Optimal city distance

Screw the math! We don't know how long it'll take to reach the 37 tiles and the population to work them. Here's a thought that considers only what we know of the game so far and no creepy speculating math: I'd only leave the full 3 tiles Big Fat Hexagon for my first city (maybe second and third too), and go 2 hexes with overlapping for the rest.
 
I'm not saying the geometric order is going to be desirable but it is cooler with hexes than with squares. But yeah, if you can only work aound half of the tiles anyway then even placing two cities next to each other means they can with the half facing away from their neighbor without loosing much.
 
Screw the math! We don't know how long it'll take to reach the 37 tiles and the population to work them. Here's a thought that considers only what we know of the game so far and no creepy speculating math: I'd only leave the full 3 tiles Big Fat Hexagon for my first city (maybe second and third too), and go 2 hexes with overlapping for the rest.

Ideally if you have decent food resources and water in your capital you'd want to overlap some cities to either share that food or to more quickly get the other tiles under control so the capital can work them as the population explodes. Later on those cities would still be able to work the tiles away from the capital and get to moderate size.

And this is not factoring in specialists.
 
I hope that I will be able to look at the map, see the ressources, rivers, coasts and other terrains, and then freely group adjacent tiles into "provinces", not caring about the theoretical max. size, but more about creating specialized, diverse cities.

"Oh, there's a river leading into the sea, the river valley is fertile, there's corn and pigs, and fish near the river delta, I'll place a city with a university there and make it a huge science center."

"hmm, there's a few forest tiles and 2 crab ressources at the coast. The crabs can feed enough lumbermills to make this my shipbuilding center. Needn't have more than 15 population anyway, I'll better make my science center bigger."

I really hope city placement is more about strategy and personal "style" (few big, many small or mixed size cities) than maths and geometry.
 
All the evidence (from reviews) suggests that population simply doesn't "explode" anymore, regardless of terrain. In the endgame, cities above 20 population seem rare - and that's before non-hex-working specialists.

Happiness adds a lot of strategy. The aim is effectively to distribute your empire's population between your cities, to get the best out of each city. Not just trying to get every city as large as possible. The wildcard is that happiness also favours several large cities, rather than many small cities, because each additional city costs happiness. And building maintenance also favours many large cities (especially focused cities).

An optimized settlement strategy is probably far less dependent on fixed distances between cities than it first seems. People are at a premium, not land.
 
I did some quick calculations to try to figure out the optimal city distance, with the aid of some hex paper. I'm assuming a regular arrangement of cities; in reality this would have to be adjusted for coastlines and other terrain.

Let D = distance between cities. Let S(D,N) = number of tiles shared between N cities for distance D. Define TPC(D) to be the number of tiles per city for distance D, assuming all terrain is claimed and the tiles are distributed evenly among the cities. Clearly TPC(D) = S(D,1) + S(D,2)/2 + S(D,3)/3 + D(D,4)/4.

For example, if D = 4 then for each city there is 1 tile (the city itself) that is not shared. So S(4,1) = 1. There are 18 tiles shared by each city and one of its neighbors, S(4,2) = 18, and 18 shared by each city and two of its neighbors, S(4,3) = 18. There are no tiles shared by 4 cities. So TPC(4)=1+18/2+18/3=16. Similar calculations can be done for other values of D.

In summary:
TPC(3) = 9
TPC(4) = 12 *
TPC(4) = 16
TPC(5) = 25
TPC(6) = 27 *
TPC(6) = 34
TPC(7) = 37

Also for D >= 6 there are gaps between the cities.

So what's the best distance? I'd guess gaps are bad and between 16-25 tiles per city is reasonable, so a city distance of 4-5 is probably best.

Any thoughts?


* There are alternate regular configurations for the even distances. The more compact configurations are generated by "zig-zagging" hexes to travel between cities, the less compact by going straight. There are no gaps in the D=6 compact configuration.

Well, despite all of the dizzying math, I suppose that 4-5 is, perhaps, the optimal distance. But will you need to have all tiles worked by every city? A distance of 3 will probably be good enough. Check my attachment for an idea of hex distances. I posted it on another thread, but I think that it is relevant here.

