getting a Great Scientist soon and finishing Education, but I'll still need to research Economics and Philosophy.
It's almost go time, so I beg some gold from Cathy and Bismarck to help stock the coffers. Kublai never did declare on anyone, and I can't follow his stack through England, so I have to assume he's either building more (the #1 AI on Soldiers has been constantly ramping up, so I assume it's him) or going all the way East to go after America, his worst enemy. There's a distance factor in warmongers deciding who to go after, but for some it's large to nonexistent (Shaka infamously will declare on you from the opposite side of another continent!).
I went ahead and tried my trick from the Saladin game here, hoping maybe Vicky lost some units in her war against Alex. Nope!
Aw yeah, praise Cathy! Whew, I was worried for a bit there! I don't actually have that many Jewish buildings, but I definitely will when I switch back to Organized Religion. ...and I show my gratitude by voting for Bismarck. Hey, Catherine won't be getting any Friendlier.
Sure enough, it bumped ol' Otto to Friendly. The only thing he has to trade for right now is Drama, but that'll change. If he keeps trading with Boudica, I might be able to get Compass and such like that off him.
A little micro in Neapolis to finish the catapult this turn, and Ravenna just whipped one as well. Kublai has neither castles nor longbows, and we need to strike before either of those change. Next turn!
Wait, what's all this then?! On the interturn, Kublai traded (or finished researching, either way) Feudalism and started upgrading! Well, again, not the end of the world, but this war just got a lot harder (as in, hard at all, we were looking at a cakewalk when I started building ).
So before declaring, always take a look at your borders and see what enemy units are around. If your culture is smushed up against theirs, be especially wary if they can attack immediately, or if they have to cross some of your tiles first (meaning they can't use roads). In this case, we can snipe a Mongolian worker, but there are 2 units that'll be teleported to friendly territory when I attack. That's all I see, so let's declare war in the diplomacy screen instead of directly moving my army in (so I can see where his units go first).
You know what? Your head would look good on the end of a pole!
As expected, they got shunted to protect the worker. This is where I wish I was Aggressive, if I could promote a praetorian to Formation (the anti-cavalry bonus) I'd go up against the swordsman, kill him first, then throw the cheaper spearman at that keshik. Nothing else for it, though.
Not an auspicious start to the war, losing two 75%s. 
Well, what can you do? I move my armies in to Ning-hsia and Samarqand as planned.
And macemen! So yeah, when I started moving troops to the frontlines, I was looking at archers, keshiks, and axes. Now I'm staring down longbows and maces, and macemen will destroy praetorians. I have numbers (for now) and the legion is a lot more cost-effective (45 hammers vs. 70), but yeah, this is suddenly looking dicey. I basically have to raze Samarqand ASAP so I can get those horses back, and then start throwing knights at the problem. You know, until Kublai somehow trades for Engineering too, despite being at the bottom in tech. I honestly don't know how he traded for Civil Service and Machinery, he had neither just a few turns ago!
The Battle of Samarqand. I got lucky once here (the praet vs. axe was 42%) but the rest was about average results. Praetorians are just strong units, and most of mine had at least 1 promotion, a majority 2. I have to leave the wounded swordsman in the city, my only unit left that can attack is the wounded spear, who probably wouldn't win. I plan on razing the city (so unlike normal there'd be no risk of him whipping another defender) so it's pretty unfortunate I can't seal the deal, but so it goes.
So I miscalculated a bit on how much I'd bulb for Education. 
No biggie, I can still finish it and then start on Economics with the gold I've been saving up.
So of course Kublai whipped a longbow. And of course I lost winning odds to take it out. At least the praetorian wounded him enough I took the city without incident and wiped it out, but man. Going to have to stop for a bit and reinforce already! And naturally he's been whipping and upgrading in Ning-hsia, it now has 2 maces. I'm going to just sit there in his face until I get some knights moving in, and then take them out.
