Whipping + Granaries

[vale]

Oh and the comparison between a grassland farm and a plains hill in that city is pretty silly. At population 3+, you will always work the grassland farm regardless of your choice about the plains hill as the only other option is a coast which is strictly inferior from a production standpoint.

So the only time where there is a decision is at population 2. And thats a pretty non-decision decision when you have a happy cap of 11.

The choice between coastal tiles and plains hill might be more interesting if we were building more small ticket items (things that couldn't be 3+ pop whipped and especially things that are 1 pop whips).

 

[DaveMcW]

I agree in general it is often a good thing to maximise the number of tiles worked. But sometimes those tiles are weak like a desert or tundra hill or a tundra farm (2FC pre Biology). Would you whip away any of those before the happiness cap? If so, how do you decide whether using the whip on the citizen is more useful than working the tile?

http://forums.civfanatics.com/showthread.php?t=243558

 

[vale]

Actually you can do pretty significantly better using the plains hill upon reflection. Initially you again focus on growth. When the time is right (you want to grow to population 6 about the same time that you have 30 hammers put into the forge), you should switch to the plains hill instead of a coast. Whip the forge as soon as the 3 pop whip is available.

Now the rest of the production is 2 pop whips from population 4. General principles:

1. Whip so that the 3 population regrows in a turn.
2. Work on the larger items first. Slow build them until 2 turns before the whip and if they aren't ready for a 2 pop whip, switch to a barracks or harbor which are 2 pop-whippable with one turn of production invested after the forge.
3. Tile preferences 1. Clams 2. Farm 3. Hill

You should be able to finish everything by about turn 39 or 40 this way which saves around 10 turns off of no plains hill usage. You will have around 3 units stacked whip anger which is fine when there essentially is no immediate happy cap and you are operating at a low population like this.

Main point is that while larger whips are more efficient than smaller whips, city population and number of useful tiles has a bigger impact. So a 2 pop whip out of size 4 is more efficient than a 3 pop whip out of size 6 when there are only 3 good tiles in the entire city. The reason to avoid that in the early going obviously is the rapid decrease of the happiness cap as you quickly stack whip anger.

 

[UncleJJ]

Thanks for answering vale. I appreciate your efforts and largely agree with your eventual conclusions. There seems to be a development in your ideas as your study of the situation became more refined.

I'll post again tonight when I have some time to get my thoughts together. However, I don't think the comparison between the grassland farm and plains hill in this case is at all silly but instead makes the point with abundant clarity.

 

[vale]

The main point is that it is very unlikely you will be in a situation where at population 2 with 11 base happy cap where the plains hill is more attractive than a grassland farm. Growth is pretty important there because there are 3 productive tiles to work and only a population of 2.

Now if you gave me multiple plains hills and multiple grassland farms the question becomes more interesting and the correct answer almost certainly use a mix of them while you do as many low population whips as possible over time.

 

[UncleJJ]

Let me try to give some theoretical underpinning for what vale has discovered.

There are basically two configurations we need to consider in determining the long term hammer output of this city:

a) Work crab, farm and any number of coastal tiles, this gives +6F and 1H
b) Work crab, farm , mine and any number of coastal tiles, giving +4F and 5H (+1H with forge, +1H with OR )

The value of the food surplus is dependent on the size of the city and the size of the whip. We have 4 sizes of whip that make sense in this city, 1, 2, 3, and 4.

The minimum city size for a whip is then 2, 4, 6 and 8 and these should be used for maximum hammers. Except a case can be made for growing to size 3 for a 1 pop whip as that allows the farm to be worked for more food output per turn. Here is a table of whipping efficiency in terms of hammers per food.

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

This shows that for small size whips of size 1 and 2 it is better to not work the plains hill. But it seems that for larger whips the hill becomes competitive as the city needs to grow larger and hence less efficient. The plains hill effectively converts 2F to 4H and that is slightly more efficient than a size 4 whip from size 8 and slightly less efficient than a size 3 whip from size 6.

