Abraxis
☮
Spoiler :
Here is a photo of the growth bonus afforded by excess Amenity, I assume there are greater yields at incremental stages beyond happy, at least one.
Based on this growth bonus here, and the way they were speaking on the amenities distribution,
I think the amenity formula could be the most central mechanic by which population growth, city expansion, building value, district timing and choice... game pacing in general, pretty much everything is controlled and balanced by. Pretty much all other things are likely designed out from this concept, or formula, like a spine.
In Civ 5 there was just happiness. Quantity was all that mattered and this was their standard for pacing civ growth. They are very hesitant to say amenity is just the new global happiness, I think because it is significantly more complicated and has a new dimension they couldn't even begin to scratch the surface of in their demonstration. Civ 6 adds of course adds a new dimension, distribution which you can only manipulate indirectly. (yes civ 4 had it, but very simplified)
I think the growing game will be a careful balancing act you must maintain indirectly. On one hand you have the obvious quantity approach, grabbing up more luxuries, but on the other you have the use of entertainment districts -their use its own branch of cascading complexity. Pop them down too early and you're not getting actual yields from your population -but you are going to get a priority on the City for amenity, which means artificial growth bonus. Build another district instead and it's more like cashing in on your population immediately, lowering amenity priority but gaining raw yields now from your effective pop. (Over time this will balance out more as the percentage to yield catches up with raw yields, but I am mainly concerned with early game here).
For just getting more amenity there are luxury resources. But just focusing on quantity won't be enough to keep you competitive in higher levels, you need to keep control of distribution in order to manage your growth bonuses.
I was reviewing the Civs too as I think this is the first thing I'll be exploring now once I get my hands on the game. So as a more practical implementation of my thoughts, let's take Egypt. I suspect she may be in the best position to achieve highly controlled amenities within her cities (probably Brazil too but I havn't given them much thought).
She's in the best position to rush the collosium, as she will probably have quick early growth from flood plains to qualify for quick early districts, can build her entertainment districts (requirement to collosium) doublespeed, will certainly have flatland (again, requirement to collosium), and then can build collosium double speed. This will give her core a permanent weight to amenity distribution and help hold growth bonuses on her central cities.
Other civs particularly Rome for example seem like they can grow fast... and they can, but in a different way. I think they will struggle greatly by necessary and very intentional design, against lack of amenity control. They will certainly have availability of amenity -quantity, because more cities means more resources (also baths help a bit) but these will be spread out over their cities much more evenly, which means they need significantly more quantity to ever achieve artificial growth bonuses, even then with less control of where and weight.
I think that is a very important central idea to the game there, it will form the method and style by which you grow your empires. Open and disorderly growth -less control over your city growth bonuses. If you instead choose to prioritize control of amenities, focusing on entertainment districts, wonders, National parks, and whatever else they've given us to manage it, you will be more efficient and deliberate in your distribution of growth bonuses. which will give your more success specializing your cities and prioritizing development gambits based around that.
Anyways, I think the automation of amenity and the "department of luxury resources" is probably the heart of most of the peaceful strategic planning in the game, the careful indirect manipulation of which will be our measure of success. The direct manipulation of the formula, likely their direct method to balance an control most of the game's pacing.
Anyways, these were just my thoughts some expressed interested in and I thought were too off topic anywhere else. I tried to be concise but doctors keep poking me with drugs at the moment, so I apologize if it's entirely senseless and illegible, I'll have to review and edit later maybe.