Ring City Placement

[DaviddesJ]

I have a detailed screenshot of my RCP strategy in GOTM20 in Post #85 of the Spoiler #1 thread in the GOTM forum. Probably almost everyone here can read that (because either you aren't playing GOTM20, or you have already qualified for Spoiler #1), but I can't post it outside the GOTM forum for another 5 days. So I suggest that if you're interested, you look it up there.

 

[jeffelammar]

Here is a little more data to look at



What I've done here is calculate approximate corruption in Despotism for connected cities at various distances. (For a non-commercial civ)

I have assumed a Standard size map at Emporer Difficulty. I have also left out the .5 distance numbers as they are close to the surrounding distances.

The scales change in different governments, but we can see some trends here that might help discuss the RCP.

I would assume that are at least 5 cities in the inner (1st)ring (adding in the capitol means that the 2nd ring would have "6" cities closer. Resulting in 42-50% corruption under despotism.

These numbers look a lot better once you start adding in Courthouses and switch to Republic.

As you can see a ring can be of great benefit even if it's city # is close to or at the optimum city count.

 

[DaviddesJ]

Originally posted by jeffelammar
I would assume that are at least 5 cities in the inner (1st) ring (adding in the capitol means that the 2nd ring would have "6" cities closer.
[/B]

I'm quite sure that the capital doesn't count as a "closer" city. For all of the cities in your inner ring, the number of closer cities is zero.
For cities in the second ring, the number of closer cities is just the number in the inner ring.

BTW, the formulas in alexman's corruption thread don't seem to be exactly 100% correct. I think they are like 98% accurate, but sometimes they are off by 1% or 2%. There must be some details that aren't accounted for exactly right, or maybe just rounding errors in the way the corruption is calculated internally.

P.S. I forgot to mention in my original RCP posting one of the nice things about RCP. Because you have many cities with exactly the same corruption, it's convenient to figure out exactly where the "breakpoints" are for each city (the number of coins or shields at which adding one more coin or shield will just increase corruption and not increase your output), so you can micromanage cities more easily by aiming for values that are just at or below the breakpoints. Of course, you can do this even without RCP, but it's significantly easier with RCP because there are only a few values to remember, instead of a different set of values for every city.

 

[jeffelammar]

Originally posted by DaviddesJ
I'm quite sure that the capital doesn't count as a "closer" city. For all of the cities in your inner ring, the number of closer cities is zero.
For cities in the second ring, the number of closer cities is just the number in the inner ring.


Correction noted. When using the table, slide thing down a level)


BTW, the formulas in alexman's corruption thread don't seem to be exactly 100% correct. I think they are like 98% accurate, but sometimes they are off by 1% or 2%. There must be some details that aren't accounted for exactly right, or maybe just rounding errors in the way the corruption is calculated internally.

Agreed, but the calculations are as you say it close enough to detect trends and basic strategy (maybe not enough for the fine grain micromanagement)

 

[Yndy]

DaviddesJ, I noticed your first Evrika comment as well as your detailed description of the RCP. I think you made a very important discovery that will shape the play style of the important players as well as improve the appearance of the city design. I can see all those nice circles in all the minimaps.

I tested the 3.5 RCP and it’s working out great. IMO the placement of the second circle/or its mere existence is linked to the city density that you prefer. I’m sorry that I can’t find my sheet with RCP planning but a 2RCP (3.5, 6.5) seemed to give me a nice 25 towns base with around 6 tiles per town (IIRC). Of course the terrain would not allow placing all of the 25 towns so the actual tile/city would be larger. On the other side a 1RCP of 3.5 with border expansion would give 9 very productive cities. The second RCP would then be at least at 7.5 to allow the first cities to grab all the land they can get.

Regarding the FP, I would rather delay it until I can use a leader to build it on a decent position and then build/rebuild another 1RCP (3.5) around it. In the end that would give me up to 18 very productive cities. I doubt I would need more for any victory type.

PS: I'll name my second town in GOTM 21 to honour of your discovery.

