The first stage of the general strategy consists of (not in chronological order)
building a good, strong and food rich core,
building a first trade route to one of your neighbors,
locating and hooking up resources and luxuries,
building some military to eventually pounce on some poor and unsuspecting AI,
building scouts
popping techs like mad from goody huts,
making contacts with all (or nearly all) AIs
stowing up some cash.
The trade route, the trading goods, the cash, the contacts, and the military will later be used to scam a lot of money from the AIs. How exactly that works I am going to describe later.
You will have to go and kill one of the AIs, but as the game is Chieftain the AI is likely to have only two cities with about two spears and a warrior at max. So, I think it is advisable to cut out building barracks and simply build one regular horseman more. A handful of those should do.
Your trade route should not go to the AI which you are going to kill with your handful. Ideally you chose a Civ with only little in the way of luxuries and resources. The more (read: different) trade goods you have that they don't, the better. If they have surplus trade goods that you don't that would be good too, but the chances are fairly slim.
Most of the time during that first stage however you'll spend navigating your scouts over the map and popping goody huts. An early settler close to your capital is sweet of course. But the main intent is popping techs with the ultimate goal of switching to the Republic somewhere between 2000BC and 1500BC or even earlier. Remember, you can only pop techs as long as you are still in the ancient age, you can only pop techs which you have the prerequisites for, and you will pop first those techs which you are not researching.
So, set your research goal to either Bronze Working or Ceremonial Burial, turn your Sci-slider to 0% and have at it. BW as research goal means that you will not pop BW, IronWorking, Currency and Construction
for now. CB means that you will not pop CB, Mysticism, Polytheism for now and Monarchy at all. The upside of BW is that it is possible to pop all techs of the ancient age, the downside that you'll see Iron only fairly late. The upside of CB is that you'll see iron sooner, the downside you do not have a chance for Monarchy.
As soon as CB/BW (or whatever you set your research on) is the last option, it is possible that you pop it too.
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The second stage of the strategy consists of (not in chronological order)
performing trade route scams to conjure up tons of gold,
performing "Another One bites the Dust" scams to conjure up tons of gold,
ICSpamming the world with towns as fast as you can,
using your tons of cash to rush cultural improvements.
To pull the trade route scam you need to make a first deal in this fashion:
They give: [Unfortunately a Chieftain AI has little to give]
We give: X gpt + a trade good
This simply assures that the AI has a nominal gpt income which you will buy back in the next deal:
They give: X amount of gpt
We give: Y amount of cash
Now the AI has a certain amount of cash, which you are going to buy back in a third deal:
They give: Y amount of cash
We give: X amount of gpt + a trade good
Now you can simply rinse and repeat this procedure for each and every resource and luxury good that you have. Lastly the AI should end up with gpt available but no more cash. What you can do now is buy that gpt with techs:
They give: gpt
We give: Techs
What is important is that everytime you pay in gpt this deal is tied up with a trade good either switching hands from you to the AI or the other way round. And that everytime the AI pays in gpt the deal is plain.
When you now go and cut the trade route all those deals where you pay gpt end, while those deals where the AI pays gpt remain. Of course this will deliver you a severe rep-hit, but as long as no other AI has or ever will have contact with your victim ...
The other type of scam works similar, but that which is going to bring half of the deals to and end is not a broken trade route, but the end of Military Alliances by means of death of the Civ the alliances are against. So what you need to do first is make war against a Civ and when you just are about to destroy them, call up the other Civs and make deals as follows:
They give: MA against Civ A
We give: MA against Civ A + gpt
This again simply assures that the AI has plenty of gpt which you are going to buy back with techs:
They give: gpt
We give: Techs
When your victim bites the dust all that remains of this type of scam are several horrendously high gpt payments from several AIs to you. The more civs you can ally against your victim the better. The more techs you can sell, the better. And all that comes without a rep-hit.
This second type of scam works, I believe, far better in Vanilla or PTW than it does in Conquests. One of the reasons is that you need to sell/give contacts to the civs that you are going to rip-off with the Civ that you are going to kill. In Vanilla you get the ability to trade contacts with Writing, in Conquests only far later with Printing Press (IIRC).
The second reason goes for both types of scam and has to do with the way the Republic works. In Vanilla there is no build-in unit support at all and each unit costs one gold upkeep per turn. In Conquests there is a certain unit support and each unit over this limit will cost two gold upkeep per turn. Now, if a civ runs negative gpt (which the AI is doing after these scams) all those units that cost upkeep will be disbanded by and by. Under Vanilla-Republic those are all units: Workers, Settlers, Garrisons. In short the AI will be gagged down completely and can neither expand nor make contacts (which is handy if you have a reputation to lose).
The real beauty of these scams however will come through if you build up your next scam on the previous. So, for example you start off with a trade route scam which will give a an income of several hundred gpt for twenty turns. With those hundreds of gpt you pull of that "Anotherone Bites the Dust" type of scam which will give you several thousands of gpt. With those several thousands of gpt (and a lot of stowed up cash) you pull another trade route scam which will now give you several tens of thousands of gpt. And another and another etc.
In the end you will end up with so much money that the rest of the game is an utter no-brainer: ICSpam the world and cash rush culture.
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Did any of that make sense so far? If not maybe the write-up of the game (Screenies!) I finished in 150 AD will shed more light.