The river adds commerce. That's more important for a CE city than for an SE city.
Why?
The CE derives most of its science from commerce, so added commerce has a bigger effect on the CE.
How?
In this case, I'm assuming that the CE has the research bar set significantly higher than the SE does since that is usually going to be the case.
If this is your answer to How, then I would only agree in the case where the SE has the culture slider set above 0%. In such as case, some percentage of commerce is essentially pissed down the drain for a benefit that you get no matter how much commerce is coming in.
For all other SE situations, I disagree. Commerce is changed to research or gold. If the CE has the research bar set higher than the corresponding SE, that is simply because the maintenance cost of the empire represents a higher percentage of the commerce income of the SE than the CE.
If maintenance is a fixed value, X, which it should be, while commerce income Y varies between the two, which it does, then it stands to reason that X is a smaller percentage of Y for the CE than the SE. That does not mean that the value of X is smaller for the CE, which is what you are implying, I think, and which I would disagree with.
One food resource is wonderful for a cottage city. Two food resources are even better for a cottage city (although not twice as good). Three or four food resources are pretty much wasted since you want as many citizens to work cottages as possible and each cottage will produce 1 or 2 food (usually 2).
Only extremely rarely do I find multiple city sites with more than 2 food resources. I'm lucky to get 1 or 2. Often in a game I'll find ONE city site with > 2 food resources, and that usually becomes my GP farm. But to find multiple city sites with > 2 food resources?
In other words, the situation you're describing is not something that I think is typical, and will be encountered only rarely, if at all.
A Cottage city wants to work as many cottaged tiles as possible. A Specialist city wants to work as few tiles as possible while maintining the highest population possible so that it can get lots of specialists.
I disagree.
The goal of a SE city is not to simply generate as much GPP as possible. For one thing, if the SE has a GP Farm, then GPP in other cities is largely wasted. The goal of a SE city thus is slightly different depending on whether the SE is running in "parallel" (no GP Farm) or "series" (GP Farm). In the latter case, where we can largely ignore the benefit of GPP, the benefit is simply a calculation of the hammers, science, and gold generated by the city in total, which is the sum of that provided by the specialists and that provided by worked tiles.
This is the exact same goal of a CE city.
So, can we conclude that the SE city wants to "get lots of specialists"? We can not. In fact, quite often, it would be desirable for the SE city to work high food tiles (to whip), high production tiles (to churn out units and buildings), and commerce tiles (to supplement specialist science and add gold).
Thus, does the SE city want to "work as few tiles as possible while maintaining the highest population possible"?
No, and no.
Obviously, a production city is different from both in that it wants as many hammers as possible and doesn't much care about how it gets them.
A production city, as you have defined it here, often exists in a CE and a SE. It is largely irrelevant to this discussion.
Imagine a city site with 20 corn or wheat. There's not going to be a lot of cottages there.
Not a lot of production, either. What's your point?
How about a city with all riverside grasslands and no resources? It's a great cottage city once it matures, but it will grow so slowly that you'll have already won or lost the game by the time it gets there.
Again, what's your point? The goal is not to have a pretty city with all Towns. This city, whether a SE or CE, will produce quite a bit of benefit to your empire as it grows throughout the game. As the city grows, so will the benefit it provides. At some point, that city reaches its upper limit on the benefit it provides (barring new techs that allow new building multipliers)... you're saying the game is often won before the city gets to this point. So what? Are you saying that the city is not worth it? Obviously not... of course the city is worth it and any player would love to found a city on an all-grassland river site. So, again, what's your point?
For a Cottage city, you want enough food to help you grow, enough production to get whatever few critical buildings are necessary and the rest you want to have grassland so that you can build a cottage without whatever food surplus you have. Balance in all things.
Again, I disagree. A large amount of food is only necessary if you plan to whip. Production could be had in many ways, from tiles to whipping to cash buying. And, many excellent CE city sites are plains with a couple of food resources to allow cottaging.
For a Specialist city, you just want as big a food surplus as humanly possible so that you can whip out whatever buildings you need, regrow and support as many specialists as possible.
Whipping is dependent upon having a food surplus, not whether it's a CE or SE. A CE wants to whip just as much as a SE.
Here's your paragraph with a few words replaced:
For a Cottage city, you just want as big a food surplus as humanly possible so that you can whip out whatever buildings you need, regrow and support as many cottages as possible.
Isn't that true as well?
Balance is irrelevant as long as you have a way to keep the population that you create happy.
Please define "balance" as I don't know what you mean.
That's a +50% commerce bonus PER TILE that is further multiplied by buildings, civics, etc. That's absolutely enormous in the beginnings of the game when you have the greatest need for that commerce. Later, the river does go back to +1 per tile if you want to look at it that way, but that just means the Hamlet gets the bonus instead. Rivers give you your bonus earlier for Financial just like Philosophical gives the Great People earlier to a Specialist city. Even when the difference isn't numerically great, the ability to get those numbers earlier is enormous. Also, rivers give hills the opportunity to get +3 commerce from a Windmill instead of just +1 commerce for a Financial civ eons earlier than a Financial Leader's city without a river.
I agree with all this. But, your response has little to do with what I was saying.
Wodan