But as vale has already mentioned the actual size of whip is affected by the number of hammers already invested in a build. For every 30 hammers invested the whip size is reduced by 1. The forge and OR (if applicable) reduce this investment by 25% each. So the size of overflows from previous builds and how close we are to having enough hammers to reduce the size of the whip by 1 is an important consideration. It is slightly more efficient to build something that would normally need a size 4 whip by investing 30 hammers in it and making a size 3 whip. So the plains hill can often be used to speed up building by reducing the need for growth and at the same time make the food

Once we know what the size of our next whip is likely to be (say we want to build a Drydock) we know we need either a size 3 whip, in which case grow the city to size 6 as fast as possible (work a coastal tile instead of the hill) or we can use overflow hammers plus the hill and a size 2 whip from size 4 (or size 5 if already that size). We can see from the above chart that each food is worth 2.14H if that whip is from size 6 and 2.40H if from size 4. So we can improve the value of food (in the granary and stored as population) by using the plains hill at a slightly inefficient rate of 2H per food as this improves the efficiency of the whip and hence the overall efficiency of the city (whip and hammers combined). From this we can see that there is a very complicated interaction between working the plains hill and reducing the size of the whip. The effects of the forge and especially OR (which only applies to buildings) complicate this interaction even further.

Generally speaking this city should be kept at the smallest size possible for the whips required (and not grown to its happiness cap as vale initially said in post #160) if what we are concerned with is maximising hammers per turn. Growing larger significantly reduces the hammer value of food, for instance for every 1 larger a city grows a size 4 whip increases in cost by 4 food. Once some useful infrastructure has been installed this city might be grown larger if it used to give some increased trade income and commerce from the coastal tiles.

I hope those of you that like bean counting can appreciate the efforts of vale and myself to resolve our little dispute. I think it has been informative. The game can get very technical and even a simple city like this one can teach us a lot that would otherwise be obscured by the detail of a more complex situation. I conclude that we can generalise what we’ve found here and a grassland farm is more productive than a plains hill in any small city as long as we have a granary and intend to whip in the future.

 

[Artichoker]

With this in mind, grassland hills are pretty high on the list, with 1F3H instead of 4H for the plains hill.

Even plains farms are pretty good, with 2F1H. Better yet, plains farms next to a river, with 2F1H1C.

 

[DaveMcW]

With this in mind, grassland hills are pretty high on the list, with 1F3H instead of 4H for the plains hill.

Even plains farms are pretty good, with 2F1H. Better yet, plains farms next to a river, with 2F1H1C.

You missed the 8 pages we spent proving grassland hills are very good.

Plains farms are only one step up from unhappy citizens, and can be sacrificed to the whip whenever you have enough of them.

 

[Artichoker]

For lower levels of food surplus (say, for instance +4F), I think a case for plains farms (and by extension, grassland forests) can be made here.

With a food surplus of +4F per turn, a comparison can be made between a size 4 city and a size 6 city with two extra plains farms.


Assume a whip cycle of periodic 2-pop whips for both cities. Throughout the whip cycle, the first city fluctuates between size 4 and size 2, while the second city fluctuates between size 6 and size 4, with the extra two tiles being assigned to two plains farms.

The 2-pop whip produces 60 hammers per whip
in both cases, but the differences between the two cases are:

1) The first city grows more quickly from size 2 to size 4.

2) The second city gains an extra +2H per turn from the two plains farms.

The amount of food required to grow from size 2 to size 4 is 12+13 = 25, and the amount of food required to grow from size 4 to size 6 is 14+15 = 29 (I think this is consistent with UncleJJ's table in post #166). With a food surplus of +4F, this means that the first city can regrow in 6.25 turns, whereas the second city can regrow in 7.25 turns.

With a whip output of 60 hammers, this means the first city is converting food at 60/6.25 = 9.6 hammers per turn, and the second city is converting food at 60/7.25 = 8.27 hammers per turn. But the second city gains +2H per turn from the two plains farms, for a total of 10.27 hammers per turn...which is more than the 9.6 hammers per turn for the first city.

If the food surplus were doubled to +8F, however, the result would be different. In this case, the food conversion rate would be 2*9.6 = 19.2 hammers per turn for the first city, and 2*8.27 = 16.54 hammers per turn for the second city. Even with the +2H from the plains farms, the second city would have only 18.54 hammers, a bit less than the first city.

The break-even point would be where the +2H of the larger city cancels out the improved whip efficiency of the smaller city. This would happen when the difference in food conversion rate equals 2H per turn, or:

60*s/25 = 60*s/29 + 2
2.4s - 2.069s = 2
s = 6.04

So, for cities with food surplus higher than +6F, the 2-pop whip from size 4 is preferable. With food surplus lower than +6F, the 2-pop whip from size 6 with plains farms is preferable. At +6F, they are nearly even.

