City Placement Analisys

[cumi]

Hello,

I have painted a few files, to visualise and analise some of the city placement strategies.

Red squares - the cities
Dark blue squares - "core" city tiles
Blue - 2 ring of city tiles
Yello - tiles divided between two cities (and only two cities)

1.) Quiet bad 3x4 with lot of lost tiles on the map:

[cumi]

2.) A little bit better but 3x4 placement, with loosing 2 tiles for each city on the map

[cumi]

3.) I like this one, 3x3 having only 2 squares per city, that are divided between two cities. That means each city has only ONE tile less, than the muximum.

[The Mad Monk]

Interesting, but it shouldn't matter as long as none of the really valuable resourses fall into a hole.

[cumi]

4.) Very loosy 4x4 city placement strategy, with loosing 4 squares per city on the map.

[cumi]

5.) A very nice CP strategy. It's a 4x2 strategy with having ONLY 6 squares per city divided with another one. So in this case, each city is loosing ONLY 3 squares. With the border cities the situation is even better.

[cumi]

6.) An interesting 3x3 strategy. All the 2 ring city tiles are divided, but only between 2 cities. So each city has 6 tiles less than the maximum to work on.

Hmmm... This is actually 2x3 strategy

[Major Guz]

I like to place my cities 3 tiles apart (city-tile-tile-city) when possible.
This is mainly because you will use only 12 tiles during most of the game (pre-hospital).
When placed 3 tiles apart cities overlap a lot (compared to some of your graphics), but when you have many cities it does not matter that much because few BIG cities = many small cities, from a pure mathematical point of view.
When taken into consideration the chance at primary resources (oil, uranium or aluminum etc) you will have an advantage in having multiple smaller cities (larger surface area covered, thus bigger chance of important resource) than you would have with fewer bigger cities.

But that is just my point of view.
Compliments on the graphical representations!
I always like it when someone analyzes the thoughts behind the game!

[Dominae]

Nice visuals, cumi.




Dominae

[Arrian]

The best laid plans of mice and men...

Nice visuals, but that will immediately fall apart when you try to apply that to anything but endless stretches of grassland. Add in river systems, coastlines, mountains... and it all goes to hell.

-Arrian

[cumi]

Originally posted by Arrian
The best laid plans of mice and men...

Nice visuals, but that will immediately fall apart when you try to apply that to anything but endless stretches of grassland. Add in river systems, coastlines, mountains... and it all goes to hell.

-Arrian

Yes, I know...

I also posted a message in this thread:

http://apolyton.net/forums/showthrea...23#post1760223

I wrote my oppinion about city placement in some of the typical and non-optimal map terrain, like cities on coaslines or surrounded only by hills.... I these cases, the cities will not (or there is no need to) grow over a limit and 3 or 4 tiles between the cities can not be a strategy, there will be no overlappings and the city will not exceed even its first ring tiles (dark blue on the images)...

In these cases the pattern must be modified - like a curved dimension or curved space where the axes (x,y) are non-linear functions.

I studied about these vector spaces in the university. There are not simple. Or a complex spaces (complex-vector spaces) with singular point. Very perverz.

cheers

[Konquest02]

Originally posted by cumi

I studied about these vector spaces in the university. There are not simple. Or a complex spaces (complex-vector spaces) with singular point. Very perverz.

Applying complex numbers to Civilization, would that mean having cities spaced by i tiles...?

I don't think city placement will ever come down to a mathematical formula because there is so much involved: geography, ressources, neighbors, etc. You can't all fit that in one formula (even using complex numbers! )

--Kon--

[Catt]

Excellent visuals, cumi!

I think the real tension in city placement strategies comes down to whether or not one is willing to sacrifice "wasted" tiles in the first half (or two-thirds) of a game in exchange for cramped cities, with all the resulting upsides (happiness and pollution, for example) and downsides (increased corruption, perhaps smaller land under one's control, absence of very powerful cities, increased mainteenence costs, for example) in the later game.

A converted 3-tiler would point out that preserving 17 or 18 tiles of worakble terrain for any given city means that, until Sanitation and hospitals, 5 or 6 of those tiles will remain unworked and fallow. A tighter spacing will prevent any one city from working 18 tiles later in the game, but from some point in the middle ages through at least the early industrial times, few, if any, workable tiles will be unproductive.

