Optimal city placement to maximize territory. (For quick Dominations)

[LulThyme]

In Misfit's Quick Domination Thread
http://forums.civfanatics.com/showthread.php?t=112335
some ppl were discussing how to predict border expansion and how to use it to maximise territory...
Here is a thread with explains the rules for border dynamics, and as far as I know, they are correct (though maybe hard to completly grasp at first) :
http://forums.civfanatics.com/showthread.php?t=106882

Now I had give some bad advice in Misfit's thread, so I decided to correct that by being useful and studying optimal city placement to maximise territory.

For sake of simplicity, I will assume all cities are the same rank (meaning they all have 9 tiles, or all 21 etc..)
although this is usually not the case, for example capital usually has bigger rank, in quick dominations this is usually the only exception, especially if you use ToA, so the difference is negligible, especially since at the start you want to maximise growth, not territory right away...

If all cities are rank 1, then the optimal city placement is to put them in a square lattice,
x000x
00000
00000
00000
x000x
as many ppl probably figured out.
In this configuration, there will be no cultural holes, and you need one city per 4x4 square in the long run, so each city controls 16 squares. (except the edge one, but they are negligible if the lattice is big enough)

Now if the cities are rank 2, then it is not so obvious...
After understanding the culture expansion rules, I tested all lattices configuration (by lattice I mean regular in the sense that the cities are on parallel lines, but not necessarly orthogonal, so 4 close cities form a parallelogram)...

CONCLUSION :
There are 2 optimal lattices for rank 2 cities, and you can combine them.
This is how you do it:
1. Choose the orientation for you axis, either NW-SE or NE-SW
2. Cities are placed on lines parallel to the axis chosen, with exactly 5 spaces between each.
3. Between each axis there is exactly 4 spaces.
4.THIS IS IMPORTANT : you must start off cities on adjacent lines either 2 or 3 (this is why i said there are 2 optimal lattices) squares off...

I will give an example after but let me point out that this configuration leaves no holes for rank 2 cities, and each city control 30 squares, so 9 (30-21) of them are eextra, given by the exception to the normal cultural expansion rule. This means that about 30% of your tiles will not be in usable radius of any city!! (this is the maximum for a lattice, I checked...)

x0000000000
0000000000x
00000000000
00000x00000
00000000000
00000000000
x0000000000
0000000000x
00000000000
00000x00000

Here is an example, mixing both type of lattices.
Columns containing x's have 4 spaces between them.
x's on a column have 5 spaces between them.
On adjacent columns, the x's are off by either 3 (see middle and left column) or 2 (see middle and right column)

 

[LulThyme]

If you look at the image above, this is an example.
Consider the line Lugdunum Camuldunum Richborough. (LCR)
This is one of my axis.
all axis are running NW-SE
The entremont-alesia augustodurum axis is 2 off from the LCR one, while the Gergovia, Verulanium , worker, Eboracum is 3 off.
You can mix 2 off and 3 off as you wish.
Intuitively, it looks like there will be holes at rank 2 because the city are too far apart.
there are MANY squares which are not in any citie's rank 2 border.
But amazingly :
TOA was finished a few turns ago, and look what happens when the culture reaches 10 in all cities :

 

[LulThyme]

A few things : the bigger the map, the more useful this configuration is as the edge effects become negligible.
Of course Im not saying all your cities should be on a lattice like this, specially at the start, but once you are just filling space, this is the optimal configuration.
Now on bigger maps by building ToA early enough I guess rank 3 could be reached for all or a lot of the cities, so if somebody is interested, I could figure out the optimal rank 3 configuration...

 

[xeroyne]

Configuring for rank 3 cities would be a challenge in both logistics and in dealing with corruption. I did it once with Babylon on a huge map, but waiting 150+ turns (depending on when you complete ToA) to fill in those gaps is dangerous. Likely some other civ is going to do it for you.

 

[Gyathaar]

Actually, before i started playing my huge domination game a couple weeks ago, I did some work on paper for this.. the most wide city placement I could find is this:

[FONT=Fixedsys]xxxxxxxxxxxxxxxxxxx
xx...xxx...xxx...xx
x.....o.....o.....x
x..C..o..C..o..C..x
x.....o.....o.....x
xx...ooo...ooo...xx
xxxxo   ooo   oxxxx
xxxx     o     xxxx
xxxx  C  o  C  xxxx
xxxx     o     xxxx
xxxxx   xxx   xxxxx
xxxxxxxxxxxxxxxxxxx[/FONT]

With this shewed 6x5 placement, each city will grab 30 tiles after a single border expansion.

