Ok, here's my starting response. I'll probably want to tinker with it, and there's a section that I already plan to add to it, but it's already pretty long, so let me get this part of it out there. I put some stuff in inline spoilers to try to make it a little bit less tl;dr.
One preliminary terminological note: Starting with point (11), I reference strands within the game that the player manages and tries to increase (gold, production, culture, happiness). The best word for these would be “resources,” but that already has so fixed a meaning within Civ games (strats and luxes), that I needed some other term, and I couldn’t find a better one than “assets.” Please do note the special meaning that I assign to that term because a lot of what I say concerns itself with that.
1) Turn-based
2) Historically themed
3) Covering the whole of human history from the founding of the first cities to the present or near future.
4) Playing out over hundreds of turns
5) Taking place on an alternative Earth that might have very different geographical features than this-Earth, but which is defined primarily in terms of a limited but rich set of terrain types
6) The player only knowing about a small portion of the map initially and needing to explore in order to determine the location of good terrain for settling, resources and other civilizations.
7) Using as its competing entities civilizations that attained some level of prominence in this-Earth—at least their names and ideally some game representation of characteristics traditionally associated with their this-Earth flourishing (In keeping with (5), though, these civilizations might appear in the game amid very different terrain than was characteristic for that civilization in this-world).
8) with a particular famous figure from that civilization serving as the in-game “face” of that civ, to humanize the player’s various forms of interaction with the civilization.
9) Victory conditions (i.e. it at least can be played as a competitive game, with one civ emerging as the winner, and not a mere sandbox—though it should ideally allow for sandbox play).
10) And multiple possible victory conditions, at that; four or five of them (not just, e.g. military conquest of whole world)
((1), (9) and (10) together mean that the game is fundamentally a race to beat every other civ to one or another of the victory conditions. The primary pleasant-tension that the game arouses is “will I be first?” But (9) and (10) combine with (4) to mean that the kind of race that a Civ game represents is a marathon. Good long-term planning will mean that one civ—and most especially the player—can eventually catch up and surpass another civ that got an early edge.)
11) Most elements making up the game are (what I will call) “assets” that can, ultimately, be leveraged toward helping to reach one of the victory conditions
12) There are multiple “strands” of such assets—money, productivity, culture, science, happiness, military units—but a comprehensible, manageable number of such strands. Basically the things that appear, color-coded, along the top bar of Civ 5.
13) The strands are partly fungible.
(I.e. you can build a building or buy it, so you can reach the same end if you happen to be strong in production or in money. Hammers or the Holy Warriors belief can supply you with troops. (in Civ 5, which is always my own reference point))
14) But the strands are not entirely fungible (e.g. the limit that wonders must be built not bought adds challenge). For some things you just need e.g. culture and nothing but culture can get you that thing, and you can’t hurry it up by using any other asset.
15) The primary building-block of the game is a city; its borders cover and control a certain portion of the map and certain resources that are located within that territory. A major activity of the game is founding cities in order to expand the overall territory controlled by one’s civilization.
16) The overall strength of cities is tied in large measure to their population, so a major goal beyond founding cities is to grow them. Many of the assets in the game derive fundamentally from the population of cities.
17) The primary pacing for the game is set by a tech tree that mirrors the developing technological sophistication of this-Earth through a set of technologies you can discover/develop
18) Once that primary pacing is in place, there is also built into the game a standard pacing for all other resources: a pace at which population tends to grow, a normal amount of money per turn, culture per turn, etc.
19) This “standard pacing” for growth of any asset—population, gold, production, culture—can be exceeded, in a particular game, based on various factors that might be present in a particular situation--terrain, natural wonders—or chosen by the player: cultural policies, religious pantheons. Against the standard pace, the player can feel that, in a particular game, he or she is moving faster than is usually the case with respect to one of the strands of assets. Anything in the game that significantly increases the player’s acquisition of any asset, I will call an accelerant. Goodie huts are an accelerant; your civ progresses way more quickly, in one of the strands of assets, than it would through its normal operations. Since the game is fundamentally a race, anything that makes you feel you are moving faster makes you feel good.
