Whipping cycles

[KrikkitTwo]

Basic Rule:
Whip if you can't get enough 'decent' hammer tiles (2+ hammers)
(one of the reasons it goes well with cottage farms.. they typically don't have to many hammer sources)

Forest Farm for example..whipping is worth it, even with a 2 whip whipping cycle (since 3 requires things like Maces, Knights and Trebs... and then you should be using things like Workshops+Caste System if you want to turn 1 food into 2 hammers)

5-'stagnation' value= 2 f 6 h
4- 8 f + h ... 2 f 5 h 15 food required
3- 7 f + h..2 f 4 h 11 food required
26 food will be needed, Almost the 'minimum' produced, the Floodplains only needs to be used for 3 turns to get it like that
so
3 turns of pop 3 w/fp = 3*3h=9 h
7 turns pf pop 4 no fp= 7*5h=35
60h+44h= 104 h

with 1 whip it is
30+50= 80 and the floodplain isn't needed

The Real secret of slavery is that a food surplus of more than ~3 or so is pretty much useless, except to recover from large scale infrastructure whips of 4 or more... 2-3 is all you need for successful slavery unit production.. 1 good food tile (and several food neutral tiles)

 

[OTAKUjbski]

I'm probably going a little off topic based on where this thread has gone over the past few posts, but I think I finally figured out how to get my thoughts down as text.

My goal was to prove the value of Food as it relates to whipping in order to determine the value of a tile in hammers-per-turn when growing a city for the whip.

I started with the most obvious calculation (the "naive" one):

It takes a certain amount of food to grow to the next population. That population point grown to is worth a certain amount of hammers. The amount of hammers divided by the amount of food is the value of the food.

So we know at Normal speed, it takes 24 + 26 = 50 food to grow from population 2 to 4. If we then whip those to citizens, we gain 60 hammers. Thus, we have a yield of 60 / 50 = 1.2 hammers per food. For a city with a Granary, this HPF yield is exactly double.

So here is a chart of those values:

Values along the left represent the size of the city.
Values along the top represent the size of the whip.

POP	1	2	3	4	5	6	7	8	9	10	11	12	13	14
1														
2	2.72													
3	2.5													
4	2.3	2.4												
5	2.14	2.22												
6	2	2.06	2.14											
7	1.87	1.93	2											
8	1.76	1.81	1.87	1.93										
9	1.66	1.71	1.76	1.81										
10	1.57	1.62	1.66	1.71	1.76									
11	1.5	1.53	1.57	1.62	1.66									
12	1.42	1.46	1.5	1.53	1.57	1.62								
13	1.36	1.39	1.42	1.46	1.5	1.53								
14	1.3	1.33	1.36	1.39	1.42	1.46	1.5							
15	1.25	1.27	1.3	1.33	1.36	1.39	1.42							
16	1.2	1.22	1.25	1.27	1.3	1.33	1.36	1.39						
17	1.15	1.17	1.2	1.22	1.25	1.27	1.3	1.33						
18	1.11	1.13	1.15	1.17	1.2	1.22	1.25	1.27	1.3					
19	1.07	1.09	1.11	1.13	1.15	1.17	1.2	1.22	1.25					
20	1.03	1.05	1.07	1.09	1.11	1.13	1.15	1.17	1.2	1.22				
21	1	1.01	1.03	1.05	1.07	1.09	1.11	1.13	1.15	1.17				
22	0.96	0.98	1	1.01	1.03	1.05	1.07	1.09	1.11	1.13	1.15			
23	0.93	0.95	0.96	0.98	1	1.01	1.03	1.05	1.07	1.09	1.11			
24	0.9	0.92	0.93	0.95	0.96	0.98	1	1.01	1.03	1.05	1.07	1.09		
25	0.88	0.89	0.9	0.92	0.93	0.95	0.96	0.98	1	1.01	1.03	1.05		
26	0.85	0.86	0.88	0.89	0.9	0.92	0.93	0.95	0.96	0.98	1	1.01	1.03	
27	0.83	0.84	0.85	0.86	0.88	0.89	0.9	0.92	0.93	0.95	0.96	0.98	1	
28	0.81	0.82	0.83	0.84	0.85	0.86	0.88	0.89	0.9	0.92	0.93	0.95	0.96	0.98

As expected, the yield is higher as population decreases and/or the size of the whip increases. (This is nothing ground-breaking.)

