Do you think you understand corruption (pre-C3C)?

Ask and you shall receive! :D
I updated the attachment in the initial post.

As for putting it in the utilities, I don't think it's that useful of a tool, but you can start a thread in that forum with a link to this thread if you like...
 
Great work, thank you Alexman.

Where do you get the figures for the boxes in the "Number of Cities" section of your calculator?

"1) Optimal number of cities, Nopt
This is an integer number equal to the optimal number of cities for the current map size, multiplied by a factor that depends on difficulty level. Both these values may be found in the editor."

Are you referring to the map editor that comes with the game? If so, it does not work with the GOTM games.

A lot of threads refer to the optimal number of cities but no one states what that number is. Is it a secret? What is that number? Is there a chart somewhere listing those numbers?

Where do you get the number that goes in the box "Closer"?

The original post of this thread is April, so I hope it is not to late to get a reply.
 
It's never too late for a CivFanatic! ;)

Under the default rules, the optimal number of cities is as follows:
Tiny: 12
Small: 14
Standard: 16
Large: 24
Huge: 32
You can get these numbers by opening civ3mod.bic with the editor, and clicking the World Sizes tab. Select a map size and you will see different values in the "optimum number of cities" field. The GOTM uses default rules, so you know the value if you know the map size.

As for the "closer" field in the calculator, it refers to the number of cities that are physically closer to the palace (or FP) than the city in question, including the palace itself. I'm afraid you have to count them yourself from looking at the map! :p
 
Alexman,

Glad to see you're still reading this thread! I have a question
for you (or anyone else who knows the answer).

About seven months ago I posted a strategy guide on how to work
around corruption and waste in order to maximize the overall
production and efficiency of one's empire, to the "Official
Corruption Solotions" thread. I'm now working on a complete
overhaul of that guide, as it's now quite out of date. Some of
the things in it are no longer true as a result of patches, and
others were based on empirical observations I had made without
fully understanding the mechanics behind what I was seeing, and
your post that started this thread has some important
implications to that. Also I just have a lot more experience
with the game now, and I've changed my mind about some things.

Anyway my question has to do with FP placement, and what happens
with cities that are more or less equidistant from your capital
and FP.

You said that the FP gives you a whole new set of cities where
Ncity starts at one. Basically what I want to know is, is the
set of cities whose Fc is determined by their distance from the
FP completely distinct from the set of cities whose Fc is
determined by their distance from the capital, or is it possible
for one city to be a member of both sets?

For example, suppose you're playing as the Americans. Your capital
is in Washington, and you built your FP in Chicago, which is 10
squares away from Washington. Now suppose you have 3 cities within
5 squares of Washington, those being Philadelphia, New York, and
Boston. The next farthest out city from Washington, after Boston,
is Detroit. Detroit is 7 squares from Washington, but only 6
squares from Chicago. Then comes Atlanta, which is 8 squares away
from Washington and 11 squares from Chicago. Philly, New York and
Boston are all at least 12 squares away from Chicago.

Now the question is, what is Atlanta's Ncity value? 3, 4, or 5?
Atlanta is the 5th farthest city from Washington, coming after
number 4 Detroit. However Detroit is closer to the FP in Chicago
than it is to the capital in Washington. Does that mean that it
doesn't count towards Atlanta's Ncity value?

In other words, do the Ncity rankings look like this:

0 Washington
1 Philly
2 New York
3 Boston
4 Atlanta

0 Chicago
1 Detroit

or like this:

0 Washington
1 Philly
2 New York
3 Boston
4 Detroit
5 Atlanta
6 Chicago

0 Chicago
1 Detroit
2 Washington
3 Atlanta
4 Philly
5 New York
6 Boston

Does each city belong in both lists, or just one?

And if each city appears in both lists, then is its Ncity value
that is used to compute corruption based on the minimum of its
rankings in the two lists, or on its ranking in the list for
whichever "capital" it's closest to? In other words, would
Atlanta's Ncity value be 5, because it's closer to Washington
than to Chicago, and it's the 5th farthest city from Washington,
or would it be 3, because it's only the 3rd farthest city from
Chicago?

The major implication of this question is that, if each city
only appears in one of the two lists, putting the FP a great
distance from the capital is much less important that it would
otherwise appear.

Whenever you have a lot of cities, Fc is going to be the primary
limiting factor to your overall productivity, rather than Fd.
Basically you get a cluser of approximately Nopt productive cities
surrounding your capital, and another cluster of Nopt productive
cities surrounding the FP. All of your other cities will have 95%
corruption, or close to it, and will be net liabilities to your
empire rather than assets. But if each city appears in only one
of the two Ncity ranking lists, then the only thing that changes
by putting your FP right next door to your capital is that you
get one cluster of 2*Nopt productive cities, rather than two
clusters each contaning Nopt. Either way you get a total of 2*Nopt
productive cities.

Of course it would have to be a bigger cluster, in order to avoid
the cities' production radii from overlapping, which means the
average distance from the capital/FP of your productive cities would
be a bit greater, which means you get a bit more Fd, which means
your empire's total productivity would take a bit of a hit. But it
would be far from disasterous, and that loss might actually be
outweighed by the advantages of putting the FP close to the capital,
such as that you can build it with the city's native productivity
rather than always having to use up a Great Leader, and your
perimiter would be smaller, making your home territory easier to
defend.

