Cottages!!

[DaveMcW]

One contradiction I see. We say it's better to use extra food to run specialists (as opposed to plains), yet in the examples of say pig + lots of grasslands, 15 happiness cap, would you in the end have 14-15 cottages, 1 pig, or would you have 12 cottages, 1 pig, 2 scientists?

13 cottages, 1 pig, whip a building every time the city reaches size 15.

 

[vicawoo]

In that case you're better off working hills with pop 15.

City hammers per food
Size Whip1 Whip2 Whip3 Whip4
1
2 2.73
3 2.50
4 2.31 2.40
5 2.14 2.22
6 2.00 2.07 2.14
7 1.88 1.94 2.00
8 1.76 1.82 1.88 1.94
9 1.67 1.71 1.76 1.82
10 1.58 1.62 1.67 1.71

http://forums.civfanatics.com/showpost.php?p=6841824&postcount=166

You're doing a 24 food to 30 hammer conversion, so for say a 4 pop whip that's 90 food for 120 hammers, but then you lose tile yield while regrowing, which is at least 10 turns x at least 1 tile of production (20 food, 10 food 30 hammers, 0 food 40 hammers, etc). In fact compared to a 2 pop whip, (47 for 60), you could probably have swapped in 6 plains cottage tiles and be superior hammer-wise.

 

[DaveMcW]

1 pig
15 grassland
1 hill
6 plains

How many tiles are in this city?

 

[lightsedge]

Great post!

And the graphs by namliaM are very helpful. Think it's possible to graph whipping multiplier buildings at the happy cap vs. whipping them early (like the granary)? I imagine the spreadsheet gets a bit messy

 

[vicawoo]

Yeah I was going to add a side comment about that.

A bigger mistake is that a grassland tile doesn't produce 20 food, so I have to redo the example.

But the point remains, at higher population when mines are better yield than whipping, do you choose mines or specialists?

 

[DaveMcW]

Mines.

 

[lightsedge]

Hmmm, I guess the hammer from growing a town helps later on too (with Universal Suffrage civic)

 

[vicawoo]

Size 15 whip 4. You have a pig.
Now size 11, 21 food. At size 11, optimal growth is just cottages.
4 turns, size 12, 22+3 food. 19 food to size 13.
4 turns, size 13. 19+5 food. 22 food to size 14.
4 turns, size 14. 22+2 food. 24 food to size 14.
4 turns, size 15. 25 food.
So after 16 turns, you're back to before with +4 food. You've lost 40 turns of unworked tiles.

If you worked

Size 15 whip 2, you have a pig.
Now size 13. Food 23. 4 turns to grow.
Now size 14. Food 23+1. 4 turns to grow. (Must stall for potential 2*6=12 hammers from tile switching).
You've lost 14 tile turns.

If you worked 14 turns of a forest tile, and switched to plains you'd be ahead.

 

[vicawoo]

Ok, I'm pretty certain you're better off at large sizes you're better off working mines as opposed to whipping as a method of building commerce buildings.

My next question was whether it was better to work mines or make plains cottages (for more base commerce, but multipliers build more slowly).

I've done some formulas, and it looks like going mines is better than relying on plains cottages for hammers in almost any realistic situation. More details later.

 

[vicawoo]

Ok, in case anyone cares, calculating tradeoffs for building gold/science multiplier buildings:

Definitions

Spoiler :

Case 1 we use 1F1H cottages. Case 2 we use 1f3H tiles (grassland mines or workshops)
Let H = hammers of building you want to produce.
k be the number of switchable (as in grassland hill cottages versus mines, obviously depends on our food surplus) tiles
h1 = hammers produced per turn in case 1
= 1+k
h2 = hammers per turn in case 2
= 1 + 3*k
T1 = turns to produce building in case 1
= H/h1
T2 = turns to produce building in case 2
= H/h2
C = commerce sans our switchable tiles (defined under k)
R1 = total gold/beaker bonus from buildings, that is, if we are at 60% gold 40% beakers and we have a library and an academy and market, it's 40%*(.75)+60%*(0.25)
R2 = additional bonus from new building, so if it's a bank and the gold slider is 60%, it is 0.5*60%=0.30.
c1= "average" commerce produced by our 1F1H cottage tiles
c2= "average" commerce produced by our 1F3H tiles

Now our model:
since building with 1 hammer tiles is slower than building with 3 hammers tiles, the building will be done by time T1 in both cases but down in time T2 in case 2 but not case 1. So we calculate gold/beakers from start to time T2 and then calculate gold/beakers from time T2 to time T1, add them up and compare.

Math

Spoiler :

Gold/beakers in time T2:
Case 1 (plains cottages):
(C+k*c1)*(1+R1)*T2
Case 1 (mines):
(C+k*c2)*(1+R1)*T2
simple so far
Gold/beakers from time T2 to time T1
Case 1:
(C+k*c1)*(1+R1)*(T1-T2)
It's the same as in the first time period, since our building isn't done!
Case 2:
(C+k*c1)*(1+R1+R2)*(T1-T2)
since we finished our building in case 2 with our faster mine produced, we switched over to cottages production. Of course in theory we could produce another building, but this allows us to make a fair comparison and then by transitive arguments we can conclude to always use mines if that's the case.