 

[Svar]

After first reading about DaviddesJ's RCP I decided to test it and compare it to OCP. I have been using OCP since at least CIV 2 and maybe Civ if the citizens have always worked the same 21 tiles I just didn't know it had a name.

I tested on a modified Civ 3 map I used to play on. I'm a builder so I like huge maps. The map has 3 continents on a world with 70% water so there is no contact until a Civ gets navigation. One of these continents is small like Australia and only had 1 starting location.

I modified this continent so I could build ring cities out to 11 tiles without working any water tiles. Except the starting location all potential city sites get exactly the same terrain (bonus grassland with cattle and river).

My only problem with this map is it's saved as a scenario with raging barbarians so the starts get a little messy. It doesn't really matter because cities grow like crazy. I play all test city placements as Carthaginians at Monarch difficulty level and conquest as the only victory condition so I really don't have to pay any attention to the other 7 civilizations.

So far 3 tests have been conducted out to 12 citizens per city. Eventually these 3 will be taken out to maximum population to see if the city efficiencies are consistant. If the efficiency is constant I will only play all the other planned tests out to 12 population which only takes a couple of hours each.

The results will be reported as ring city distances because the corruption for any given ring is the same regardless of the number of cities in the ring.

All tests with 12 population are recorded when the civilization is in it's golden age and every city is celebrating WLTK. All improvements for the ring cities are barracks, temple library and marketplace. The capital improvements are more extensive but I don't record the capital efficiencies so it is not important I hope.

The first test is a classic two ring of cities where the first ring is at a distance of 5 tiles while the second ring is at a distance of 9 tiles. This is as close as I could get to the OCP. There are 6 cities in the 5 ring and 12 cities in the 9 ring.

The 5 ring cities produce 52 shields with 2 lost to corruption for an efficiency of 96.2%, commerce is 80 gold with 4 lost to corruption for an efficiency of 95.0%. The 9 ring cities produce 52 shields with 7 lost to corruption for an efficiency of 86.5%, commerce is 77 gold with 11 lost to corruption for an efficiency of 85.7%.

The second test is a classic OCP with 6 different rings. There are 5 cities in the 5 ring, 2 cities in the 5.5 ring, 2 cities in the 8.5 ring, 2 cities in the 9 ring, 6 cities in the 10 ring, and 2 cities in the 11 ring.

The 5 ring cities produce 52 shields with 2 lost to corruption for an efficiency of 96.2%, commerce is 80 gold with 4 lost to corruption for an efficiency of 95.0%. The 5.5 ring cities produce 52 shields with 2 lost to corruption for an efficiency of 96.2%, commerce is 80 gold with 4 lost to corruption for an efficiency of 95.0%. The 8.5 ring cities produce 52 shields with 6 lost to corruption for an efficiency of 88.5%, commerce is 77 gold with 10 lost to corruption for an efficiency of 87.0%. The 9 ring cities produce 52 shields with 8 lost to corruption for an efficiency of 84.6%, commerce is 76 gold with 12 lost to corruption for an efficiency of 84.2%. The 10 ring cities produce 52 shields with 9 lost to corruption for an efficiency of 82.7%, commerce is 75 gold with 14 lost to corruption for an efficiency of 81.3%. Finally, the 11 ring cities produce 52 shields with 13 lost to corruption for an efficiency of 75.0%, commerce is 73 gold with 19 lost to corruption for an efficiency of 74.0%.

There are some surprises here. First the inner ring of the OCP has exactly the same efficiencies as the RCP no matter the slight difference in radius of the 2 OCP rings. My suspicion is that the program ignores the fraction but will have to verfy that in test 7,8,or 9. Yeh the more I test the more I find out and that leads to more planned tests. I think I have about 10 on paper waiting for the chance to get to them.

You will note that the 9 ring cities in the RCP are more efficient than the 9 ring cities in the OCP. Also note the big drop in efficiency when the radius goes to 11.