However, even though this food:hammers ratio is accurate, it has a limit, because there is a limit to how often and how much you can whip.

So I simply want to use this value to determine how "good" my tiles are for whipping.

My first assumption is simple. If I'm working a tile while growing in preparation for the whip, its hammer value should be its amount of +FOOD times its HPF whip-yield (from the chart) plus any 'raw' production it grants.

So my test city is similar to other cities in this thread: cap of 5 with assorted food and production tiles:

Grassland Pigs
Flood Plains Farm
Grassland Farm
Grassland Forest
Grassland Hill Mine
Grassland
Plains Forest
Plains Hill Mine
Plains Hill Mine​

I want to whip 2 citizens at population 4 for 60 hammers, so my HPF yield should be 2.4. If this assumption is correct, then the individual hammer values of those tiles should be:

TILE			+FOOD	*VALUE	=WHIPHPT+RAWHPT		=HPT?
City Center		2	2.4	4.8	1		5.8
Grassland Pigs		4	2.4	9.6	0		9.6
Flood Plains Farm	2	2.4	4.8	0		4.8
Grassland Farm		1	2.4	2.4	0		2.4
Grassland Forest	0	2.4	0.0	1		1.0
Grassland Hill Mine	-1	2.4	-2.4	3		0.6
Grassland		0	2.4	0.0	0		0.0
Plains Forest		-1	2.4	-2.4	2		-0.4
Plains Hill Mine	-2	2.4	-4.8	4		-0.8
Plains Hill Mine	-2	2.4	-4.8	4		-0.8

There are plenty of tile combinations other than the ones here, but these are the values I used:

POP	TILE			+FPT	PROD	HPT?
	Grassland Pigs		4	0	
	Grassland Hill Mine	-1	3	
	Plains Forest		-1	2	
	Plains Hill Mine	-2	4	
	Plains Hill Mine	-2	4	
5	TOTAL			0	14.0	14.0

	Grassland Pigs		4	0	
	Flood Plains Farm	2	0	
2	TOTAL			8	1	20.2

	Grassland Pigs		4	0	
	Flood Plains Farm	2	0	
	Grassland Farm		1	0	
3	TOTAL			9	1	22.6

	Grassland Pigs		2	0	
	Grassland Hill Mine	-1	3	
	Plains Hill Mine	-2	4	
	Plains Hill Mine	-2	4	
4	TOTAL			1	12.0	14.4

There may be better combos than those, but that's not the point. Based on the amount of food (times 2.4) plus the raw hammer yield of the tile combos, I presume the hammer value of that combination is as posted under "HPT?".

Now let's observe one whip cycle:

TURNS	POP	+FPT	HAVE	NEED	PROD	HPT?
0	2	8	27	24	61	20.2
1	3	9	23	26	1	22.2
2	4	1	19	28	12	14.4
3	4	1	20	28	12	14.4
4	4	1	21	28	12	14.4
5	4	1	22	28	12	14.4
6	4	1	23	28	12	14.4
7	4	1	24	28	12	14.4
8	4	1	25	28	12	14.4
9	4	1	26	28	12	14.4
					158	157.6

The total amount of production during that cycle was 158 hammers.

The total amount of production assumed by my HPT? values during that cycle was 157.6. (I attribute the .2% inaccuracy to rounding.)


And that's where I leave it for now. I'm sure you could use similar charts to determine the best whipping tiles in a city to compare their whipping hammer yield to the non-whipping yield, but I'm not certain how to do that simply.

It took me long enough just to create that example, so that's the only one I have for now. I think it adequately shows that "naive" value of food does apply but only for a certain amount before the food-limit is reached.


At any rate ... I'm very open to critique and suggestions (especially to how to make any of this more applicable).


-- my 2

 

[ajil]

So whipping is most powerful when used in a cycle, but that requires you to be building the same thing over and over right? I am curious about the really early game, whipping libraries, granaries, settlers, courthouses, monastaries and such. I'm starting to think I hurt myself more than I help myself. I'm going to reread the thread and try to get a better handle on this stuff.

 

[Quechua]

@Otaku,
Your calculations are pretty much right, but more lengthy than they need to be. When you add up all the food modified with the ratio you just get the hammers due to the whip, this is because you already matched your food over the cycle to be exactly what you need. You never needed to use the ratio here. You planned out exactly which tiles you would work in advance (but forgot the city center btw), so you already take into account both the loss of population and diverting the surplus you can't convert through whipping to hammers at 1:1.