What do you think?

Also, anyone from Firaxis want to comment on this?
 
Originally posted by artax
...is the set of cities whose Fc is determined by their distance from the FP completely distinct from the set of cities whose Fc is determined by their distance from the capital, or is it possible for one city to be a member of both sets?
Click to expand...
The latter. A city is always member of both lists when you have a FP.


...if each city appears in both lists, then is its Ncity value that is used to compute corruption based on the minimum of its rankings in the two lists, or on its ranking in the list for whichever "capital" it's closest to?
Click to expand...
The former. Its ranking is the minimum rank of that city out of the two lists.

Basically, if you want maximum productivity in your empire, you have to arrange so that each city that appears in the first half of the capital's list, appears in the second half of the FP list, and vice versa. This is very difficult to do in practice, but there are many ways to at least come close. But this is not for here. I'll let you cover those ways in your strategy guide! ;)
 
Got it. Thanks for the clarification!

Too bad Firaxis didn't make it work the other way, though. I
think that would make it more playable. It would give more
flexibility in terms of what shape your empire can be, and
still be maximally productive.

I agree that making it so that each city that appears in the
first half of the capital's list appears in the second half of
the FP's list, and vice versa, would be difficult. However
that's only important if you don't have much over 2*Nopt
total cities. My strategy guide is going to be mostly aimed
at people who like to win by total world conquest, and
end up with lots of cities. In that case, all you have to do
to is make sure that your capital and FP are far enough
apart that the cluster of productive cities surrounding the
capital and the cluster of productive cities surrounding
the FP don't overlap. All cities outside those two clusters
will have 95% corruption anyway, so it doesn't matter
what order they're in within each of the two lists.
 
Hi folks,

This is an interesting thread - I would particularly like to hear some more tips on the placement of the FP and the Palace, as this is a very important decision that always fills me with doubt.

Many players are no doubt aware of this, but after seeing numerous posts on rushing the Forbidden Palace with a leader, I thought I'd point out an alternative strategy that I nearly always use. When I first get the entire world map, I try to make some long term plans about where the final borders of my empire should lie. On many maps, a reasonable goal is simply to conquer the continent on which I started. I then estimate two reasonable sites for the Palace and the FP, and then I immediately build the FP at the site nearest to my current capital (using plain old shields). Later, when I've conquered the territory where my second palace should lie, I rush build a Palace with a leader at that site, thus jumping my capital there. The old core of my empire should still be pretty near my FP.

The main advantage of this strategy is of course that you get the FP as soon as possible, yet at an optimal site. Another advantage, if you avoid building any wonders in your capital, is that you can always resort to moving your capital by abandoning it, in case you have no leader on your hands.
 
Thanks Rider for the excellent FP tip. I will sometimes move my capital to a more centralize location by abandonment to save time and leaders if I have not built any wonders there. I often will not build any great wonders preferring to obtain them as spoils of war.
 
Thanx 4 the nice beakdown guys.

Quetions:

1. Does anybody know the optimal # of cities for each map size?

2. Does % water/landmass ratio affect these #'s?

3. Is it possible that government type affects the optimal #?

Hope to hear a reply!

Cannon
 
very good analysis...
Can I ask you a question? Is it necessary a Courthouse in the Capitol?
 
Cannon- #1 is answered if you scroll up a little on this page.
#2 - No
#3 - Not really. Governments affect the distance from capital part of the corruption formula. Communism is not affected by distance but only by # of cities.

Lord Guilhon- Most of the time, no. But sometimes I do lose a shield and 1 or 2 gold in the capital and recover this when I build a courthouse. I wouldn't bother building a courthouse in your capital until you actually see corruption/waste in it. And even then, it may be debatable sometimes whether it's worth building the courthouse.
 
Looking for info about that lone gold of corruption lost in the capital and that single shield wasted, I found this excellent analysis by Alexman. It says that the game counts the capital as being one tile away from itself, and thus has one shield of waste and one gold lost to corruption.

This is in contradiction with the Civilopedia that says that the palace eliminates corruption and waste in your capital. But since we all see this happening, either the Civilopedia should be adjusted, or its a bug that needs fixing in the game if you are indeed supposed to have no corruption/waste there.
 
I've discovered a correction to the corruption formula posted by alexman.

Distance to the palace or forbidden palace is not computed using Euclidean distance (square roots). Instead, the distance is based on the shortest path, where each orthogonal move costs 1.0 and each diagonal move costs 1.5.

I discovered this because the corruption for a test city at distance (4,3) is not exactly the same as the corruption for a test city at distance (5,0). However, a test city at distance (4,3) has exactly the same corruption as a test city at distance (5,1).

Another way of writing the formula is

Distance = max(x,y) + 0.5*min(x,y)

where x and y are the distance in the NW/SE and NE/SW directions, respectively.
 
That really is very interesting. And while I was just re-designing my build pattern, this news is music to my ears. Thanks a lot DaviddesJ, and alexman.
 
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