Our first Great General! Due to the "General of the Legion" stipulation, we're using him on a reinforcing praetorian. This guy will be our medic, with Woodsman 3 first (2 first strikes will help him clean up safely and get XP, as well as having better healing than Medic 1). And after thinking about it, I pull my mini-stack from Ning-hsia and get ready to merge it with my main group. This war is suddenly at tech parity, so I need numbers to wrap it up quickly, that means smashing each city in a turn or two instead of gradually whittling down two.
I get an "enemy spotted near Mediolanum" warning, and it's Kublai with a keshik and archer. This is a good chance to get an enemy kill in my borders, and Rome is about to produce a knight. 
Down go the keshiks! See, this is what I was expecting when I decided to go after Kublai, not... stacking up maces and longbows everywhere. Anyway, it's been a few turns (though not that many, really, my 10-turn beg treaties just now expired) but I finally push back into Mongol territory with the full army. More knights are coming, and 3 AIs have Engineering now, I should be able to trade for that soon and get the extra movement speed on reinforcements and the ability to start making trebuchets to crack these cities faster.
Dude, what part of "We have enough on our hands right now" doesn't translate?! Ugh, I hate that the AI can do this when you can't pull them into a 2-front war. Gotta give him props for fighting this entire time, though, despite not actually getting anywhere....
I get another "enemy approaching" warning, and it's a small squad, presumably detecting that Neapolis is poorly defended. I'm going to regroup my reinforcements such that they can all hit the horse tile next turn (which is where I assume he's going) and wipe it out with the double Great General XP from doing it in my borders.
Great Merchant! Always useful. If you don't know, the modifiers that go into a trade mission are the same ones that apply to regular trade routes, including the +100% from Temple of Artemis (meaning you always get +200 gold from hitting the city with it). Fortunately, Merchants can cross closed borders; unfortunately, they can still get killed by keshiks. I have the choice between putting him on a galley and dropping him off in England and hoping Kublai doesn't have any units nearby, or running him the long way east, through America and up. ...you know, I haven't scouted that yet, so let's do that! And let's see if I can get Engineering and make that trip faster....
...ah. Yes, that would explain things. 
So this is how Civ4 balances tech trading being the most effective way to "research": arbitrarily capping the number of times you can do it before AIs stop playing along. There're some things you can do about it, like making Friends with a civ or just waiting (they will very gradually "forget" trades and decrement the "fear" meter), but if you really want a tech and see that red text come up, it's not good times. If I'd known Alex was at that point, I would've considered joining the war, and that plus converting him to Judaism might well be enough to make him Friendly. Ultimately, I think I'd be better off buttering up Bismarck, any 1 "fair trade" point should put him back to Friendly (he was there before I declared on his "friend" Kublai). I'll wait 'til Philosophy comes in (3 turns if all goes well) and keep an eye out to see if any other opportunities open up.
Looks like Kublai wasn't expecting us to go straight for his capital! He'll definitely whip a defender, and probably run some keshiks in, but I have enough catapults and forces I may well be able to attack the following turn, and if not definitely the one after that, which should limit how much he can throw at me. The 4-unit squad retreated back, by the way.
Kublai gets Engineering!? How?! He's pretty much completely caught up in tech despite being at war and not, y'know, having anything to trade when the war started. I have no idea what happened, and now he can use pikes to counter my knights (he doesn't have any spearmen running around, and the AI doesn't really build enough, so the answer is still "more knights," but in any case).
I also see the first serious Mongol counterattack, heading toward Corfinium. It's building a knight already, and instead of going for research overflow to the next project, I put just enough in to get Philosophy this turn, so I have enough gold to upgrade the warrior there to a spear to help deal with those keshiks. He'll bombard at least a turn, so I'll have time to whip and send reinforcements.
I can bombard about half Karakorum's defense away. Normally I'd finish the job, since the city's on a hill (because of course it is), but I think it's more important to attack immediately, sacrificing the non-Accuracy catapults and replacing them with trebs once I get Engineering. Whether he whips another longbow or castle walls, it'll probably be worse than +36% defense on the units he already has, and that's not accounting for any reinforcements he might send if I wait. So....