Catt

[badams52]

Good visuals Cumi it's good to think about city placement and even better that we can analyze and see what cities get to use what tiles, and you did a great job showing different plans.

Originally posted by Arrian
The best laid plans of mice and men...

Nice visuals, but that will immediately fall apart when you try to apply that to anything but endless stretches of grassland. Add in river systems, coastlines, mountains... and it all goes to hell.

I've come to place little importance to making sure a city is next to a river anymore. It's nice, but I prefer building cities based on a grid layout till coast or mountains that is.

If I knew where all the resources were going to pop-up, I might change my building layout, but once your cities can work all the tiles within your cultural borders (aside from the outer cities), the layout becomes little more than a person's preference (when playing SP). I feel that whether you win or not more often comes down to the amount of land owned and the placement of the cities acts little more than window dressing. But I could be wrong.

[vmxa1]

Someone posted (way back) a pattern map for size 1-23 or something. I attacked the pat19. I had to blow it up in paint and turn on the grid to see, but it has no lost tiles and all cities have 19 tiles that can be worked.
Yes, you will often run into terrain issues and things that force a a change, but it is a good guide.
When you want to use closer spacing use a smaller pattern.

[Chemical Ollie]

I tried your #6 strategy a couple of times tonight. After 3-4 trials, I finally found a map where it could work. This could be a very funny game inded.

[Chemical Ollie]

Normally I let the terrain decide where I place my cities.

Prefered:
- River or lake
- Coast
- Strategic resources within limits
- Luxuries within limits
- Annoying neighbours by pushing your cultural borders

Not build on top of:
- Wheat
- Cattle
- Game
- Wine
- A single flood plain

In the map above, the geometric approach fit well, but most of the times it doesn't.

[Master Zen]

Cumi:

good work , personally I'd like #3 #5 for games below Monarch but #6 for Emperor/Deity.

Of course, as many have already said, terrain will dictate in a large way on how much you will deviate from the basic layout and if it is actually usefull or not.

[cumi]

Originally posted by Konquest02


Applying complex numbers to Civilization, would that mean having cities spaced by i tiles...?

In the complex space: yes.

i - can be the y - axe

for example:

f(z) = z^2 + z + 2

z=x + i * y

[cumi]

Originally posted by Master Zen

Of course, as many have already said, terrain will dictate in a large way on how much you will deviate from the basic layout and if it is actually usefull or not.

Does this means, that these patterns can represent a kind of "maximum city spacement" ?

[cumi]

Thanks for the numerous comments.

Many of you have wrote, that the terrain can modifie the CP strategy, and these patterns are rarely usefull. I aggre with that.

But, do you prefer to use denser CP when possible? Or you think there are some useless tiles, it is better to have sometimes more tiles than the pattern dictates.

If you have a given size of a territory on the map, that can be settled and used by you, are you trying to build as much as you can cities (but still to able to have metropolises and some very productive cities later)?

Is a city size of over 30 a must, to be productive in modern era? I usually don't have cities over 30. My cities having size 20 can sometimes be more productive, than the bigger ones (building in 2 turns MA - not bad I think).

The reason why I am analysing the CP strategy and trying to visualize it, is because I think I am placing my cities too far from each other. I have been quite like shocked, when I read here, that most of you are using 3 (or less !!!) tile CP strategy on higher difficulty game levels.

Thansk again for your oppinions,

-- cumi --

[badams52]

# 6 is as close as you get to the true 3-tile strategy employed by a decent portion (see corresponding poll) in the strat forum. The idea behind a "true" 3 tile strategy is to get as many cities as possible within 3 tiles for working land and faster reinforcement by roads. Sir Ralph showed the most effecient 3-tile system here in the city placement redux (for the third time) thread.

I took his plan, and made it into a tile plan with your same coloring code except I added a green color for the tiles that are in the 2-ring of the city but shared. This method works out for 12 workable tiles per city on the inside and the center city had 3 spacing with the 4 closest cities.

We've had many recent discussions about city placement with the newest thread right here.

