Doc Tsiolkovski said:
Aeson, I don't understand how the 'Milking Curve' exactly works, but from what I can tell, a delayed expansion (solely required for 20k, Space or UN are not affected) will hurt a lot - is that correct?
It depends on when you finish and how long the delay is.
There are different and rougly equal (from a base score viewpoint) approaches to getting to the Domination limit.
One is to always be fighting somewhere. Use Swords/Horses, then when available Knights, then when available Cavalry. Territory expansion is constant, somewhat slow, and more resources are used in claiming territory. Focus is on military for almost all of the time, so happiness and population growth suffers. Slow and steady.
Another is to build up a strong core, beelining for Knights or Cavalry (to use Knights or Cavalry is interesting itself). A massive upgrade and rush finishes things off quickly. Territory expansion is pretty much limited to what you can grab peacefully early on, then a quick jump out to the Domination limit when the Knights/Cavalry are available. Focus is on tech rate, getting enough cash for upgrades (Leo's), happiness suffers, but population growth should be high.
Moonsinger even did well with Infantry/Artillery in some games. The wait for expansion is longer, but the efficiency of the units is almost 100%. So more resources can be devoted to making what you have happy and productive instead of building military. This is more for higher difficulties and larger maps where Knights/Cavalry won't be enough to finish things off.
Then there is everything inbetween. Just about any approach, played right, can get to about the same point by 1400AD.
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20k mostly cuts out the opportunity for the first option.
If the first 40 turns of the game are spent simply building up the 20k city at the expense of all else, the Sword/Horse rush will be 40 turns behind. So basically it's out of play. (Leader farming isn't though... opening up the military small wonders and rush them still helps, as does having empty armies to put Knights/Cavalry in.)
Knights will come before the military gap can be completely made up too probably. Starting here can still be a good idea.
Cavalry give enough time to get the necessary forces together in most cases though. You only need so many Cavalry, and usually the limiting factor on how fast Cavalry can get to the Domination limit is not how many Horses+Gold which can be put together, but when Military Tradition rolls around. Very shortly thereafter the Domination limit should be reached, whether there are 100 Cavalry (adjust for mapsize and difficulty) or 6000.
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Also the map plays a big part. If all players have to wait until Navigation/Magnetism to claim a good portion of the Domination limit, 20k games may not lag behind at all. By then you can have built up the 20k city, moved on, and claimed/built up the entire starting continent either way. In that case the only tradeoff would be a small amount of early score (compared to conquering the continent right off) or a bit of tech rate (compared to pushing the tech rate as much as possible).
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The other main factor will be how the predicted scoring curve matches up to the actual possible one. Different approaches will maximize the difference between their curve and the predicted one at different times. Different map situations will change things too.
Using Swords/Horses, that point may come rather early (I don't think it's going to be before 1000AD very often), while waiting till Cavalry will have that point much later in the game. Some maps, where initial terrain is very bad (low food and/or little of it), and the good terrain (high food and/or lots of it) is only reachable later in the game, 2050AD will be that point.
Generally you can beat the predicted curve most after having fully maxed out population and happiness and played a number of turns at that level. 20-40 probably. The later in the game Domination is reach the higher the number will be.
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So the answer is, it varies by map and the approach to it. 20k Ottomans on a small initial landmass and no crossings till Navigation should be able reach Domination the same time as anyone else. 20k with a good Ancient UU civ on a high difficulty smaller map pangaea might be giving up a whole lot.