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Arrian
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Kneel before Grog!
Jul 2001 time: 00:17
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On Monarch with 1.17, the AI is dead broke until at least the middle ages, but then it starts to build up a cash surplus... I've seen AI civs with around 1000 gold. That didn't last, but they did actually amass that much money.
Planetfall,
The way that I jumpstart my tech is building the Great Library. Since I play on Monarch, I'm usually way behind in the ancient era (sometimes WAY behind) until the GL is done. Then I pick up a ton of techs. Then I concentrate on my economy. #1 beeline is for literature for the GL, then for currency. Cities (those that aren't terribly corrupt) build a defender, a temple, maybe a worker or two, a library, and a marketplace in the ancient era. My military is paper thin at this point. Once my core cities all have libraries and marketplaces, and have grown in size, I can usually keep up and even eek ahead by a tech or two. Holding that lead is very hard with 1.17, due to the tech trading.
Here is your main problem, I think: Tech devaluation. The "value" of a tech is calculated based upon how many civs know it. If no one knows currency, for instance, it retains its full "value" both in terms of how many beakers required to research it, and how much it's worth in a trade. HOWEVER, if 1 out of 2 (in your case) civs know it, that's a 50% reduction in value. Therefore if you, or the Aztecs, discover a tech, the cost of researching that tech immediated drops by half. Thus, holding a tech lead is gonna be awfully hard, even on warlord.
-Arrian
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Arrian
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Kneel before Grog!
Jul 2001 time: 00:17
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Well, sometimes it seems to be that the AI researches the same stuff, but I have had many occasions where they research one way, and I the other. This divergence is usually most pronounced in the industrial age.
I have a set patch through the Industrial techs:
Steam Power, Industrialization, (buy nationalism), medicine, electricity, scientific method, atomic theory, electronics, replaceable parts, and then I click on motorized transport.
The AI will research communism, sanitation and espionage, and will get nationalism via trade (just like me) from a scientific civ that got it for free.
I actually managed to pull away by 4-5 techs last night, and got Tanks before the AI got infantry. Not much before, but I captured half of the Roman Empire before they started fielding infantry. The momentum is unstoppable now. 
-Arrian
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Arrian
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Kneel before Grog!
Jul 2001 time: 00:17
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Planetfall,
First off, Firaxis already added "reduces corruption" to police stations.
Second, my tech path is designed to do two things: get Theory of Evolution and get Hoover. Especially now that ToE works like CivII's Darwin (you can choose the techs it gives you), it's really important to me. ToE gives me Atomic Theory and Electronics. Then Rep. Parts so I have infantry to fend off any silly AI's until I have Tanks. With factories & hoover, I can crank out tanks in 2 turns from my core cities. I build a LOT of Tanks, even if I don't necessarily plan to use them. I want them around, just in case. After all, they upgrade to Modern Armor for 20gold each I sometimes delay flight (if I have the Colossus). Bombers are good, I build 20 or so of those.... and I might build more this time around b/c they weakened bombardment in 1.17.
I do get around to building a navy, but usually don't bother until I have established control over my continent, or at least the part I want. Then I start building Battleships. Lots and lots of Battleships. I have on occasion gone overboard with that... I had one game (keep in mind this is on a normal size map) where I had over 40 Battleships.
Modern Age tech choice depends on which victory condition I want to go for. I always start w/Computers. Then it depends on how close the AI is to me... if they're right with me, I'll go for Fission to make sure I get the UN. If not, I will go for Ecology first. After that... like I said, it depends. Synth. Fibers if I want a Domination win, the various SS techs if I want to win via SS launch.
-Arrian
p.s. By the way, I know my tech path is land based. In my opinion, that's the most important part, because with RR's, mobile defense vs. invasion is easy. So getting the good ground forces first makes me invulnerable to assault (or securing hegemony over my continent), and then I can set about preparing to do damage to someone across the ocean.
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Arrian
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Kneel before Grog!
Jul 2001 time: 00:17
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Planetfall,
The Hoover Dam Great Wonder gives you a hydro plant in every continental city, river or no (I'm 99% sure of this).
I don't edit the game. I may later, once they're done patching it, but for now at least, I play it with default settings. Besides, in this case, it makes sense that such a great production booster (nuclear plant) has a potential downside (meltdown), whether or not France has ever had one.
I never build coal plants. Not worth it. If all goes well, I will have Hoover built pretty soon after the rest of my cities have built their factories. Even without the nasty pollution, they would be obselete (by the hydro plants) too quick to be worth building.
Have a good weekend too 
-Arrian
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