As you can see in the poll, many people use many different style of spacing. 3-tile spacing has the added benefit of fast movement between cities for the ancient era, less pollution and less unhappiness when the cities start to grow as they cannot get much larger than 12. Also allows more free units when under despotism and monarchy.

In short, 3-tile spacing is much more condusive to building an army and going to war which most people on this forum (like me) use when playing a higher difficulty level. Often going to war and taking a few of the AIs cities helps out loads in the later stages of the game. More land = more production. It also allows a person to work more of the land inside his cultural borders before hospitals come into place and allow cities to grow in size.

Optimal city placement (OCP) which is seen in your plan #3 allows larger cities which may be able to build tanks and other units in 1 turn but have more pollution and take more luxuries and improvements to keep the city from revolting. OCP is better for builders and reaps it's rewards in the late stages of Civ where cities get large and use all 19-21 tiles in it's workable radius.

Most people don't like to go larger than OCP cause then you lose valuable workable tiles inside your cultural borders, and what if one of those tiles happens to have aluminum, rubber, oil, etc. on it which increases your productivity for the city?

By the way, I try to keep my cities from going over the 20 population barrier since you can mine most of the tiles that will put you over 20 and use them for production instead of entertainers, scientists and taxmen. Though I don't know if it's "better" it just gives most cities its maximum productive capability given the land arrangement.

I used to think overlap was bad, but having read much about city placement, I'm more likely to overlap than to leave any gaps when REXing. Now when you're conquering other civs, then that's a different matter and I often leave the AIs city placement alone.

[badams52]

Originally posted by cumi

Does this means, that these patterns can represent a kind of "maximum city spacement" ?

We prefer to think of it as "optimum"

[Master Zen]

Originally posted by cumi


Does this means, that these patterns can represent a kind of "maximum city spacement" ?

I would rather call it "optimum city spacement" in that it serves a a model strategy but one that will me slightly modified depending on the terrain or game condition.

Of course this might confused with "optimum city placement" or OCP, a popular layout in which there is no overlap. Personally, I cannot but find the title "optimum" misleading since anyone trying this will get his @$$ kicked in Emperor/Deity.

[Grandpa Troll]

Well, having some from Call To Power for over Four years I tried this strategy and wanna thanks, true I am new to Civ III PTW but am learning.

This helped me immensely over my strategy of looking for what would be considered

"Optimum" city placement, best land, lots of walking ect.

Hope to learn more from all the greats!!!


Grandpa Troll

[pedrojedi]

It is interesting seeing different people's approaches on the very different topics on Civ; one of the most curious is CP.

I was a puritan when it came to CP, and tried to have the largest possible cities with big enormous population/production. But after seeing the arguments posted on many threads here, I came to the (paying to my pride) conclusion that some overlap is interesting, if not necessary. So I'm practicing it. Still on Regent and far from going up, since I don't have a good stable practice, but sticking to the change!

[Chemical Ollie]

I have mostly used the "optimal" city placement but after trying the 3-tile strategy in a couple of games, I might rethink my plans. The ancient era is really where you win or lose the game, so getting many cities fast will make you stronger. And packing the cities close will help you do that.

I might come back with an AAR on the map I posted above. Doing pretty well so far.

[Brizey]

As Theseus and Arrian and others have said, reality tends to get in the way of plans. I think that the most “workable” heuristic is to simply count tiles between cities. In other words, place your cities “about” 3 tiles apart, taking into account the actual terrain. Anything stricter than that is going to fall apart on a real map.

This is the important point: since some tiles can be 5 or 6 times as productive as others, schemes that treat every tile as having equal value make no sense. That is why I do not use pattern schemes for my city placement heuristic.

[Master Zen]

Originally posted by pedrojedi
It is interesting seeing different people's approaches on the very different topics on Civ; one of the most curious is CP.

I was a puritan when it came to CP, and tried to have the largest possible cities with big enormous population/production. But after seeing the arguments posted on many threads here, I came to the (paying to my pride) conclusion that some overlap is interesting, if not necessary. So I'm practicing it. Still on Regent and far from going up, since I don't have a good stable practice, but sticking to the change!

You will REALLY start seeing the difference when playing at Emperor/Deity. On difficulty levels below those, even in Monarch, it is quite possible to play a competitive game using OCP or other spaced-out placement styles. Try it, and you won't go back!