When to break camp

[vulture]

Warning: may get too mathematical for some (although a mathematician would laugh at that statement, I'm sure).

Many Civ III players use temporary cities to try and get the most benefit from their empires (a technique often referred to as 'Ralphing' around here). This is an attempt to derive some criteria for when camps help, and when they should be disbanded to improve the overall production of the empire. Much use is made of the corruption formula, deduced mostly by Alexman. If you aren't familiar with the two types of corruption (OCN and distance) then you'll probably want to read that to make sense of this.

The basic criteria here is that the time to abandon temporary cities is when the loss in production due to abandoning those cities is exceeded by the increase in production due to reduced corruption in the rest of your cities. Cities further away from your capital (or FP) than the cities being abandoned decrease corruption by an amount that depends only on the number of temporary cities being abandoned, and is the same for all cities (assuming that all camps being abandoned are at the same distance from the capital - on the other hand, if you have in order of distance capital-camp-city-camp-city then the first city gains the benefit of having one camp disbanded while the second city gains the benefit of having both camps disbanded). So the total increase in productivity for these cities depends on the number of camps disbanded and the total number of tiles worked by the further out cities. The production you lose depends on the number of tiles worked by the camps, and the total corruption in those camps.

If n is the number of camps being disbanded, T is the number of tiles worked by camps that are being disbanded, C is the total fractional corruption in those camps (between 0 and 1), e=1-C is the efficiency (also between 0 and 1; 0 efficiency is 100% corruption, 1 efficiency is 0% corruption), U is the total number of tiles worked by cities that are further away from the palace/FP than the camps, and N is the modified optimal city number for the map size, difficulty level and other OCN modifiers, then the break even point (where the presence or absence of camps makes no difference) is:

e T = U n / (2 N)

If we define A=T/n as the average size of the camps, then the criteria for camps to be beneficial is:

A > U / (2 N e)

So once you have claimed as much territory as you can, without going to war (i.e. you've run up against AI borders or coastline in all directions), and you want to know if it is worth putting down some camps, what you have to do is:

1. Decide where you want your camps to go
2. Count how many tiles are used by cities further out from the palace than the camps U (don't forget the city square: number of tiles is total population points plus number of cities)
3. Calculate the corruption (and therefore efficiency e) each camp would have (this requires you to either know how to do this from the corruption formula, or be satisfied with a rough guess)
4. Know what the effective OCN N is
5. Calculate U / (2 N e)

The number calculated gives you the average number of tiles each camp has to work before you are gaining a net benefit from the presence of the camps. If this number is less than 2, building camps will be of immediate benefit (a size 1 camp works 2 tiles). If it is larger than two, you'll have to do some kind of estimate of how long it takes the camp to grow large enough to be a benefit. For example, suppose you have 8 size 6 cities outside your intended camp placements, giving U=56. Suppose you are playing deity, on a normal sized map, and are a non-commercial civ, in despotism. Then N=11.2. And you are placing your camps 3 tiles from the capital, with no cities closer in, giving e=0.863 if the camps are connected to the road network. Then U / (2 N e) = 2.90, so size 1 camps are going to reduce the efficieny of your empire. But if they grow in 10 turns (while the size 6 cities mostly can't grow, for the sake of argument), then in 10 turns time the camps will be of net benefit, and will be of increasing benefit as they continue to grow.

One of the (perhaps) surprising features of this is that as long as it is advantageous to add camps, it is advantageous to add as many as possible. There is no optimum number of camps. And once the number of camps you have becomes more of a hindrance than a help, the the best number to have is zero - get rid of them all. To judge when to get rid of camps, you use the inequality above. Generally, your camps stop growing, but you continue to add outer cities (and improvements to cities you already have) until U / (2 N e) > A, at which point it is time to get rid of those camps (or, once you see that point approaching, start turning those camps into workers).

Improvements are a consideration here. Courthouses (and WLTKD) are an obvious factor that changes the effective OCN for a single city. If all your cities have courthouses, the effective OCN is raised by 25% (which actually makes the camps more desirable, since their effect (and hence the benefit of getting rid of them) is reduced). Libraries and marketplaces also have an effect - due to the increase in science and gold, they increase the effective number of tiles worked - a city with a university and bank gets double the benefit for each tile, so the number of tiles it is working is effectively doubled, although the number of shields it is producing isn't affected. Obviously, judging the effects of such improvements is not an exact science (although it can be done exactly), but with some kind of estimate of the number of improvements you have, it is possible to get a rough correction to U to judge when the camps have outlived their usefulness.

I've ignored the problem of having cities that are 95% corrupt, and which won't get any benefit from disbanding camps. I'm assuming that the camps lose usefulness some time before you get that many cities, so it should never be an issue unless you've kept your camps for far, far too long.

One last issue to address is the resources used to make camps. Obviously, they use up one settler. Plus, before they produce any units, they need to build a barracks. That is a cost of 70 shields (50 for a militaristic civ) and one population point (two used to make a settler, making a size one city). The population point is quickly recouped, by virtue of having a new city that is growing. So as long as your camps hang around long enough to produce 70 shields worth of units, they represent a net benefit in shields, and as long as they produce at least 1 gpt to cover the barracks upkeep, they are pure profit in the science/tax department. So most of the time, the cost of building a camp is quickly overtaken by the production from that camp.

