Whipping cycles

[DaveMcW]

130 in 10 turns from raw production alone.

Some options to use the 2 surplus:
Find 2 and work 2 more grassland hills for 60
Whip 1.33 citizens for 40
Work 2 plains hills for 20

 

[OTAKUjbski]

Some options to use the 2 surplus:
Find 2 and work 2 more grassland hills for 60
Whip 1.33 citizens for 40
Work 2 plains hills for 20

Your math is always spot on, but you seldom give mathematic proof, explanation or clarification for some of the more ambiguous statements.

For example, how do you "Whip 1.33 citizens" and what math did you use to come up with either of those numbers .?

Am I missing something I should already know?

 

[Quechua]

Edit: whoah I completely missed your point.

No mines please, they don't add anything to the discussion

 

[Quechua]

Here is a city that has the kind of terrain I'm thinking of.

Oyzar also provided a save for BtS, for people to experiment with. I can't check it out but I trust he got the idea right.

 

[MyOtherName]

Ok, this is the kind of thing I'm looking for. Unfortunately, I think your numbers are a little off, the granary doesn't always give 15, it gives half of level you are growing from (e.g. 13 growing from 3 to 4). And also you're going to have to deal with an unhappy citizen growing back to 20/30 at the end of the cycle.

I'm assuming that this is correct: the granary stores 15 food when the city grows from 5->6, and doesn't shrink after whipping. Rereading it, it now seems slightly ambiguous, and I need to test for myself sometime. *sigh*

Also, I made sure that I spent 10 turns at size 3/4, so that when I grow back to size 5, the citizen is not unhappy. This method seemed to be slightly better than constantly staying at size 3/4 and whipping 2 pop instantly upon hitting 5.

 

[Quechua]

It looked like you were always using 15 regardless of the pop size. When I tried to test what I though you were writing out I ended up getting lower numbers. But I'll try again.

 

[KrikkitTwo]

OK, in Pig pen you have 2 factors
1. Tiles produce 3
2. Hammers and food can be exchanged at a 1:1 ratio by tile shifting

So
5 pop= 11 h or f
4 pop= 10 h or f

so
over ten turns
5 pop =110
4 pop =100 - 14 (if you whip immediately after going from 4 to 5) +30

so 116 from slavery on a 1 whip basis

2 whip basis

5 pop = 110
3 pop = (9 per turn, 1 guaranteed hammers) going from 14 to 26 food so 2 turns
4 pop = 8 turns at 10

so
2 turns at 3 pop =18
8 turns at 4 pop =80
=98 - 26 to grow to 4 -28 to grow to 5 +14+13 from granaries +60 from whip
=98 - 27 +60
=71 + 60
=131

So whip
1 pop= gain of 6
2 pop = gain of 21

Mines seriously complicate this by making the food:hammer ratio from tile switching less than 1:1 (easier to get hammers, extra food becomes expensive)


The ~2h:1f conversion is accurate, but a few things need to be considered
1. you are giving up one or more tiles for up to 10 turns... tiles usually have a positive net output of 1 (2 if mines, 3 in the modern Era)
2. food becomes more expensive when tile switching with mines
3. Happiness limits how Much food you can put into whipping to recover the lost food from not tile working



So slavery seems to work as a regular part of a cities production if your best 'stagnant production' tiles[the ones that will be whipped away] are Minimal net benefit "tiles"

Citizens (10 production) -1 net
Engineers (20 production) 0 net
Tundra/Desert Hill Mines (30 Production) +1 net
Also Plains Forests (20 Production) +1 net

The last two are less certain

 

[Quechua]

Krikkitone you are saying pretty much the exact same thing as me.

I didn't bother to check your numbers as your final results of 11.6 and 13.1 hammers are roughly the same as what I got. Note the first case is barely any better than not whipping.

But the thing is you're numbers are ~13 per turn for the 2-pop whip. That is far less than the naive 17, and the not-quite-as-naive 16.

Why do you still say ~2h:1f is accurate, when you make a very similar point as me?

