Dimorier Maximus,
Great work with the 4 city spaceship!
I agree with Fergus Horkan's assessment of areas in which you can improve and his overall comment - no delays.
At some point you will need phalanxes to defend your cities but time and settling new cities is so important in the early game that I generally start off with warriors.
It's good to see that you're building settlers to found new cities in the early game. Civ2 rewards large civs.
2 or 3 defenders plus a counter-attacker in every city is way too much (IMHO) unless you're in the mid to late game and your city borders an AI who attacks often. You can get away with just one defender in interior cities. Pre-republic you may need some warriors for martial law. There are other things (settlers for more cities sooner, explorers to get huts and to inhibit the AI from expanding, caravans for wonders or trade, ...) that are more worth your time and shields, especially in the early game.
Overlap seems to be a personal preference. ICSers intentionally overlap. Some people overlap special resources to share them between cities. You're in very good company if you find overlapping to be an anathema on purely aesthetic grounds or due to perfectionism or a compulsion to avoid "waste".
The Great Library used to be my favorite wonder. However, as Fergus Horkan points out, any tech you get via the Great Library that's not on your current research path is slowing down your research. (The cost to research your next tech depends on how many techs you already have - including "free" techs from the Great Library.) Not only do you not need all the techs, but WHEN you get your techs is very important. The Great Library takes away your control of your research.
I, too, think you're researching monarchy too late. It looks like your research path is:
1. bronze working for phalanxes (and Colossus?)
2. literacy for the Great Library
3. mysticism (why? improved temples? Oracle?)
4. monarchy
I usually go for:
1. monarchy
2. trade (for caravans for wonders)
3. techs for early wonders.
I think you should try to make monarchy your top goal and research early wonder techs only when you can't research something towards monarchy. While you may feel you're going for monarchy early, you can go for it even earlier. Monarchy
1. reduces your corruption and waste
2. increases your production from special squares and from improved terrain
3. lets you crank up your science (or taxes) to 70%
The earlier you get it, the longer these advantages are working for you.
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What are the most vital things to making the Republic -> Democracy Space Race thing work in y'alls opinion?
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1. Preparation. Before going republic, you need to have only one military unit per city in the field (unless they're supported by Shakespeare's Theater or in a fortress near a city). You should have a temple in every city. Also, I often switch just after getting a happiness wonder since the switch really hits hard in the happiness department.
2. Don't make the switch too late. Switch as soon as you've founded all your cities. (Switching before then really cramps expansion since settlers start eating two foods each.)
3. Take advantage of "We Love"-ing up your population. Under a republic/democracy you can temporarily crank up your luxury rate, celebrate in every city, and grow every one to size 8 (the limit without aqueducts). Fiddling with your luxury rate and looking at hour attitude advisor will tell you the minimum luxuries you need. This does take preparation since your quickly expanding cities prematurely run into happiness (courthouses are a cheap "happiness" improvement if your a democracy) and food (coastal cities can use a harbor and thereby avoid having to waste time irrigating) problems. However it's effects are incredible.
4. Deliver a lot of caravans to make trade routes while a republic/democracy. I can't overstate this. Until you have 3 trade routes for a given city, a caravan from that city is generally better than anything else you can build. Even after that, a constant stream of caravans makes your research rate skyrocket. (When you get your delivery bonus in gold coins, you get an equivalent number of research beakers.)
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What are the most important things to making Monarchy -> Communism -> Fundamentalism World Conquest thing work?
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For world conquest (as you already know) the sooner you start the better. You can get a good early army via aggressive hut hunting. I generally go for
1. monarchy
2. trade (for wonder-building caravans)
3. Hanging Gardens
4. Sun Tzu's War Academy
5. Michaelangelo's Chapel & crusaders
If you've founded a lot of cities on your way to Mike's, you should be able to make a lot of crusaders, even if you haven't developed your land or cities. You can achieve victory by superior numbers. Crusaders can move two square, usually eliminating the need for sieges (tedious one-move phalanxes, catapults, and fortress building) and generally speeding your conquest. Make sure you have a decent attacking force (8 or so attackers if you wait for crusaders) before you begin your assault. Don't be afraid of heavy losses.
While conquering I'll slowly get the techs for the Statue of Libery (communism/fundamentalism) and Leonardo's Workshop (eventually upgrade to dragoons).
The Statue of Liberty is the key to getting communism/fundamentalism early. Once you have the Statue, your happiness problems are over (no more riot factor under these advanced governments). Use fundamentalism and maxed taxes for conquering. You can temporarily switch to communism if you need a tech (say leadership or railroad).
Unlike with AC, research is not an overriding goal. You don't need a SSC and all it's trade/research wonders. You won't need the Great Wall since you'll always be on the offensive. You don't need graneries or any city improvements (except maybe a temple). These'll all just delay your start. If you start early, you'll be surprised how little resistance you get once you've toppled your first few cities. It's much more effective to attack sooner rather than wait and research better units or build up your cities.
While some players conquer the world with hut units, I find that I'd rather have a number of (admittedly small and crummy) cities to constantly churn out units. But with a number of cities (plus all the ones you capture) you either need communism/fundamentalism (which don't come until democracy's Statue) or a couple happiness wonders. Sun Tzu eliminates the need to build barracks in all your cities (a drain on coins that could be spent on crusaders, but more importantly a delay before conquering).