As a rough guideline, on a standard map, regent level, camps in a ring around the capital remain useful until the number of tiles being worked by permanent cities outside the camps exceeds the tiles worked by the camps by a factor of 6-8 (7-9 for courthouses) depending on government type. So 4 size 3 camps (working 16 tiles) will be useful until you have about 112 tiles being worked by cities beyond those camps (in a republic, ignoring courthouses).

The same principles apply for those who prefer building camps beyond the first ring of permanent cities - you just need to worry about the cities beyond the camps, and the corruption in the camps themselves. The cities further in have no effect on this.

Is it worth posting a table of OCN for various map sizes and difficulty levels?

[Theseus]

Whoa.



So, as a rough guide for the less precise of us ( ), it seems that having roughly 15-20 decent towns / cities outside of the camps would be turning point, when one would start to consider disbanding. Is that about right?

[UnOrthOdOx]

Very interesting. I would definately appreciate the tables as well.

However, I have one possible problem in your formula, or perhaps it is simply a difference in my personal play style.

So once you have claimed as much territory as you can, without going to war (i.e. you've run up against AI borders or coastline in all directions), and you want to know if it is worth putting down some camps, what you have to do is:

I place my camps first, as my first goal is the forceable pruning or take over of the nearest enemy. The camps are close, remain small, and designed for producing a barracks/granary and either military or settler/worker pumps depending on the terrain. They are specifically placed in order to utilize 7 tiles for a given time.

However, I will definately look more closely at this removal formula and see how well it works. I would think that it would NOT be advantageous to remove them all at once as you seem to suggest. Two cities may be improved by the removal of a camp between them while two other cities may not be to that point yet. I typically see it as a per-city assessment rather than empire wide. I'll have to look at that and try out using this formula.

[Arrian]

/me flees in terror

[Harovan]

/me (who's name was abused for the camp thing due to a brainfart he once had) flees too, then stumbles over a full crate of St Georgen Keller beer, falls and doesn't get up till the crate is empty.

j/k, good work, vulture. I'll show it my son, who's a student of maths. Let's see if he laughs.

[alexman]

Gotta love your analytical nature, vulture!

Your general conclusions are certainly useful, even if going through the calculations to get U, and N is not very practical in a normal game.

A couple of comments:

1) Camps often outlive their usefulness when they are restricting the growth of permanant cities, which sometimes comes before corruption considerations, depending on your city spacing. Obviously when all camp tiles can be worked by large cities if they grow, the camp is a bad idea.

2) Forbidden Palace core: There is a bug that messes up rank calculations for cities around the FP, so the evaluation of your formula is extremely tedious in practice for the FP core.

Again, nice job trying to quantify the usefulness of camps!

[Master Zen]

Originally posted by Sir Ralph
* Sir Ralph (who's name was abused for the camp thing due to a brainfart he once had) flees too, then stumbles over a full crate of St Georgen Keller beer, falls and doesn't get up till the crate is empty.

A very useful brainfart on huge maps if you ask me...

[Master Zen]

Here's a camp city placement scheme I've learned to love...

the premise:

1) 4-tile core around the capital (o-x-x-x-o) with two camps mingled inside.

2) core cities 3-tile (o-x-x-o) apart from each other and apart from all subsequent rings. Two camps around these cities.

So, in this example you have 12 cities. This scheme was done before RCP so as you can see there are 4 different city distances but by moving the top and bottom cities one tile closer to the capital you can get RCP-3 which is better.

The two camps usually can make a barracks pretty quick as a mil civ and with a well timed chop can also do quick with any other civ. After that, start cranking units like crazy... btw, the camps around the capital tend to hog the productive tiles. This is good. I usually use the capital as a settler pump anyways.

EDIT: forgot to mention, the VP locations represent cities, while the huts represent camp cities.

[vulture]

I was working on the premise of a city layout that allows permanent cities to reach size 12 and camps to reach size 6, with later disbanding to allow something closer to OCP (size 19 cities, usually a bit smaller in practice due to the nature of ring cities). That way the camps don't impede the growth of cities until hospitals. It is fairly obvious that once you get to that point, it is best to build the hospitals and transfer all the camp population to the permanent cities ASAP - you end up with the best of both worlds (working all the tiles, plus the lower corruption).

I suspect a lot of the usefulness of this depends on what kind of city placement scheme you use. The Forbidden Palace bug would be annoying.

Of course, if you want to test how well this works in a real game, you just have to make saves at various points as you come close to any go past the predicted break even point. Later on you can reload the saves, look at the f11 stats (manufacturing and GDP I think) with the camps in place, abandon them and see how the f11 stats change.

The break even point is different for shields (no help from improvements until factories) and trade (helped by markets, libraries etc.), so a good point to get rid of camps will probably lower your manufacturing output and raise your GDP slightly. If both fall, it was too early to break camp. If both rise, it was probably too late.