One interesting extension of this result is regarding grassland forests. In some cases, especially when worker turns need to be maximized, it may often be desirable to leave grassland forests standing for some time during the early game. Since grassland forests require no worker improvements to exist, they can be temporarily utilized for their whipping potential during the early game, and then cut down after Mathematics is gained, for the extra chopping potential.

Another obvious advantage of the 2-pop whip from size 6 with grassland forests is the option to take a 3-pop whip when necessary. The application of this is likely to occur when access to Forges is not available for some time, until the necessary tech is gained, but city buildings still need to go up before that time.

 

[Artichoker]

Some food for thought...the original comparison was between a coastal tile (with yield +2F) and a mined plains hill (with yield +4H).

The real question is whether the comparison of 1F vs. 2H favors the 2H, in some situations. According to the previous discussion, there are indeed situations (even for small cities) when 2H is favorable to 1F.

With grassland forests, the yield is +2F1H. Now, take just the 1H...that is 1/4 of the hammers of a mined plains hill. This means that the comparison made in the previous discussion can be extended to 0.5F vs. 1H.

If 1H can indeed be better than 0.5F during whipping, then the yield of a grassland forest will be, in some situations, better than 2.5F. It might not be as good as a grassland farm (3F), but at least the grassland forest can exist without the help of worker improvement.

 

[Artichoker]

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

These numbers show that both 2-pop and 3-pop whips from size 6 have food-to-hammer ratios of higher than 2.

Therefore, the yield of a grassland forest (2F1H) is better than a mined grassland hill (1F3H) when using these conversion rates.

The utility of the grassland hill and plains hill, therefore, is more limited to situations related to adjusting the timing of the build, but not on a regular basis.

It should also be noted that the breakoff point for the superiority of grassland forests (as compared to grassland hills) seems to happen at city size 6.

 

[DaveMcW]

These numbers show that both 2-pop and 3-pop whips from size 6 have food-to-hammer ratios of higher than 2.

Therefore, the yield of a grassland forest (2F1H) is better than a mined grassland hill (1F3H) when using these conversion rates.

The utility of the grassland hill and plains hill, therefore, is more limited to situations related to adjusting the timing of the build, but not on a regular basis.

It should also be noted that the breakoff point for the superiority of grassland forests (as compared to grassland hills) seems to happen at city size 6.

So given two cities with a happy cap of 5 (and HR, to allow unlimited whipping):

1 non-irrigated rice, 4 mined grassland hills

1 non-irrigated rice, 4 grassland forest

... the forest + whipping produces more hammers? I thought for sure the hills would win.

 

[Ibian]

Easiest way is to look at whipping efficiency at a given size.

At size 5 and whipping when you grow to size 6 each food is worth 2 hammers. A farm is 6 hammers (3 food), a grass forest is 5 hammers and a grass mine is 5 hammers.

At size 10 and whipping when you grow to size 11 each food is worth 1.5 hammers. A farm is 4.5 hammers, a grass forest is 4 hammers, and a grass mine is 4.5 hammers.

So from size 1-4 its better to work grass forests, at size 5 move them to grass mines, and at size 10 move farms to grass mines.

 

[UncleJJ]

Spot on Ibian, exactly how I think about it . So Dave I'd expect the two cities to be exactly the same productivity as long as the rice and grassland forest were grown to size 6 and whipped for 1 pop. Obviously a bigger whip removes some of the tiles we'd be working and reduces output but produces the item several turns quicker. Generally grassland forest should be chopped and turned into grassland farms (if they can be irrigated). Farms are much more productive than hills or forests in this situation, and hopefully the rice would be irrigated too

------

The posts by Artichoker have inspired me to do a bit more work on my spreadsheet and I have produced these tables for this situation. The tables give the effective hammers gained for working the type of tile at that city size assuming the city will be whipped once the city grows to the size needed to be whipped. This means for a 2 pop whip that all the food produced at size 1, 2, and 3 contribute the same marginal rate for the whip at size 4. Similarly the food produced at size 5 and below are treated as equivalent for the 3 pop whip at size 6.


The effective hammer output for the two types of hill are then calculated by subtracting the hammer value of the food needed to work them from their actual hammer output.

