Thanks for the wonderful ideas quoted below. They all seem to be quite sound. However, I do doubt that you use pure CE through Military Tradition. You may have all cottages worked through this point in time, but I suspect that you have also hired some specialists too, as you will see from my comments below ...
The calculations you are trying to do are very difficult. I don't know what is better, I guess the best strategy is a pure CE till Liber+MilTra.
Yes, the calculations are difficult, but that shouldn't stop us from trying.
However, the pure SE strategy trounces the pure CE strategy in one almost certainly critical area, number of Great Artists born by PA time. If you really aren't hiring Artists and presumably not building many Wonders, where does the pure CE strategy get its Great Artists? Are you really waiting until Military Tradition to generate Great Artists?
Are you hiring two Scientists after building the Library to generate one Great Scientist that will build an Academy? Are you making at least this exception to your pure CE strategy till Liberalism+Military Tradition? If so, technically you are switching to CE/SE earlier.
With both the pure CE and pure SE strategy, early farming/working of a food resource (like corn) is very important for quick early growth. However, cottaging flood plains and grasslands will slow early pure CE growth and reduced Population as compared to early pure SE that immediately farms these tiles.
You are understating the value of a cottage. A riverside cottage in Liz's hands is already 3bpt the turn you build it. With PP it is one more. Then with Bureaucracy a 50% is added, that you will not add to the Pyramids-powered artists. Two cottaged FP are much much much better researchwise than two farms and an artist, no matter how you look at it.
Sorry, I assumed that the cottages were being farmed over far earlier than you say you are doing it. In any case, I did allow for the cottage to grow from a Cottage at 3 Bpt to a Village at 5 Bpt (4 Bpt average, assuming the Financial trait). I assumed that all cottages would be farmed over well before Printing Press had an effect (presumably a short time after Lib/MT). Not accounting for the +50% Commerce effect of Bureaucracy was a critical omission on my part and it does tip research strongly in favor of pure CE (versus farms and early Representation/Artists). In retrospect, it seems that Bureaucracy in OCC is overpowered, because a simple Civic change should not increase both hammers and commerce Civilization wide by 50% each.
Pure CE is better at research than Representation/SE, but we also need Great Artists:
However, pure CE generates no Great Artists, so SE must be utilized sooner or later (preferably sooner). Since the Great Artists can't create a Great Work in a PA partner city, late Great Artists will at most shave one turn off the end date. Thus, only Great Artists born before or shortly after the PA signing date will have a significant effect.
With pure CE and CS slingshot you can get MilTra in 500BC. But then you pollute your artists.
Yes, this is a good use of The Oracle, but I'd prefer not to deal with the extra Great Prophets this may generate. Bulbing such an unwanted Great Prophet for Theology may be a good immediate use for such a GP. Bulbing Philosophy may be another.
My recommendation (I can't demonstrate this is the best way) is pure CE till no more 2-food-cottages available, then work the mines if you are building Library or Oxford, hire artists if nothing special is being built. When MilTra is reached, continue researching towards Radio, but don't try to research it yourself but transform all your cottages into farms and hire as many specialist as you can.
Now, you seem to be saying that you do hire Artists before Military Tradition when not building something important to finish fast. So, you seem to be switching citizens between hammer tiles and Artists before Military Tradition
depending on what is being built. Perhaps, you have a different definition of pure CE than I do?
Don't we want to research Communism (to sign the PA) before Radio (allow The Eiffel Tower)? Having your PA partner build The Eiffel Tower is a good alternative to building it in our only city.
Oh, and save all your GE till the PA is signed. You don't want them to build a WW in a city that won't have the Hermitage in it later on.
Yes, gifting early Great Engineer is a big risk, but you don't build The Pyramids and thus never face this potential problem, right?
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It seems that even for OCC with PA and a Cultural goal, there isn't a simple formula for the earliest win date. Unlike Incan Conquest!
Sun Tzu Wu