The last test was a Hybrid of the first 2. The inner ring was identical to the RCP and the results were identical. The outer ring was made up of three ring distances, 6 cities in the 9 ring, 2 cities in the 10 ring and 4 cities in the 10.5 ring.

The 5 ring cities produce 52 shields with 2 lost to corruption for an efficiency of 96.2%, commerce is 80 gold with 4 lost to corruption for an efficiency of 95.0%. The 9 ring cities produce 52 shields with 7 lost to corruption for an efficiency of 86.5%, commerce is 77 gold with 11 lost to corruption for an efficiency of 85.7%. The 10 ring cities produce 52 shields with 10 lost to corruption for an efficiency of 80.8%, commerce is 74 gold with 16 lost to corruption for an efficiency of 78.4%. Finally, the 10.5 ring cities produce 52 shields with 10 lost to corruption for an efficiency of 80.8%, commerce is 74 gold with 16 lost to corruption for an efficiency of 78.4%.

OK, the results were not exactly what I expected. The 9 ring was exactly the same as the RCP because it was the second ring but the 10/10.5 rings were less than the OCP 10 ring and the 10 Hybrid ring was only the 3 third ring while the 10 OCP ring was the fourth ring if my theory about the 5 and 5.5 ring counting as only 1 ring is correct.

The goal of reducing the corruption in the outer ring of the OCP worked even if the 10 ring is less efficient. Based on shield production, the outer ring efficiencies for the Hybrid test was 83.65% average while the OCP outer ring efficiency is 82.7 % average. The efficiency of the RCP outer ring was 86.5 so you can see the power of RCP.

I have yet to finish these tests to see which 19 city arrangement produces the highest overall production when all available tiles are being worked.

One of the many tests yet to be run is a three ring arrangement with 4 cities in the 3 ring, 8 cities in the 6 ring and 14 cities in the 10 ring.

I want to thank alexman for his work on corruption and DaviddesJ for his invention of RCP. The power of this discovery is tremendous. I used to place what people here call settler factories 2 or 3 tiles away from my starting city and disband it when the capital grew to over 12 population. I now know that if I want to do that I need to put them in the first ring so they wont decrease the efficiency of the first ring.

For those people just trying this, once you build a couple of test maps it just becomes second nature after you decide what the radius of each ring will be.

 

[ControlFreak]

What a cool and novel placement idea!

Here's my initial take. The corruption at low populations is much less that the cities actual corruption. (95% corrupt is 20corrupt sheilds for 1 non corrupt. But if a city is only making three shields, it looks like its 75% corrupt.) So in the very beginning, expansion and despotism, the cities are not showing their true corruptness. That means the advantages of RCP aren't there YET.

An interesting approach to maximize the efficiency throughout the the entire game would be to build your second city to be the FP site. This should be at a very close radius to the capital so it can get the maximum shields. Then start building ICS like at distances greater than the FP site. Make sure that the ICS builds include cities in your preferred ring around the FP. Also Make sure that the ICS builds include another core that is far enough away from the first core and includes cities in rings around their center. Once the FP is built the other core is ready for a jump, start disbanding the cities that aren't on your desired rings. starting with the ones closest to the FP (including the old capital) and closest to the new capital.

This would take advantage of the ICS build in the early years, but will take advantage of the RCP in the later years. It also has an advantage that the AI won't settle in the middle of your rings and mess up your RCP.

I think this approach would take a TON of pre planning and could only be executed correctly by the accomplished ICS builders but it does seem to give them a way out of the late game waste that occurs with ICS.

 

[Catt]

Great idea DaviddesJ I probably won't employ RCP as a method, but I certainly will take note of city distances in my core areas, and where terrain permits, take advantage of certain cities "sharing" a lower city rank for corruption purposes.

 

[DaviddesJ]

Originally posted by ControlFreak
Here's my initial take. The corruption at low populations is much less that the cities actual corruption. (95% corrupt is 20corrupt sheilds for 1 non corrupt. But if a city is only making three shields, it looks like its 75% corrupt.) So in the very beginning, expansion and despotism, the cities are not showing their true corruptness.