EDIT - messed up the post, so have removed some bits. Will replace them shortly with a very approximate table.

[vulture]

Originally posted by UnOrthOdOx

I place my camps first, as my first goal is the forceable pruning or take over of the nearest enemy. The camps are close, remain small, and designed for producing a barracks/granary and either military or settler/worker pumps depending on the terrain. They are specifically placed in order to utilize 7 tiles for a given time.

However, I will definately look more closely at this removal formula and see how well it works. I would think that it would NOT be advantageous to remove them all at once as you seem to suggest. Two cities may be improved by the removal of a camp between them while two other cities may not be to that point yet. I typically see it as a per-city assessment rather than empire wide. I'll have to look at that and try out using this formula.

I'm working with a scenario in which the camps all have the same corruption as each other (or to put it another way, you group your camps into groups of equal (or roughly equal) corruption, and find the criteria to get rid of each camp). I was surprised with the way it came out, but if the corruption formula is accurate (and it is certainly very close), then the important quantity is the ratio of average tiles worked per camp to total tiles worked by other cities. There can be complications if your camps are of different sizes (disbanding a small one boosts the average size, so it may be right to disband the smallest camp, and then find that the right thing is to keep the rest of the camps a little longer).

I was actually expecting to find some kind of formula for the optimal number of camps for a given set of cities, but it just didn't turn out that way. Which is rather non-intuitive to me. But at risk of repeating myself, different placements strategies will have very different results. If, in terms of distance, your camps are mixed up with your cities, I'm pretty certain that you'll find you need to disband the inner camps relatively early, and the further out a camp is the later it will still be useful.

One last general point: I don't expect the formula to be useful in a game. I mostly put it in to show who I'd reached my conclusions. The aim was just to get a rough idea of what part of the game you should be thinking about getting rid of temporary camps (are they never useful? are they useful the whole game? just in the ancient era?). I think the criteria, based on average camp size and total city population beyond the camps is relatively easy to work with, and gets you in the right ball park. Which is the point. It might be nice to be exact, but we don't need to be perfect, just good enough.

[vulture]

Here is a table of the modified OCN for different map sizes and difficulty levels (i.e. the map OCN multiplied by the difficulty % of OCN factor). As it happens, if we assume a case where camps are size 6 (work 7 tiles) and cities are size 12 (work 13 tiles) - or will be once the camp population in transferred to them, then for camps fairly near the capital (up to 5 tiles away, at a rough guess) the number of cities you can have before camps become a hindrance is 0.97 times this number, so it essentially is this number to a fairly good approximation. That's just a coincidence based on these assumptions about camp/city sizes though, not a general principle.

So just look up your preferred difficulty and map size, and that tells you how many good cities you are want when your camps are all gone (making modifcations for libraries, markets, courthouses etc., which on average will probably make it around 2/3 of this number).

World Size
Chieftain
Warlord
Regent
Monarch
Emperor
Deity

Tiny
12
11.4
10.8
10.2
9.6
8.4

Small
14
13.3
12.6
11.9
11.2
9.8

Normal
16
15.2
14.4
13.6
12.8
11.2

Large
24
22.8
21.6
20.4
19.2
16.8

Huge
32
30.4
28.8
27.2
25.6
22.4

[UnOrthOdOx]

Originally posted by Master Zen
Here's a camp city placement scheme I've learned to love...

the premise:

1) 4-tile core around the capital (o-x-x-x-o) with two camps mingled inside.

2) core cities 3-tile (o-x-x-o) apart from each other and apart from all subsequent rings. Two camps around these cities.

So, in this example you have 12 cities. This scheme was done before RCP so as you can see there are 4 different city distances but by moving the top and bottom cities one tile closer to the capital you can get RCP-3 which is better.

The two camps usually can make a barracks pretty quick as a mil civ and with a well timed chop can also do quick with any other civ. After that, start cranking units like crazy... btw, the camps around the capital tend to hog the productive tiles. This is good. I usually use the capital as a settler pump anyways.

EDIT: forgot to mention, the VP locations represent cities, while the huts represent camp cities.

Ah, I knew MZ would chime in eventually. I am a fan of his 'Zenning' as well. And, yes, modified for RCP it is quite nice...

[Master Zen]

If you want to see "Zenning" in action, read my DAR for round 2 of the AUSG101. There's also a thorough explaination on the camp theory.

http://www.apolyton.net/forums/showthread.php?s=&threadid=97286

[Vlado]

Maybe it's just me but I can't stand the thought to disband cities. Rase cities, yes, but never disband. I know it's something that cramps my style, especially in the late game when you really whish that some of your towns weren't, but I just can't...

Edit: Spelling

[vulture]

S'Okay Vlado - it's not compulsory. I suspect quite a lot of players (and good players too) have things that they don't do because it just doesn't feel right, or fun, or whatever.

I still have trouble disbanding cities. I have a bad tendency to give in and build just one or two improvements in them when I think I don't need any more troops, and then I can't bring myself to get rid of them. Sometimes I've been disciplined enough to do it (and I find that combining it with the ring cities scheme works better for me in this regards actually).