 

[KrikkitTwo]

^ because with a Happy cap of 5 the whip populations must always be less than 5 (because there will always be 1 extra whip unhappiness)

Also the ratio is about accurate, But there are additional factors that come in
1. the loss of population that can't be fully recovered for 10 turns (because it is unhappy) which will normally have some cost

2. the limitation on how much whipping can be done to recover it

Imagine one is whipping Modern Armor in a similar modern city...all flatland with a mix of Modern Farms/Workshops (non state property, non river)
[4 total hammers or food on each tile]


Modern Armor =120 Base Hammers (Factories) allow whipping of 4 pop at a time

go with a happy cap of 12, and a Pig pasture

pop 12 = 29 hammers or food
pop 8 = 21
pop 9 = 23
pop 10 = 25
pop 11 = 27

food required
8->9 = 36 - 21 granary (from 11->12 transition)
9->10 = 38 - 18 granary
10->11 = 40 -19
11->12 = 42 -20
Each is achievable in 1 turn so the 'output' is
8=21
9=23
10=25
11=27*7
total = 258
The whip did
120 hammers - 78 food to recover the pop... the Ratio still is ~1.6

so total for whipping an extra Modern Armor every 10 turns=
300 base hammers
but
290 base hammers for the 12 pop

The problem is the loss of 1 hammer producing tile for 10 turns due to the happiness limit drop.
You need to offset the loss of that 1 tile with the gain in Hammers from the whip ratio.


We are probably talking about the ratio in different senses.

The fact is, the Ratio is NOT what matters in Slavery, but the Total production of your last best stagnant hammer tile.

So it is 'whip size' - 'food cost'* - 10 turns of last best stagnant hammer tile (ratio matters in the first two terms)

* 'Food cost' = food to recover from the whip v. how many hammers you have to give up to get that food.

Using Dave's example (after mining hills and farming grassland+ with 6 happy cap)
6 pop = 17 h (1 pl, 4 gr)
5 pop = 15 h (2 pl, 2 gr)
5 pop grow = 2 f 13 h (4 gr)
4 pop = 3 f 10 h (3 gr)
4 pop grow = 9 f 1 h (3 farms)

4->5 =28-16 12 food
5->6 =30-14 16 food

so
4 grow = 1
4 limit =10
5 grow 8 turns =13*8=104

so
60 whip+115 normal=175 h
straight pop 6 is 170 h
net gain =5 can also determine that from

benefit =60
cost from food= ~30 (from ratio)
loss of advanced tile for 10 turns = 20 (mines =2 benefit per turn)

so you get a benefit of ~10 or 1 per turn. (its actually 0.5 per turn but that's because it doesn't work perfectly)

looking at the best case for slavery
all Flat Grassland+a Pig tile, 4 pop limit
4 pop stagnant = 4 h (3 citizens)
3 pop 'stagnant' = 2 f 3 h (2 citizens)
2 pop 'stagnant' = 4 f 2 h (1 citizen)

2->3 = 24 -13 = 11 3 turns
3->4 = 26 -12 = 14 7 turns

60 whip + 6 + 21 = 87 hammers
or
30 whip +30= 60 hammers
or
0 whip + 40 = 40 hammers

2 or 4.7 extra hammers per turn... and not all of the excess food was used, most was used to support citizens

 

[Quechua]

Again, your analysis of your hammer output is very similar to the way I'd approach it (which is subtly different from the post quoted from DaveMcW and OTAKUs spoiler earlier, but I don't wanna get into this). So I'm pretty sure I'd agree with your numbers.

The thing is I'm focusing on the real loss in efficiency you get from:

1) Losing productive population
2) Possibly having unhappy citizens (which don't show up in your case)
3) Using your food surplus to work food-poor terrain, which is equivalent to reducing your surplus so as to avoid unhappy citizens. Everyone that has provided a detailed analysis so far has done this. Since this converts food to hammers in a 1:1 ratio it is less than the potential from whipping.

I don't think you can get around these factors. You haven't gotten around them, and you point out a couple of them. The thing is, you are getting the ~1:2 ratio (or it's equivalent in your second example) during a step in your analysis...I'm looking at it after the analysis is over, when we have the real hammer per turn values.

 

[KrikkitTwo]

^ the advantage of the ~1:2 ratio is that it is constant for a particular population

It only looks at the Food cost of slavery (food:hammers) not the happiness cost. (which is more complicated and depends on what tiles are available)

 

[Quechua]

Yes it has advantage in your analysis. You need to know how much food to grow back to your original size, and you need to know how many hammers you get from the whip. These numbers make a ratio that only depends on the population size.

I am talking about the complicated stuff though.

 

[vale]

Here is a totally different approach to measuring whip efficiency. First we need to understand the general principle that tiles and specialists are just means for converting population-turns to other units. In this case, the units we are most interested in food and hammers. As some have pointed out before, when stagnating, the production value of a tile is equivalent to its food surplus value plus its hammer value. So a mined hill of any type is a +2 production tile, a forest of any type is a +1 production tile, a pigs of any type is a +4 production tile, a citizen specialist is a -1 production tile, an unhappy citizen is -2 production etc.