Total by time T1
Case 1:
(C+k*c1)*(1+R1)*T1
Case 2:
(C+k*c2)*(1+R1)*T2+(C+k*c1)*(1+R1+R2)*(T1-T2)

Now we subtract out an invariant in both examples, that is, C*(1+R1)*T1
we're left with
Case 1:
k*c1*(1+R1)*T1
Case 2:
k*c2*(1+R1)*T2 + C*R2*(T1-T2) + k*c1*(1+R1+R2)*(T1-T2) =
k*(c2-c1)*(1+R1)*T2+C*R2*(T1-T2)+k*c1*R2*(T1-T2)+k*c1*(1+R1)*T1

subtract out k*c1*(1+R1)*T1 and we get a simple
Case 1:
0
Case 2:
k*(c2-c1)*(1+R1)*T2+C*R2*(T1-T2)+k*c1*R2*(T1-T2)=
k*(c2-c1)*(1+R1)*T2+(k*c1+C)*R2*(T1-T2)=
(k*c1+C)*R2*T1+(k*(c2-c1)*(1+R1)-(k*c1+C)*R2)*T2
so we're comparing
(C*R2+k*(c1*(1+R1+R2)-c2*R2))*T2 (advantage case 1)
with
(k*c1+C)*R2*T1 (advantage case 2)
or
h1*(C*R2+k*(c1*(1+R1+R2)-c2*R2)) (advantage case 1)
with
h2*(C+k*c1)*R2

I'll have to do the rest later, I made a different assumption.

 

[vanatteveldt]

@vicawoo

Thanks for sharing that with us

 

[JujuLautre]

These rules of thumb are great, but there is still something that troubles me:

Food score for various cottage terrains:

• -1 Plains (including forest)

Rule 6: Plains should be ignored until Scientific Method.

So, count plains? Or ignore them ?　And what about grassland hills ? They have the same output considering cottaging.

 

[DaveMcW]

Build the city before Scientific Method, build the plains cottages after Scientific Method.

 

[JujuLautre]

So if you have a city, like, 2 food resource (+4 and +3), 1 flood plains, 4 coast, 2 grassland, 11 plains, that makes enough food to feed 10 cottage pre-bio (+10 food including the city center for 1 flood plains + 2 grassland + 7 plains), but you just build 3 cottages and run specialists until SM ? Am I correct ?

What about grassland hills ? Build cottages on them before SM ? After ?

 

[DaveMcW]

1. Yes, with some whipping or mines mixed in too.

2. Mine grass hills before SM, only cottage them after all the plains are gone and commerce multiplier buildings are built. A city with lots of grass hills might work better as a production city.

 

[JujuLautre]

Thanks, I understand better. But then, don't you think that you term "cottage city" is misleading? I mean, you consider a city which will have 3 cottages for the main part of the game as a "cottage city", only because in the future it will have some more.

I'm sorry I can't get with a better name though, but perhaps it could be made more clear in your article.

 

[DaveMcW]

I mean, you consider a city which will have 3 cottages for the main part of the game as a "cottage city", only because in the future it will have some more.

If it looks like the game will be over before the cottage reaches town status, you should consider building a different tile improvement.

 

[JujuLautre]

I do not deny that fact. But I still have real trouble with the name "cottage city" if you use it for, potentially, cities which won't see any cottage of the game. I could be mistaken, but I'm quite confident I am not the only one in that case; thus my remark. After all, I understand now, so I'm OK myself

 

[Airefuego]

I am missing something, why is scientific method the key? I would have thought biology?

 

[noto2]

hey, Dave, I'm going to debate you about this plains business. Okay, until universal suffrage, cottages produce no hammers, so with commercial cities you either need to build hammer improvements (like mines) or use other means to build the infrastructure in the city (like health/happy improvements and commerce multipliers). Whipping is one way. I have found, however, that some of the best sites for cottage spamming are actually when I find a lot of plains tiles near food resources. This could either be special food resources, like pigs, wheat, etc, or flood plains. Working the food resources and farming grasslands and flood plains gives me surplus food to work plains cottages. What this means is that the city will grow very quickly at first from working those food tiles, and the citizens can then start working the plains cottage tiles quickly. Thus this city will have quickly growing pop, quickly maturing cottages, and each of those tiles also produces a hammer, so this city will generate some hammers from the cottages to be used to build infrastructure. In fact, if I can position a city to have high food yielding tiles and many flat plains tiles in the BFC I will usually use it as a commercial city. Working flood plains and brown plains at the same time is like working grassland tiles in terms of food, but you get extra hammers out of it. Cottage spammed cities are notoriously hammer poor, so placing the cottages on plains tiles alleviates that problem.