@ajil,
Don't forget that pretty much everyone here is assuming a granary. I'd say key points are avoiding 1-pop whips, growing back to recover lost population as quickly as possible, but not growing back so fast that you run into unhappiness.

 

[UncleJJ]

Excellent work OTAKUjbski You have clearly set out my position on this subject. You have saved me the trouble of writing this (which I was building up to in my irritation with the seeming inability of others to see things my way ). For that; I thank you

Your method and calculations correspond very closely with my own. My spreadsheet is laid out differently but the same numbers appear. I draw similar conclusions. Like you, for the purposes of Slavery, I see the food produced by a tile as "virtual hammers" with a value that varies dependent on city size and to a lesser extent the size of the future whip. Furthermore I see the city population and granary as a store of hammers that can be drawn on in opportune circumstances.

 

[Quechua]

UncleJJ,
I think you posted before seeing my response to Otaku, but do you see the role that picking the tiles to match the food exactly to the requirement has here?

By adding the food as production using the ratio (after you've already matched everything to work), you are just distributing the 60 hammers over the cycle in your calculation. It isn't necessary, you could just ignore the food and add 60 hammers to the normal production. This calculation is hiding the fact that you are losing production due to population loss and you are using a fraction of your surplus food for normal production to make things balance. What is considered the surplus that you multiply with the ratio? This tripped me up too at first, and is why I started this thread.

 

[UncleJJ]

Well Quecha, obviously I do see that you are matching the food production over the whipping cycle here and therefore you could simply average the "virtual" hammers over 10 turns. But that is a degenerate way of looking at Slavery and that is why it is causing you and many others problems understanding the true value of food as a source of hammers. As stated in my first post I consider the 5 happiness cap to be a situation that is to be solved as quickly as possible. The situation is mundane and of little interest to me.

The method so clearly expounded here by OTAKUjbski, which is so similar to my own , is a general method that applies throughout the game and in many circumstances. It allows us to understand the use of the whip when the city is not under the confines of a happiness cap and it can integrate city growth with whipping. It allows us to assess the productive power of a fishing village. It allows us to study a city with limited useful tiles. It allows us to study the conflicts in a SE between taking food for hammers (for infrastructure or units) and using food to run specialists to generate GPPs instead of hammers. It has many uses and clearly shows the productive power of each tile, both its actual hammer output and its virtual hammers.

That is why I am so suspicious of the statements made by Dave McW and by vale and maybe others in this thread. They do not seem to correspond to my own view of a tile's inherent productivity. Some of the problems with other people's work might be due to semantics or implicit assumptions they do not realise they are making. I don't know exactly what they are saying and I am not prepared to criticise explicitly until I am surer of their position.

Anyway; this is an amazingly interesting thread and I want to congratulate everyone and thank them for their contributions

 

[Quechua]

UncleJJ,
I don't think you understand what I meant about the 60 hammers. Otaku's calculation has the food worked out to be exactly what it takes to regrow the N food required to get the pop back. He then multiplies it by 60/N. He then adds up N food and magically it agrees with adding the 60 hammers, surprise?

This may help you if you want to use the ratio in a somewhat useful way to evaluate production:

You have 5 happy cap, 6 surplus food. You want to 2-pop whip for 25 every 10 turns. So 2.5 of your surplus will go towards slavery giving you 6. The other 3.5 will support deficit-terrain for 3.5. So our estimate for the surplus is 9.5.

This still ignores population loss, and unhappy citizens (which are necessary in some optimal strategies), and in some cities you can't convert the rest of your surplus in a 1:1 ratio. For the last two points consider my Forestfarm city.

EDIT:

Rereading your post, I think I should be a little fairer and use your situation. Say we have a fish and clam in a fishing village, for a surplus of 9. We have no hammer tiles in the city. After ten turns, the surplus gives us 90, and the best 6-pop whip takes us 16+17+18+19+20+21 = 111 to grow back from. So if we can grow to size 12 or greater, and don't whip for less than 6 pop, we can get the full production from the surplus that the ratio tells us.

I hope you realize though that these are very limited situations, and this way of thinking falls short in Otaku's example.