I don't really agree. E.g., a city generating 3 shields with 5% corruption will give you 3 shields and no waste, but with 20% corruption it gives you 2 shields and 1 waste. (Corruption is multiplied by the total output, and then rounded off to the nearest integer---this should be added to the corruption thread.) So that early city is 50% more productive (from 2 to 3 shields output) if you can lower its corruption using RCP....

I do think your overall concept (build cities without much regard to early corruption, but with careful planning so that in the midgame corruption will be very low and the palace and FP will both be well placed) could be a very good approach.

 

[Txurce]

Originally posted by Svar
I used to place what people here call settler factories 2 or 3 tiles away from my starting city and disband it when the capital grew to over 12 population. I now know that if I want to do that I need to put them in the first ring so they wont decrease the efficiency of the first ring.

The catch with the effect of a settler factory on RCP is that you rarely have a choice of where to build the factory. If anything, the location of the factory would be more likely to determine the distance of the first ring. In cases like this, I wonder if the best practical solution would be to build the factory (rarely later than the second city or third city), and then - if it's impractical to build a ring at that distance, build a ring just outside it, so that the capital is #0, the factory is #1, and the first ring has #2 city status.

 

[Moonsinger]

This RCP strategy is very good, but I don't think I will use it any time soon. As of this moment, I'm done testing it. Sure I will have a couple cities 2 squares away from my Palace and FP as I usually do, but I won't use the RCP. I figure...if it take 30 shields to build a horseman, with 100 cities, I would still be able to produce at least 100 horsemans in 30 turns.

 

[Cartouche Bee]

I think that people are overlooking the power that can be extended onto a second ring type cities, especially on larger maps. My posts in the HOF last November with the Egyptians, used a 5 tile radius around the capitol for the first ring, an 8 city version, although the mini map distorts the graphics very severely you can see the patterns of the rings in the shots. It's those next set of cities that can benefit greatly and make you total empire output soar that leverages the corruption reductions so much. More complex problems are how to incorporate the system to apply to both the palace and the FP at the same time and when to switch over to fringe ICS.

 

[Qitai]

First of all, great discovery DaviddesJ.

For me, I'll probably still expand in the initial stage as I do now with emphasis on accessible terrian more than anything else. In most cases, early growth, which has a cascading effect, is much more important than considerations for 2000 years later. However, knowing RCP means sites with same distance with any existing city will be given a slight bonus in city placement decisions.

Later in the stage of growth, for those cities which are hopelessly corrupted, I will probably give a heavy weight to the RCP consideration. I get concern about corruptions only when it gets significant, like 40% and above.

And since I always have a palace Jump backup plan so as not to relay on getting a GL, the RCP outer ring will be put around the FP instead of the Palace. I may even consider abandon any existing hopeless corrupted cities to shift them to a more appropriate placement whenever it makes sense.

 

[Moonsinger]

Ok Cartouche Bee, you are driving a hard bargain. I will see what I can do. Will setup another test run.

 

[jeffelammar]

Originally posted by Cartouche Bee
I think that people are overlooking the power that can be extended onto a second ring type cities, especially on larger maps.

I agree completely. I don't think that the placement of the first ring has that much effect. It is the 2nd ring where you get the big win. I intend to try a modified version of the placement.

In the early game I will have 3 types of cities.
1. Inner cities (at about dist 3.5 or 4).
2. Ring 1 cities (at OCP distances)
3. Ring 2 cities (at 8.5 or 9 depending on terrain)

As the game progresses I will disband/worker build the type 1 cities out of existance. I will do this at the dawn of the industrial age. This will give me a core of 6 cities. As they become metropolises will be true power houses. This will gain the advantages of the OCP - Metropolis while allowing for the advantages of close in placement in the early expansion times.

The main disadvantage will be that I will probably disband some decently built up cities, but I will try to minimize that by careful building.

The one warning here is that the comparative advantages are map size dependent (as well as difficulty to a lesser extent). On a huge or large map I intend to try for 2 rings of widely spaced cities (with closer pack in early game) and then my RCP ring.

