What is mimimum number of turns for 6 cities?

25 turns for 6 city ("Improved DaveMcW Algorithm"):

City-1: produces sttler-2, settler-3, settler-4

city-2: produces worker, settler 5

City-3: produces settler 6

City-1 produces 3 settlers:

city 2: up by turn 8 + 2 = 10
city 3: up by turn 8 + 7 + 2 = 17
city 4: up by turn 8 + 7 + 7 + 2 = 24

City-2 produces a worker and a settler:
Founded at turn 10.
Worker first:
Marble hill city center plus grassland deer gives 3F 4P.
Expansive boosts it to 3F 5P.
You get the first worker in 40/8 = 5 turns.

Start working on settler at turn 15
City 5 is up by turn 15 + 8 + 2 = 25.

Summarize:
Worker: produced by turn 15
City 5: up by turn 15 + 8 + 2 = 25

City 3 produces settler 6.
Founded at turn 17
Receive a worker at turn 17, start chopping
produces a settler in 6 turns (turn 23)

City 6: up by turn 17 + 6 + 2 = 25

All 6 cities are up by turn 25.

Can someone top this?
 
[HIJACK]

Anybody care to do this with a more realistic, plausible setting that doesn't leave you bassackwards and defenseless -- perhaps one not involving 6 Marble Plains Hill cities?

[/HIJACK]
 
Assuming a valid upper bound assuming ideal conditions for expansion will be found, there will be a baseline to which compare your rex. I don't find that useful because the assumptions made are practically impossible, but maybe someone will consider that useful information.
 
@OTAKUjbski

For realistic setting I guess Joao settling on coastal plains hill, with forested/stone/marble plains hill and two fish in first ring is a possible (excellent) start. Could even add plains forest deer (2F2P) or plains hill forest deer (1F3P) to the mix, and allow for 10+ forests for chopping.
 
We are seeking theoretical upper bound.

While 3F4P start is not common, 1F4P and 2F4P are quit common:

(1) Settling one a hill (2P) or elephant (2P);
(2) Working on a Hill (1F2P or 3P).

This can easily generate 1F4P, which is not far away from the 3F4P upper bound. Remember 4P is the more important factor here.
 
[HIJACK]

Anybody care to do this with a more realistic, plausible setting that doesn't leave you bassackwards and defenseless -- perhaps one not involving 6 Marble Plains Hill cities?

[/HIJACK]

Actually the 25-turn requirements are:

(1) Joao II;
(2) City-1 starts with 3F4P or 0F6P;
(3) City-2 starts with 3F4P plus a forest for chopping;
(4) City-3 starts with 3F4P or 0F6P;

so only three Marble Plains Hill cities.
 
I say you spend use some worker turns to build some plains hill copper mines (or grassland hill). That's 9 production, imperialistic becomes 13, maybe chopping overflow would alter things.

In the longrun, settlers make +7 (without a copper mine) to +9 production. Workers give +2*average number of mines built+chopping rate. Normal speed it's 20 for 3 turns 1 move, so 5 a turn, fast 3 moves, 15 hammers?
 
My gods though. What do you do with six cities and no tech?

Besides choke that is.

-abs

LOL.

Obviously, you are behind in tech at this point.

The logic is this: there are somthing that grows linearly, there are somthing that grows exponentially; in a long run, the exponential functions will win over linear functions.

Early expansion is for exponential growth.

Unit production is the best example, though same applies to tech and gold:

Within x number of turns:

(1) 1 city produces y1 units.

(2) 1 city becomes 2, 2 cities produce (y1 - z1) + y2 units;

(3) 1 to 2, 2 to 4, 4 cities produce (y1-z1') + (y2 - z2') + y3 + y4.

...

If x is large enough, z1, z1', z2, ... are small, so here is what you have:

(1) 1 city produce y1 units.

(2) 1 city becomes 2, 2 cities produce y1 + y2 units;

(3) 1 to 2, 2 to 4, 4 cities produce y1 + y2 + y3 + y4.

Again, the assumption is x is large enough.
 
We are seeking theoretical upper bound.

But what is the application of this theoretical upper bound?

The necessary conditions outlined in this thread are nigh to impossible and are only likely to be seen in a World custom built for this application, so the thread as it stands serves no real applicable purpose.

This is more the type of question I would like to see answered now that we know what perfect conditions can yield:

What is the mimimum number of turns to meet these conditions:
  1. 6 cities of any size
  2. All cities defended by at least 1 military unit
... given these starting conditions:

  • Normal speed
  • All cities settled on Plains Hills
  • All cities possess at least two 0F3P, 1F2P, 2F1P, 3F0P1C tiles and a resource of your choice
  • You start with Mining and a starting tech of your choice
  • You start with Imperialistic and a trait of your choice
Those circumstances are still a little fantastic but still realistic enough to serve as an acceptable 'litmus test'.

so only three Marble Plains Hill cities.

Seeing as how that's still an equally outrageous circumstance, I still fail to see the application here.

The logic is this: there are somthing that grows linearly, there are somthing that grows exponentially; in a long run, the exponential functions will win over linear functions.

Early expansion is for exponential growth.

But it is still very possible for linear growth to beat exponential growth given a finite period of time -- which is exactly what we have to work with in Civ4's turn system.