The Battle of Karakorum in one bloody turn. The two losses to longbows were to 1.4 health dudes at 91% odds, but I did win a 40% in there, so I guess it balances out. Ugh. Unfortunately his General spawned in his capitol, so he was unceremoniously killed before being able to be settled (warmongers seem to like having them Warlord units too, though, so it may be for the best). We move some defenders in and I'll probably heal up a bit before going after anywhere else, I can't risk not taking a city immediately when he can whip castles and pikemen now.
Finally, here's what we've been saving the Great Artist for! Friends, RomMongols, Countrymen, lend me your... uh... well, that didn't work. Yeah, so, I tested this in a previous game, but I guess it's different against a Creative civ (plus 900AD is a bit later I think than when I fought last time). As long as the Great Work gives you enough culture in the target city, it instantly brings it out of revolt... but it didn't give us any tiles to work, so what's the point? Is it worth trading a Great Person for 2 soldiers to whip before the city starves down to 1? I didn't think so either. So we're going to reload, and I have a different plan. First, we need to get Engineering.
Fortunately, Alexander forgets one of the tech deals and he's open for one more. 2 civs already have Philosophy, so I'm going to use it to help get some things done. He's the last one to not have Theology (boy, that got around quickly ), so we use that too to get Engineering plus his gold.
I'd love to get Divine Right for a reason I'll get to next, but Cathy is showing the one exception to Friendly AIs' waiving of trade restrictions: if they're building a wonder the tech unlocks. So that's out. I'm going to need Gunpowder and Bismarck is within range of becoming Friendly too, and one way to do that is to get an AI to join a mutual war. So:
Let's get Bismarck to join in on Kublai, and hopefully distract him a bit (and pressure him to capitulate earlier, since he's now got more power arrayed against him). Sure enough, that takes him straight to Friendly. I'm not going to trade for Gunpowder until I need it (again, let's let some turns pass so maybe AIs will forget a trade or 2), but I know I can get it now.
So what am I playing at here? Well, we lost our tech advantage over Kublai thanks to unforeseen trading (and I'll make manual autosaves over the last couple and check what happened later, I'm 90% sure someone gifted him Civil Service, which is insane but fits with the luck I've had), and we need to get another one. There are 3 paths we can go from here:
1, and the one I recommend if you're playing to win instead of for fun, is to beeline Rifling, since we already have Banking to get Replaceable Parts. There's nothing Kublai can get that can stop riflemen, and we can draft them.
2, and what I need to get eventually given our challenge, is to go Grenadiers instead. Chemistry is a great tech and I can now access Gunpowder to get to it, and in addition to researching Military Science, it lets use Lib Steel, and cannons are again an unstoppable advantage until your foes get to the Industrial era.
3, and what I decided on because it won't obsolete praetorians, is to get cuirassiers and add them to our stacks. They ignore castles and can rush lightly-defended cities, and when we do bombard, they can take out maces and free up our legions to sweep everything else. I like this idea because we have legionnaires on foot, and legionnaires on horses (also with guns ).
To get there I have to start building back up, so my plan now is to put every city on building units, trebuchets if they can put out 20+ production in 2 turns (thus taking it to 2-pop whip range), pikes and other anti-Kublai miscellanea otherwise. That'll hopefully be enough to take his eastern half, at which point I'll take a capitulation if one's offered, or go back west. After those units are whipped, I'll go into a Golden Age. It's very risky to try to build up your cities while you're at war-- that's why we pumped units nonstop after we declared-- but I think it'll be better to push to Military Tradition ASAP than try to grind him down with a "fair fight."
So far I've kept the Paper monopoly (it's a low-priority tech for most AIs because the Education path doesn't do much itself, but what it unlocks), since I want to get the University of Sankore and Kublai's stone to help build it, but obviously that's run into a snag. I won't make this deal, of course, there are other ways to get Compass.
My bad luck continues: Kublai pulled back from Corfinium to try to retake his former capitol, throwing all of his stacks at my army. The one good thing is that each one only has 1 or 2 units that actually get a defensive bonus from these hills, the keshiks and catapults don't. So I should be able to intercept them with knights and do some damage. I was really hoping to fight some battles on my culture. At least defensive battles in Karakorum itself will count.