My basic intent is to make sure that my RCP ring is placed such that some of the cities in it would have been past the Optimum City Count.

 

[Svar]

Originally posted by jeffelammar


The main disadvantage will be that I will probably disband some decently built up cities, but I will try to minimize that by careful building.

When I identify cities that I will later abandon I rename them Extra # so I don't waste shields on improvements. All I use these cities for is unit production, mostly settlers and workers

 

[GhengisFarb]

This RCP has some of the same elements of the Camp Strategy system, although the screenshots look similiar to the Pre-Fabricated Settlement strategy I used to utilize in some of my first Diety level games.

Camp Strategy Thread

 

[Bamspeedy]

Ok, here was my attempt at using this new RCP style:


I hope I calculated the distances right. I found my own easy way of figuring the distance, but I was pulling my hair out at first trying to figure it out.

As you can see, the first ring is pretty dense, but I needed to utilize the lake as best I could (only fresh water source on the whole island). This might be a good model for those that like to do an ICS kind of start. The capital itself, is a little squished, but every other city is utilizing a full 12 tiles (I missed 1 grassland square-but the wheat was more important, and a few odd water tiles are unused).

Standard map:
Four cities at 2.5 distance.
Ten cities at 7.0 distance.
Five cities at 11.0 distance.

There normally would be more chances for sites, but of course the shape of the island dictated the number of sites.

Here is some figures for later on in the game.
In democracy:
First ring: ~2% waste with factory, courthouse, WLTK day (just 1 shield)
~6% waste without courthouse, factory, or WLTKD (~2 shields out of 30+).
The first ring built the pyramids, Hanging Gardens, and all the wonders after the ancient era (monarch level)

Second ring: 10% waste if you have factory, courthouse, WLTKD 20% without any of these.
If you include the capital, that is 15 cities with 10% or less waste for a map where 16 cities is the 'optimal' number.

Third ring: 30% waste with factory, courthouse, WLKD, 63% waste without any of those.

Note, these % would get better when you get Hoover's (I had no rivers on my island ) or other factory enchancements, and when you get police stations built.

If this was a pangea map, where I wouldn't be so restricted in how many cities to put in that 3rd ring, I can imagine you could have double the optimal number of cities and the worst city would have less than 50% corruption, without a forbidden palace needed.

 

[Bamspeedy]

Ok, I had trouble figuring the distance and trying to decipher the formula, so I have included my 'easy' version of figuring out the distance. ilovetoast's color coded chart helped for up to distance 5, but I was lost after that. I was getting confused because I would get different distances depending on which path I took to get there-until I realized one way wasn't really the 'shortest' path.

Picture that the map is divided in quadrants, with the capital being the very center, and the map is divided going straight north to south, and east to west. (The yellow lines in my screenshot).

You need to see which tile the quadrant would go in, to be able to accurately count the tiles and give you the 'distance' of that tile. If the tile is to the NW of your capital, then count how many tiles you should go NW to be parallel to it, counting each tile as 1. Then when you are parallel to it, go NE/SW towards it and add on .5 for each tile. (More easily explained in the screenshot).

If the tile is 'straight' east or west, south or north of your capital, then just count each tile on the way there as 1.5.

 

[DaviddesJ]

Originally posted by Bamspeedy
If the tile is to the NW of your capital, then count how many tiles you should go NW to be parallel to it, counting each tile as 1. Then when you are parallel to it, go NE/SW towards it and add on .5 for each tile.

This is certainly valid. Another approach, which some might consider easier and others harder, is to move diagonally (at a cost of 1.5 for each step) until you are in a straight line with the city, and then straight toward it (at a cost of 1.0 for each step).

So, in your example, Konya is 4*1.5 + 1 = 7.0. Denizli is 4*1.5 + 5 = 11.0.

I tend to use a hybrid of these two methods: I use your method if the city is "nearly" along the NE/SW or NW/SE line. If it's "nearly" N/S or E/W, then I move diagonally first.