 

[LulThyme]

Yes Gyathaar, thats basically one of my 2 lattices...
I add some flexibility, as you can mix mine, so if there are mountains or lakes or whatever messing it up, it is possible him to correct it and still make it work.
In your examples, if you move the two bottom cities one square left or right, it still works.

 

[LulThyme]

Configuring for rank 3 cities would be a challenge in both logistics and in dealing with corruption. I did it once with Babylon on a huge map, but waiting 150+ turns (depending on when you complete ToA) to fill in those gaps is dangerous. Likely some other civ is going to do it for you.

Assuming ToA is built early with a SGL, we might me talking more like 70-100 turns.
Corruption is usually not an issue in fast Dominations, and if the diff is low enough, the other civs arnt a problem.
This mostly a low diff thing, since at high diff, it is usually more efficient to just take cities...

 

[Mistfit]

The one thing that I've been taking into account recently is the fact that the Palace will have 2 expansions before the game is over. So in you example above I would have started with Alesia -> 1 tile N. Lugdunum -> 2 tiles E. Camulodunum -> 1 Tile E. For me it is a little less formulaic and a bit more guess work. Don't feel bad about giving me bad info because I prolly wouldn't have been able to follow all of your X's and O's. You see I'm not that bright To me Gythars pic makes absolutely sense to me. It looks like a strange picture of Mickey Mouse. I appreciate all of your work on this and if I have time I will sit down and really think on what you are trying to tell me. It would be nice to be able to get 30 tiles per city but I've not seen it work yet in one of my games.

 

[BlackBetsy]

Lulthyme,

This is important work in the field of Domination Theory, for which I (unilaterally) award you the March 2005 prize for outstanding achievement in the field of cultural expansion.

I would only add that you can probably adjust for the Rank 3 capital expansion pretty easily - it's going to happen in most games.

Using Lulthyme's grid, it is possible, with the right map, to achieve a victory with only 10 cities on a 300-tile domination map (an easy limit to find a map below).

If you pop an early settler and get an SGL for ToA, I now believe it is possible to beat Smirk's 1450 bc. record - even if it's probably not by much. I figure you would need to pop a settler before turn 10, have the capital produce 5 settlers by 1700 bc or so and have city 2 produce 3 more in the same time - leaving a lot of room for the Imm/GS produced in other cities to run. Grabbing a couple of the AI cities should pretty much seal the deal.

I doubt the possibility of a pre-2000 bc domination, however.

 

[LulThyme]

Misfit, of course you have to adjust for capital city, as it is very likely to get to rank 3, but as I mentionned, the very first few cities will probably be placed to maximise their factory potential, and later cities are placed to occupy territory, and the grids use is to fill territory.

Black Betsy, first, thanks.
second, dont forget that the 30 tiles per city does not happen on the border of the grid so for 300 tiles, if you consider this, plus the fact that the first few cities wont be optimally placed, I would say something like 13-15 cities is more realistic? Maybe someone can try and report how it goes. This pattern becomes more useful as you move to bigger maps and I expect somebody doing a huge domination on chieftain would be well advised to have most of his cities in such a pattern.

 

[xeroyne]

I've been playing this Huge map game and just noticed that my ToA is over 1000 years old, and my Temples are still only producing 2 culture per turn.
Shouldn't they be producing 4 CPT?

 

[LulThyme]

No there was something about that a long time ago, but temples gained through ToA never produce 4 CPT....

 

[Ronald]

I now believe it is possible to beat Smirk's 1450 bc. record - even if it's probably not by much.

I did beat Smirk's 1450 BC but as you said by not much. My domination was in 1525 BC (I wrote a thread: Ronald's domination). I think another 3 to 5 turns earlier could be possible.

 

[LulThyme]

Yes I submitted a Warlord tiny in the 1500s BC, using my grid
I could check exact date but Im a little lazy
(I got 2 SGLs, no good huts, but got very lucky and was able to very early capture 2 AI cities, one of them empty...)
It was my first try and I got SGL on first tech, and 2 cows and wheat, so I said why the hell not
BTW I figured about half the way through, like Ronald, that apart from 3-4 initial cities which will produce settlers, from then you fill in outside in, because the last cities built are what will be slowing you down.