	Early game 1 pop whip			
	G farm	Gr hill	Pl hill	Pl farm
1	 2.73 	 0.27 	-1.45 	1.00
2	 2.50 	 0.50 	-1.00 	1.00
3	 2.31 	 0.69 	-0.62 	1.00
4	 2.14 	 0.86 	-0.29 	1.00
5	 2.00 	 1.00 	 -   	1.00
6	 1.88 	 1.13 	 0.25 	1.00
7	 1.76 	 1.24 	 0.47 	1.00
8	 1.67 	 1.33 	 0.67 	1.00
9	 1.58 	 1.42 	 0.84 	1.00
10	 1.50 	 1.50 	 1.00 	1.00
11	 1.43 	 1.57 	 1.14 	1.00
12	 1.36 	 1.64 	 1.27 	1.00
13	 1.30 	 1.70 	 1.39 	1.00
14	 1.25 	 1.75 	 1.50 	1.00
15	 1.20 	 1.80 	 1.60 	1.00
16	 1.15 	 1.85 	 1.69 	1.00
17	 1.11 	 1.89 	 1.78 	1.00
18	 1.07 	 1.93 	 1.86 	1.00
19	 1.03 	 1.97 	 1.93 	1.00
20	 1.00 	 2.00 	 2.00 	1.00

	Early 2  pop Whip			
	G farm	Gr hill	Pl hill	Pl farm
1				1.00
2				1.00
3	 2.40 	 0.60 	-0.80 	1.00
4	 2.22 	 0.78 	-0.44 	1.00
5	 2.07 	 0.93 	-0.14 	1.00
6	 1.94 	 1.06 	 0.13 	1.00
7	 1.82 	 1.18 	 0.36 	1.00
8	 1.71 	 1.29 	 0.57 	1.00
9	 1.62 	 1.38 	 0.76 	1.00
10	 1.54 	 1.46 	 0.92 	1.00
11	 1.46 	 1.54 	 1.07 	1.00
12	 1.40 	 1.60 	 1.21 	1.00
13	 1.33 	 1.67 	 1.33 	1.00
14	 1.28 	 1.72 	 1.45 	1.00
15	 1.22 	 1.78 	 1.55 	1.00
16	 1.18 	 1.82 	 1.65 	1.00

	Early 3 pop Whip			
	G farm	Gr hill	Pl hill	Pl farm
1				1.00
2				1.00
3				1.00
4				1.00
5	 2.14 	 0.86 	-0.29 	1.00
6	 2.00 	 1.00 	 -   	1.00
7	 1.88 	 1.13 	 0.25 	1.00
8	 1.76 	 1.24 	 0.47 	1.00
9	 1.67 	 1.33 	 0.67 	1.00
10	 1.58 	 1.42 	 0.84 	1.00
11	 1.50 	 1.50 	 1.00 	1.00
12	 1.43 	 1.57 	 1.14 	1.00
13	 1.36 	 1.64 	 1.27 	1.00
14	 1.30 	 1.70 	 1.39 	1.00
15	 1.25 	 1.75 	 1.50 	1.00
16	 1.20 	 1.80 	 1.60 	1.00

I think it is interesting that there is not a great difference in the efficiency of the 2 and 3 pop whips but of course larger whips reduce the unhappiness penalty for a given hammer output and are easier to manage.

These tables show that it is more efficient to use food, work farms and whip at city sizes around 5 rather than work hills. As city sizes grow hills become increasingly competative. As Ibian notes the breakpoint that is memorable and a useful rule of thumb for deciding which tiles to work for maximum output is size 10 ;when a grassland farm = grassland mine and a plains farm = plains hill.

 

[Artichoker]

The posts by Artichoker have inspired me to do a bit more work on my spreadsheet and I have produced these tables for this situation. The tables give the effective hammers gained for working the type of tile at that city size assuming the city will be whipped once the city grows to the size needed to be whipped. This means for a 2 pop whip that all the food produced at size 1, 2, and 3 contribute the same marginal rate for the whip at size 4. Similarly the food produced at size 5 and below are treated as equivalent for the 3 pop whip at size 6.

You can also produce food at size 4 when in 2-pop whip mode, or at size 6 when in 3-pop whip mode. The effect of this is (I think) the extra food you have accumulated at the pre-whip pop level is carried over to the food storage at the post-whip pop level.

What this means is that working more food tiles at size 4 (for 2-pop whip) or size 6 (for 3-pop whip) actually contributes toward the growth of the city from 2 to 3 (for 2-pop whip) or from 3 to 4 (for 3-pop whip).