20) The player’s own building choices can improve the pace of one of the strands of assets, and most particularly Wonders speed the pace of acquiring one of the game’s assets significantly; i.e. there is a big payoff, in one dimension of the game at least, for building a Wonder.
21) Most player actions center on developing one or another of the game’s assets.
22) There are hard choices to be made in deciding which asset to further develop, trade-offs; to develop one means that you miss or delay the possibility to develop another. You can prioritize a building that increases your civilization’s money, but through the set of turns you are building it, you will not be progressing on a building that could increase its culture, or happiness, or faith, etc., each of which is valuable in its own right (and those values are balanced to keep those hard choices hard).
23) Success in the game is primarily a function of maximally leveraging the advantages that you get in terms of terrain, your civ’s special abilities, etc. to pull ahead of the other competing civilizations. There are good overall strategies; there are good ways of exploiting your civ’s built in advantages; but ultimate success also involves some per-game improvisation based on the particular site in which one’s civ happens to start (terrain and neighboring civs particularly).
For me, (19) is the most crucial element: feeling one is racing forward, relative to a normal pace for asset X. Oh, and (22), the "hard choices from among competing priorities"
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There are two things that I think are crucial to the Civ formula that I wanted to treat at greater length.
First, (24) players should be able to play in sandbox mode.
I have said in (9) that Civ should have victory conditions. One should be able to win. Civ shouldn’t be fundamentally a sandbox game. But a lot of people like to play in more of a sandbox mode. One key element of this, in my view, is there be the various strands of assets (gold, production, culture, faith, etc.), that there be no clear best one among them (if they have been well balanced), that they are partly fungible, and they are fun to go after in their own right. Then, going into a particular game, or after seeing the initial roll, a person can say, “Let’s see how wealthy a nation I can build; let’s center everything around money." Or, let’s see how much culture I can generate. Or let me see how far I can spread my faith. The systems are complex enough and interlocking enough that a player can just invent his or her own goals for a particular game.
I don’t terribly like jungle starts in Civ 5 because they tend to be low in production, and for me production is king. But if I roll Brazil in a big jungle, I sometimes say “ok, let me see if I can build a jungle empire.” I try to get the Sacred Path pantheon, so I’m getting culture out of tiles I’ll be working anyway. I know that once I get my universities built, all those jungle tiles will really bump my science. Is there some other way I can make up for the lack of production? You just start interacting with the terrain, with the various game systems in mind, and see what happens.
Second, (25) the other kind of player that you should try to cater to (and this is not altogether distinct from the sandbox player, or the victory-condition player, for that matter) is people who like the narrative that emerges as their civilization grows. Here I think the key is just to have lots of historical flavoring to the different assets, so that there are details around which to build that narrative. In the Civ 5 social policy trees are policies that are essentially a package of game-advantages. But the designers haven’t left it at that, but have given the policies a name, so when I get “Warrior Code,” I imagine my society developing a warrior code (and I often name it after the great general who is generated as a result of getting that policy). The great works in Civ 5 and 6 are actual great works that were produced in our world, so when expend a great writer to get one of those, as one poster here said, you feel like it was your civilization that produced Romeo and Juliet. (The codices in Civ 7 don’t give that feeling because they are generic, don’t have historical flavoring).
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More thoughts:
26) It should be possible to play peacefully, but difficult. Even if you don't want to wage war yourself, you should be at some risk of being attacked, so you should feel pressure to build at least a defensive force.
27) There should be mechanisms (happiness, corruption) to keep success from being simply a matter of empire size. A larger empire should on the whole be better (more room for resources to appear within your territory, e.g.) But it shouldn't be the case that the first civ to have military success just steamrolls from that point on. I actually like what they tried to do in Civ 5, where tall empires could be equally viable with wide ones.