On normal speed, when you whip X people out of a city with population Y and a granary, you are converting 10X + XY - X(X+1)/2 food and at least 10 population-turns into 30X hammers. In our production terms that is a net gain of 20X -XY + X(X+1)/2. So if the lost population-turns were providing less than that, we have gained. Except not quite because I have neglected to mention an important point: Tiles worked while in "growth" mode might be significantly different than those worked in "stagnate" mode and this can significantly impact the analysis(5 turns of irrigated corn is just as good as 10 turns of a mined grassland hill and conversely, 10 turns of farmed grassland is only as good as 5 turns of a mined plains hill).

Therefore, there are several important factors determining what makes whipping efficient or not:

1. Presence or absence of granary/sacrificial altar
2. Size of city: larger decreases production created by whipping.
3. Size of whip: larger increases production created by whipping.
4. High food surplus tiles: decreases population-turns lost in larger whip cases.
5. Good food surplus tiles: increases population-turn efficiency during regrowth.
6. Sufficient numbers of good food deficit tiles: increases population-turn efficiency during stagnation.

The net conclusion though is that there is no magic formula for saying things like "it is always inefficient to whip away a mined grassland hill above population 6" and such statements are untrue. For instance, consider a city with unlimited grassland hills, two 6 food specials, a granary and a happy cap of 7, and go through the various options for optimizing production. Any whipping option that creates a situation where you can work both 6 food specials most of the time is going to blow away a stagnation option.

I should have mentioned this before but edited to add that any option that includes allowing unhappy citizens for any significant length of time is crazy and should be avoided. This is why having good food deficit tiles is important for both stagnation options and whipping options.

 

[Quechua]

^ This is a great way to think about it, and I think everyone that is confused by what I was saying should look at it (I didn't think of the nifty X,Y formula though ). Thanks for providing a very clear summary.

 

[UncleJJ]

A very interesting analysis Vale. That can almost certainly shed some fresh light onto the problem. I do have a problem with some of the conclusions that this approach is leading you to.

Except not quite because I have neglected to mention an important point: Tiles worked while in "growth" mode might be significantly different than those worked in "stagnate" mode and this can significantly impact the analysis(5 turns of irrigated corn is just as good as 10 turns of a mined grassland hill and conversely, 10 turns of farmed grassland is only as good as 5 turns of a mined plains hill).

In particular it is hard to see how a plains hill can be considered more productive (in strictly hammer terms) than a grassland farm for a small size city. You seem to be equating 1 food to 1 hammer somewhere in your reasoning so that 4 hammers / turn is somehow twice as good as 3 food / turn.

But for a city at size 5 I would say 1 food is worth 2 hammers since that is the Slavery conversion rate. So by my reckoning the farm produces 3 food (and costs 2 food) which is equivalent to 6 hammers, and the hill produces 4 hammers (and costs 2 food) which is only equivalent to 2 food. The farm therefore produces a net 1 food but the hill has no net gain. Therefore I'd say the grassland farm is more "productive" than the plains hill... One of us is obviously wrong, but I can't see where either you or I are making a mistake. Can you explain?

 

[Diamondeye]

I appreciate the work done by OTAKUbjski, but I myself simply can't find the motivation for those stunts with numbers. Not reading them, either. And definately not understanding them

 

[OTAKUjbski]

I appreciate the work done by OTAKUbjski, but I myself simply can't find the motivation for those stunts with numbers. Not reading them, either. And definately not understanding them

I think that sums up how I feel right now. There's a lot of good math and examples all over this thread, but it seems to be more overwhelming and confusing than enlightening.

The net conclusion though is that there is no magic formula for saying things like "it is always inefficient to whip away a mined grassland hill above population 6" and such statements are untrue.

There are no hard-and-fast, always-applicable rules. Exceptions always exist. But there have to be "rules of thumb" ... otherwise it's just over-complicated.

So, I think the goal of any analysis should be to break it down to the lowest common denominator in such a way that makes it easy for anybody to understand and apply.

Based on what I've observed, it appears DaveMcW's "rules" are generally applicable; and following them will result in a correct decision a majority of the time. Those kinds of rules make it simpler to comprehend and more likely to be helpful in a game than nearly any formula.

However, I don't think that was the original direction of this post. (In fact, I think the original goal was proving whipping isn't near as effective as originally portrayed -- something I feel has already been done.)

That being said, I feel like "when to whip" and "when not to whip" is starting to come together for me, but I have no idea how to express or prove it yet with a formula or even rules. If I do figure out how to put my thoughts into words and numbers so they can be checked, this'll be the place I do it.