The effective hammer output for the two types of hill are then calculated by subtracting the hammer value of the food needed to work them from their actual hammer output.

	Early 3 pop Whip			
	G farm	Gr hill	Pl hill	Pl farm
1				1.00
2				1.00
3				1.00
4				1.00
5	 2.14 	 0.86 	-0.29 	1.00
6	 2.00 	 1.00 	 -   	1.00
7	 1.88 	 1.13 	 0.25 	1.00
8	 1.76 	 1.24 	 0.47 	1.00
9	 1.67 	 1.33 	 0.67 	1.00
10	 1.58 	 1.42 	 0.84 	1.00
11	 1.50 	 1.50 	 1.00 	1.00
12	 1.43 	 1.57 	 1.14 	1.00
13	 1.36 	 1.64 	 1.27 	1.00
14	 1.30 	 1.70 	 1.39 	1.00
15	 1.25 	 1.75 	 1.50 	1.00
16	 1.20 	 1.80 	 1.60 	1.00

I think it is interesting that there is not a great difference in the efficiency of the 2 and 3 pop whips but of course larger whips reduce the unhappiness penalty for a given hammer output and are easier to manage.

I agree, and I think these tables are very informative!

These tables show that it is more efficient to use food, work farms and whip at city sizes around 5 rather than work hills. As city sizes grow hills become increasingly competative. As Ibian notes the breakpoint that is memorable and a useful rule of thumb for deciding which tiles to work for maximum output is size 10 ;when a grassland farm = grassland mine and a plains farm = plains hill.

Also very significant is the breakpoint of when a grassland forest (or plains farm) = grassland hill...size 5. This is very significant because the utility of existing grassland forests, which don't require worker improvement, can be maximized in this situation.

As more technology is gained, chopping efficiency is increased (upon gaining Mathematics), and also chain irrigation becomes available (upon gaining Civil Service). Before that approximate point in time, grassland forests can claim a very active role in a city's economy.

 

[vale]

Conditions needed for food to hammer ratios to be the end all about whip efficiency:
1) there is essentially no happy cap so that you can whip essentially whenever the mood strikes rather than worrying about things like stacking whip anger
2) there is no pressing reason to grow large in the given city
3) there is a guaranteed way to be able to perform your whip at will for the size you want

I'll say it again: the food to hammer ratios are very misleading in the early going when condition 1 below is very unlikely to be met. In that case the religious farm user better make sure that he accounts for the hammer value of the -2 food each unhappy citizen is making.

 

[Ibian]

Sure, but thats theorycraft for ya. It usually exists in a vacuum.

 

[vale]

Except it doesn't have to exist in a vacuum. The early game with static happiness cap is very easy to analyze and leads to much a different conclusion than the idea that a grassland farm is spectacular. There is a limit to how much food your city can absorb while regrowing from a whip. At some point, the inefficiency of supporting unhappy population overwhelms the food value of the grassland farm. Good food deficit tiles become much more important to whipping efficiency there especially in the presence of good food resources.

 

[Ibian]

Right. So decrease growth in order of descending hammer efficiency. Simple enough.

 

[Artichoker]

Except it doesn't have to exist in a vacuum. The early game with static happiness cap is very easy to analyze and leads to much a different conclusion than the idea that a grassland farm is spectacular. There is a limit to how much food your city can absorb while regrowing from a whip. At some point, the inefficiency of supporting unhappy population overwhelms the food value of the grassland farm. Good food deficit tiles become much more important to whipping efficiency there especially in the presence of good food resources.

This strengthens the argument for grassland forests and plains farms.

According to my knowledge, whip unhappiness goes away after 10 turns. To maximize the utility of grassland forests, city size should go no higher than 6.
This means that for a 3-pop whip from size 6, the amount of food need to regrow is 13+14+15 = 42.

In order to prevent the accumulation of unhappiness, the whip cycle should be at least 10 turns. With these numbers, it means that the amount of surplus food should be no higher than:

42/10 = 4.2

So, let's assume a tile configuration of one rice (4F), and the rest grassland forests (2F1H). Adding the 2F from the city tile, this equals a food surplus of +4F per turn.

So, the whip cycle for a 3-pop whip from size 6 is:

42/4 = 10.5 turns

This means that after the 10-turn period of unhappiness ends, there is a 0.5 turn period of happiness, and then the next whip happens.