Having recently completed a domination win with Napoleon I noted that the starting position was ideal to test the merits of rushing to National College (NC) first or after about 3 more cities were built.
I made two scenarios - first with an NC first strategy, second building 3 additional cities and then NC.
My conclusion is that on almost all measures it is better to build at least 3 additional cities before NC.
Game Setup: Napoleon, King, Continents, Large, Marathon
Starting Position
Spoiler :
On a standard sized continent. The only other Civ on the island is Alexander, and he is on the opposite side of Singapore which blocks the route between our parts of the island. To the south is Bucharest, which nearly blocks the passage to a third, uninhabited part of the island. There are good coastal/riverside positions for a number of cities not too far away from the capital. The capital has 1 marble and 2 golds in the next expansion ring.
Initial moves - and moves common to both strategies
Spoiler :
Build second warrior - use the two warriors to suppress all barbarian activities, then build a worker
Research (throughout the game - both strategies): Mining/Masonry (to exploit the gold and marble) Pottery/Calendar to exploit silk to the south, then Writing, then Animal Husbandry/Trapping - then beeline Navigation. (Interestingly although I did the same sequence in both scenarios the automated beeline to Navigation took different paths through the techs - in the NC first scenario it went Philosophy/Theology in the NC second scenario it went Sailing/Optics/Compass)
Policies (throughout the game - both strategies):
Tradition/Liberty/Aristocracy/Legalism
Improvements (throughout the game - both strategies):
Marble, 2 Gold mines, farms near capital, Silk to the south
(in the NC first case I built one farm near the capital before the gold mines - this may have been a mistake as gold was always a bit of a problem with this scenario)
In both scenarios the Capital built Stonehenge when there was nothing else to build.
NC Second scenario
Spoiler :
Build 3 settlers and found cities immediately - start building workers in newly founded cities (but none of the workers had completed before NC was built)
As soon as Writing was completed (which happened after the 3 cities were settled) change production in all cities to Library. (No rush buy as there wasn't enough money)
There was a food shortage in the capital - which was fixed by allying with Singapore (one of the bordering City States).
Once all libraries were built, switch the capital to National College.
The National College was built on turn 242 (1080BC)
NC First strategy
Spoiler :
Prebuild about 1.3 settlers while waiting for Writing and also while waiting for money to rush buy the Library!
Rush buy Library once enough money was available (Turn 117)
Couldnt' afford to ally with Singapore - but bought Friendship with them on turn 185 - but I couldn't afford to renew the friendship when it expired.
Continued to build settlers and found cities as quickly as possible.
The third city was founded on turn 196 (1540BC)
For comparison purposes this scenario was continued until turn 242 (1080BC) the same date as the NC second strategy completed.
Results:
Spoiler :
NC Second strategy completed on turn 242 with
Beakers per turn 39, Gold per turn 12, Happy 2, GA 1002/1540, Culture 250/1405 +18
Totals for all cities: Citizens 16, Food 13.5, Production 23
(note there was an alliance with Maritime Singapore)
NC First strategy Turn 242
Beakers per turn 31, Gold per turn 10, Happy 3, GA 1445/1540, Culture 900/915 +18
Totals for all cities: Citizens 13, Food 11, Production 20
(note in this case there were no alliances or friendships - couldn't afford them at this point).
Analysis:
On every measure the NC second strategy gives a better position at turn 242 (which is when the NC is complete in both scenarios and the three additional cities are built.) Perhaps if I had improved the gold mines sooner it would have been possible to maintain the friendship with Singapore - in which case the position might have been a bit better for the NC first scenario!
Also further testing could be done to test for the 2 additional cities or 4 additional cities scenarios - but I'll leave that to someone else.
btw: I've been playing Civ V for about 6 weeks - and have been a close follower of this forum. This is my first post - so please forgive me for any errors!
Hammers are king, and beakers queen. You are correct, 4city NC works very well. Its best done via settling on 2 luxuries, and having at least 4 luxuries total in your empire. Otherwise, I recommend 3city NC or 2city NC.
1city NC is crappy without a WONDERFUL start, in which case it may be slightly better than alternatives.