-- my 2

 

[vale]

Can you explain?

Sure. First it is important to keep in mind that this is just to discuss the efficiency of the whip. If we spend 30 food to get 60 hammers, at some point during the next 10 turns we need to get back that 30 food to prepare for a subsequent whip. However, excess food may be putting us into an unhappy state which is grossly inefficient and thus may be unwanted.

Therefore, my assumption was that each whip cycle will start and end with the same population level and stored food. If that assumption is met, then the net whipping production plus the tile production (food + hammers -2 for each tile) during the cycle will turn out to be exactly the total hammers produced during the cycle. Similarly when stagnating, since you are balancing your food to make it sum to 0, the total production of the tiles worked (in terms of food + hammers - 2 again) will give exactly the total hammers produced.

So if you are whipping away a couple of plains hills, but have to work grassland farms to regrow the population in time for a new whip cycle, you are losing more than the population-turns as you are sacrificing production efficiency during your regrowth. Your intuition about grassland farms being better than mined plains hills is based on your experience that those tiles are necessary to regrow from a whip which is true. That doesn't mean its a wonderful thing that you are having to sacrifice turns on a mined plains hill to work it.

Let me just do the math both ways on a city that has a grassland pastured pigs, unlimited mined plains hills, unlimited mined grassland hills, and unlimited grassland farms. Happy cap will be 6, population is 5 with 29/30 food stored. The non-whip option will work the pigs and nothing but mines, taking care to grow on the first turn by working enough of the grassland mines and then storing food or stagnating at population 6 either while working pigs and mines exclusively to get a total of 168 "production" (At least one of that production is food).

The whip option will whip 2 population immediately, work one turn of just pigs and farms to grow back to population 4, one turn of pigs, farm, mined plains, mined grassland to grow back to population 5 as efficiently as possible, then will work 7 turns of pigs and only grassland hills to store food while producing efficiently and finally one turn of pigs, a plains hill, and the rest grassland hills to get the last food necessary to complete the cycle, still while working as efficiently as possible. The total production (this one is all in hammers) is 174. So the net result of alot of micromanagement was a gain of 6 hammers. But note though that we did our regrowth in the most efficient way possible, front-loading all our inefficient farm usage to quickly remove lost population-turns, then moving back to mines as soon as possible to avoid further inefficiency. We have gained 6 production, and we can break it down as follows:

33 gained due to slavery (27 food transformed into 60 hammers)
12 population-turns lost (2 on whip turn when population 3 vs 5, 2 on second turn population 4 vs 6, 1 on each subsequent turn population 5 vs 6).

But we were whipping away mines which technically only produce a net gain of 2 per population-turn, so we should only be losing 24 production due to population-turns lost.

Ok, but now we are losing some due to the relative inefficiency of working the grassland farms. Each turn of grassland farm is losing one production compared to the mine we would be working at stagnation, so the three farm turns cost us 3 more production.

33 - 24 - 3 = 6 bingo.

Based on what I've observed, it appears DaveMcW's "rules" are generally applicable; and following them will result in a correct decision a majority of the time. Those kinds of rules make it simpler to comprehend and more likely to be helpful in a game than nearly any formula.

Just to play Devil's Advocate here: This is a city that is not "exceptional" but one that violates this rule of thumb. I think the idea of never whipping away a mined grassland hill with a happy cap of 6 is closer to being always wrong than always right if a city like this is an exception. Even more crazy is the idea that killing off a plains forest is somehow a bad thing at happy cap 6. You would have to work very hard to produce an example where that is true. These rules are based on the idea that these tiles are magical machines that take as input food and give as output hammers when in reality, they take as input population-turns and give as output production. When starting with a flawed assumption, the conclusions are flawed as well.

 

[DaveMcW]

These rules are based on the idea that these tiles are magical machines that take as input food and give as output hammers when in reality, they take as input population-turns and give as output production. When starting with a flawed assumption, the conclusions are flawed as well.

Yes it's flawed, but not as flawed as you think.

The correct way to state it is: Tiles are expensive machines (average 30 to build, double production with granary) that take as input , , , and output production and commerce.

 

[vale]

The correct way to state it is: Tiles are expensive machines (average 30 to build, double production with granary) that take as input , , , and output production and commerce.

I ignored commerce since I just assumed we were interested only in maximizing hammers over time. If commerce comes into the mix we also have the cost in upkeep (both city and civ) that a tile consumes and the military support it provides. Going that route gets things way too complicated though since I'm not convinced that the formulas for city and civ upkeep have been nailed down precisely yet so I'm sticking to pure production analysis.