Adding even more plausibility for linear growth to come out on top: this level of REX'ing is very likely to start your Civ at least 30+ turns behind with an economy teetering on the brink of stagnation.

I haven't crunched the numbers, but I have a feeling a REX of this magnitude in a real-game situation (especially at Monarch+) will leave your Civ too far behind and starting with too little to actually catch up.


-- my 2:commerce:
 
>>
What is the mimimum number of turns to meet these conditions:
6 cities of any size
All cities defended by at least 1 military unit
<<

Theoretically speaking,

(1) If it takes N turns to get 6 cities up, it takes N+2 turns for all cities to be defended by at least 1 military unit.
(2) In addition, it it takes N + 2 + 5 turns for all cities to be defended by at least 1 military unit and each city has at least 1 worker.

So
Turn 25: 6 cities + 1 worker.
Turn 27: 6 cities + 1 worker + 6 warriors.
Turn 32: 6 cities + 7 workers + 6 warriors.

It might be faster than this because of overflow.
 
My brain hurts.

But in all seriousness I agree with OTAKUjbskim; practically speaking the hypotheticals in here are a tad unrealistic.
 
If someone goes to the trouble of working out using highly optimistic setting, we can take the work done and apply it to more realistic setting. So if you have some patience and interest in the matter, even the hypothetical scenario you aren't interested in will yield results you can use further.
 
Oh, don't get me wrong. I understand the value of a theoretical meter-stick.

I also grok the difference between linear and exponential growth. However the theory that going exponential is good needs to be offset by the realization that city maintenence starts your exponential growth curve at a negative point on the X axis relative to the linear equation.

Basically yes, I get that lots of cities are good.

I also get that at turn 25 our research will be almost totally not done yet. I also get that our upkeep will be so high we'll be very lucky to be able to research at 20%. Twenty percent of a very low total as well since we won't have a lot of tech for gaining commerce on tiles, nor worker turns to have built those improvements.

So clearly the maximum isn't anything anyone would want to achieve in a game, except perhaps to prove they can perhaps. However knowing it's 25 turns does allow us to ask comparison questions that can guide our actual gameplay. Questions like . . .

Does anyone care to analyze how many turns are desirable to add to our 25 turn minimum?

How much commerce do we need to support a 6 city empire, and if we know that how many turns does it take to get it?

From there we could begin to grapple with, "If I have this many turns to use that are not devoted to REXing how should I spend them?"

I think some of those are very good questions to get theories for. So I definitely think knowing 25 turns is possible is useful. I just think we want to follow that line of reasoning further and consider what is optimal.

-abs
 
If someone goes to the trouble of working out using highly optimistic setting, we can take the work done and apply it to more realistic setting. So if you have some patience and interest in the matter, even the hypothetical scenario you aren't interested in will yield results you can use further.

Not saying I'm uninterested or impatient. On the contrary I like these discussions and appreciate the efforts of those more knowledgeable than me and with more motivation to explore possibilities in civ 4. Just pointing out my concurrence with one of the posters. Come to think of it absimiliard also summed up pretty much what I think as well; the theoretical foundation allows further discussion on what is actually favorable for winning a game.
 
Delaying the settlement of the cities that will not generate settlers may help with the tech issue. There's still the whole question of defense, of course - but maybe that won't be so immediately urgent, as you have all of these settlers sitting around busting fog....
 
Compact 6 city empire where cities are very small (size 1-2) should have total maintenance of 8-15 gpt (from memory). This is still something we can manage.

For one, each city can generate two coins (city tile + 1 1cpt trade route - although as we might not have workers to connect cities only a lucky river will give us even one trade route).

And coastal tiles still generate two coins each. Again going back to Joao with two fish setup, we get 13 coins in the capitol from palace + tiles working those two fish. We can get a bit faster rex with unimproved plains hill forest deer or plains forest deer (haven't checked which one is better) but the two coins may be worth it. Also, if two other cities are coastal (and it should be so, as we're settling compact empire and thus from coastal capitol at least two cities will be settled along the coastline) they may generate coastal commerce, maybe even seafood too.

Also, assuming we do train workers in all such cities that don't participate in settler builds, we should have one worker per city soon enough. This means improved tiles for each city to work. Hopefully we'll have some early commerce resources around.

I've once expanded to 8 cities without a single library or cottage. Sure I did kill my economy - for a while. Climbing up from that pit took time, and I admit 8 was indeed too many. Six sounds reasonable still.
 
>>
Does anyone care to analyze how many turns are desirable to add to our 25 turn minimum?

How much commerce do we need to support a 6 city empire, and if we know that how many turns does it take to get it?

From there we could begin to grapple with, "If I have this many turns to use that are not devoted to REXing how should I spend them?"

<<

For transition, 3F4P can generate a settler in 8 turns, a very common 1F4P-start can generate a settler in 10 turns (7*10 > 65).

We will get to reality later. For the moment, I am not yet convinced this is best we can do by turn 32:

Turn 25: 6 cities + 1 worker.
Turn 27: 6 cities + 1 worker + 6 warriors.
Turn 32: 6 cities + 7 worker + 6 warriors.

We might be able to do much better. The upper bounds are easier to study than real situations.
 
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