Screw the math! We don't know how long it'll take to reach the 37 tiles and the population to work them. Here's a thought that considers only what we know of the game so far and no creepy speculating math: I'd only leave the full 3 tiles Big Fat Hexagon for my first city (maybe second and third too), and go 2 hexes with overlapping for the rest.

Well, I kind of agree... but I would reverse that. For your earlier cities, it would probably take a while for them to reach a level where all of the hexes could be worked. I would say that the priority at the begining would be expanding, but you would probably not want to space your citied too far apart (remember, maintenance on roads and such). I think that the cities that would best utilize enough room for all hexes would be cities placed later. Growth should be much faster by then, and maintenace shouldn't be as much of a factor. Just my thoughts!
 

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I think it depends on empire shape of course. I think I may go for 5 tiles between each city for the most part (assuming I want a geometric spread), making it so each gets 2 tiles in each direction for only itself, and then the third is shared...
But since each city is able to use 3 in each direction, you can have the cities on the edges or corners of your empire that are closer to one another and have more empty space towards the outside of your boundaries and your enemies. Ugh I wish I had a diagram...

I think having the extra space around the outside of your empire would be useful in a few ways.
1. It would allow for more space for combat tactics and defensive structures to fit.
2. It would allow for a culture buffer that has more terrain between you and your enemy. More terrain that can be used defensively and more terrain for ZoC and time before they advance to a city.

I am a builder personally, and while a little war is always a good thing, I prefer fewer large cities over many small cities. Maximizing my Terrain is hugely important.

EDIT: and ah as I say this, someone provides a way to make a diagram. editing now
 
Don't you think the number of cities would be the limiting factor?
In Civ 4 maintenance depended on number of cities so that was the first Civ in which you no longer needed to build as many cities as possible so the distance between cities grew.
Here, happiness is spread over cities. So if you build cities close then you won't cover a large area, and probably won't have a lot of different resources. If you build them further apart...well, you get the idea.
 
You guys forgot about roads. If I place a city in the most optimal spacing possible with little overlap. It would mean I would have a longer road to build and trade road to maintain, no?
 
You guys forgot about roads. If I place a city in the most optimal spacing possible with little overlap. It would mean I would have a longer road to build and trade road to maintain, no?

I guess that's secondary, the most important factor would be the waste of precious space. If you align your cities without any overlap (which is possible!) you'll probably not work most of the tiles until lategame. Is suppose another player accepting overlaps would have an advantage by using these tiles inbetween earlier.

Hopefully, it's a tactically challenging balance between early game advantages (easier defending, cheaper roads,...) and lategame optimization. With many variations being viable (especially mixed city sizes).
 
If all you're looking for is a good filling factor without overlap, this is it:

optimalfilling.jpg


It has a threefold rotational symmetry (which is pretty obvious for regular hexagonal patterns). The translation vector from one city to the next is 7 right, one down. (Or, if you use a skewed coordinate system, 4 right, 3 up).

In the game, I'd rather go for resources. Regular city placement isn't so important in my opinion because it's unlikely you want to grow every city to max size, except maybe for India. In Civ4 the limiting factor for me was practically always food supply and time. I usually didn't even get into the full-grown city case because the game was ended by the time technology allowed me to do so.

Edit: I just realized I inadvertently drew up a hexagonal RGB monitor sub-pixel pattern, lol
 
Nice, how did you create this?

I hope the ciy outskirts will look more like actual, natural provinces, like here on this island (not my work):

civV.png


I'd love to see players picking the tiles they find useful for a certain type of specialized city and form their inland borders accordingly.
 
I forgot where I saw it but I am pretty sure the axis direction for the grid is East-West and not North-South. Thus, those grids should all be turned 90 degrees.
 
OoOoOoh! So many colors! :crazyeye: Looks like overlapping will live on.
 
Nice, how did you create this?

Made it myself in Photoshop. Here are some other possible placements to consider. The first is one where the third ring is shared between cities, the others are a little less dense. With hexagonal tiles it's actually much easier to not waste space without a lot of overlap.

If you want to do some stuff yourself, here's an empty canvas (careful, large, and it's a few pixels off). The easiest way to go about things is to start with cities close together, then move a city one tile out, and so forth.

By the way: Of course, in the game the cities aren't going to be placed so regularly, but studying these "perfect" patterns will still help you get a feeling for where to best place cities for good coverage.
 

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