Let's whittle down some units in the open. First, I promote a knight to Shock to deal with that mace, then I can run some defenders out of Corfinium to deal with everything else. It's pretty by-the-numbers except the pikeman drawing a catapult instead of the keshik, I forgot about that. Catapults are actually pretty tough stack defense if you don't have enough mounted attackers! I had good luck on the odds, not losing any, but bad luck on flanking damage (there shouldn't have been any full-health cats by the time my knights were done!). A Shock-promoted crossbow draws a catapult as well but kills it, then a Drill crossbow kills that mace. Finally, the power of longbows, I barely get winning odds despite a high-Strength Cover-promoted praetorian! I'm going to bite the bullet and reinforce on that hill, promoting my own longbow to Guerrilla 2 and counting on the river crossing penalty to hold off the keshiks.
Hey, this doesn't look like Greece! Indeed not. Thanks to Bismarck's map, I can see that the Temple of Artemis is in Sparta, which isn't coastal (and is pretty small, too). There are a variety of factors that go into trade route income, but suffice to say, you want a big city, and you want one with a building that increases trade routes. The Temple of Artemis does that... but so does a Harbor, and Bismarck has Compass, so it's no surprise his capital city has one. This is probably the most cash I can get at this point in the game, so I make the deal. Time to turn research back on!
Aftermath of the 
frenzy. Golden Age soon! I was going to do it immediately, but I need to wait for Karakorum to come out of revolt, so I can whip all its population down, then switch. It stings to lose population going into one, but I plan on using it to catch up on Great People (my religious civic will be Pacifism, then Organized Religion when I'm done) and I'll be in Caste System, so no further whipping and my cities will have time to regrow. Nationalism first, so I can get started on the Taj Mahal for another Golden Age. Liberalism will keep until AIs at least get Paper, and even then it'll take awhile for them to get Education.
Alex is the first to Paper?! 
I guess it's because he's Philosophical, and thus gets the discount on universities? Well, oddly enough he's one of the few who doesn't have Philosophy, so Liberalism is a little secure... but I'll still be starting on it as soon as Nationalism is done. I may have to just Lib Military Tradition instead of anything deeper in the tree, depending on how the AIs' research is going. I trade Abe Engineering for Compass plus his gold, I want harbors of my own and he's the only one without it.
Oof, this is gonna suck. Kublai merged his stacks together and he can attack next turn, and I can't intercept him thanks to that hill. The best play is honestly to turtle in Karakorum, even though it has no defenses: catapults don't do a ton of collateral damage, and some of it will be targeted at my catapults, which are immune and thus won't take any damage. My hill longbow should absorb most of those attacks. Makes me wish I had one with Drill, though....
And actually, it's 1000AD, and this is a nice cliffhanger, and this update is a monster thanks to all the full-screen images required for showing military sitreps, so let's stop here. First, what's the war done to our economy? Well....
We're still leading on commerce, but it's close. Also, "GNP" is just a measure of research, not pure commerce, so our scientists count, as do bonuses to specific techs like meeting extra prereqs or other AIs having it. So this is actually better than it seems, it means we have the best research engine (probably thanks to the Great Library). We're top 3 in military, and it's going to spike once we hit Military Tradition and upgrade our knights and train new horsemen. Considering we're in the middle of a grueling war, this is all looking good.
We just had a tech pic, and being first to Education is looking to really pay off. WFYABTA is also starting to rear its ugly head, but we have reasonable moves to deal with it (espionage, 1 Friend and one on the borderline, a potential vassal soon).
And a look at the battlefield. The master plan is to have my main stack in Karakorum head east to New Sarai, and the new one with the trebs take out Turfan. As its new capitol, Kublai is going to defend it hardest, so I expect to have to bombard it down pretty far, which means I'll have some reinforcements to deal with. This is why I made sure to drive through the middle first, we might be able to intercept some units moving in and pick them off piecemeal when they don't have city defenses. We're almost certainly going to win, but we'll have to manage diplomacy to keep Kublai from vassaling to someone else. Come back next time to see how it all goes down!