 

[OTAKUjbski]

@Quechua: I did factor the city center. I just didn't note it in the table. You'll notice all the total values are 2F 1P greater than the sum of the values listed.​

I must admit I speed read the last few posts, so forgive me if I repeat or overlook anything ...

Because I tend to skip important information, my example was intentionally lengthy.

You're right, I was simply dividing 60 hammers over the whipping cycle. Because, whether you whip at population 4 or 400, a whip size of 2 will always only yield 60 raw hammers.

You're also right that my example used exactly the right amount of food per cycle. But that doesn't matter. Whether you put the food in on this cycle or that cycle, any food that is "invested" into a population bound for the whip is worth a certain amount of hammers.

So if I put food into growing population #3 and #4, it doesn't matter if I use them immediately after growing to size 4 or when I'm about to pop size 5 or 73 turns from now when there's a Barbarian uprising threatening my city. When I whip population #3 and #4 at population 4, I'm "withdrawing" the hammers invested.

I'm not sure if this is what you were getting at, but the first whipping cycle begins one turn before the non-whipping cycle (which isn't really a "cycle" at all, but who's playing semantics?) The reason being is because the non-whipping cycle doesn't begin until the city has reached its happiness limit (in my example, 5). The whipping cycle on the other hand begins 1 turn before reaching the happiness limit (i.e., with the food bar full), which has already been proven as the optimal time to whip, because it minimizes the number of turns necessary at smaller populations.

That knowledge can actually be put to strategic use, which I'm not sure can be applied a hammer value. Knowing I can whip immediately upon reaching population 4 (instead of continuing to grow to pop 5 to attain peak non-whipping production levels), I can "withdraw" my hammers from whipping (and begin the "whipping cycle") long before I would otherwise be able to begin 'normal', non-whipping production.​

Vale mentioned earlier tiles aren't "magical machines that take as input food and give as output hammers".

But by using the hammer-per-food ratio as a calculation of a tile's hammer-per-turn value, I feel like I was able to show tiles can be viewed as magical machines.

If you're in the process of growing a city in preparation for a 2-pop whip at population 4, then every point of food you put into growing to population 3 and 4 is worth 2.4 hammers. Conversely, any tile costing food is worth 2.4 hammers less per food by comparison.

I think this is valuable information, because everybody talks about the production you lose by whipping down the population like it's an unfathomable value, when it's actually extremely simple to compare.

In my example, the 5-pop non-whipping production was 14.0 hammers-per-turn. My chosen 4-pop "raw" production was just 12.0 (while still growing at +1). My city had enough food to grow from pop 2 at the beginning of the whipping cycle to pop 4 in just two turns -- leaving 8 turns of 12.0 HPT for 12 * 8 = 96 hammers + 60 (from whipping) = 156 hammers per cycle / 10 turns per cycle = 15.6 hammers per turn.

Since 15.6 hammers per turn is greater than 14.0 hammers per turn, my city benefits from whipping.


But as noted before, these hammers are all "front-loaded". The beginning of any number of whipping cycles is going to have a lot of production, whereas the end will see a short lull in production (while regrowing). This doesn't mean there is any decrease in whipping's effect, because you have to remember the "non-whipping" cycle begins and ends at the same food value (one turn before growing to 5). This is simply the nature of the whip.


That was essentially my goal, because the ability to apply the hammer-per-food ratio directly to a tile allows us to easily compare a tile's whipping and non-whipping values without having to calculate how many turns we'll be at pop this or pop that.

In my example using the applied hammers-per-food value, I saw that the whipping HPT values at populations 2, 3 & 4 were all higher than the "raw", non-whipping HPT at population 5. In practice, knowing this means it doesn't matter how long the city stays at any of the lower population levels when using those food-per-turn levels.

The city clearly benefits.

On the other hand, if we saw any of the different values (especially the one for pop 4) were substantially lower than the 5-pop non whipping HPT, then we would know we need to look a little harder and make a few extra calculations to check the average HPT value over the course of the whipping cycle.


That's what I was looking for -- a simpler way to "glance" at a city's production levels to determine whether whipping does or might have a positive effect on the city's production level.


Damn, this post was long ...


-- my 2

 

[Quechua]

You're right, I was simply dividing 60 hammers over the whipping cycle. Because, whether you whip at population 4 or 400, a whip size of 2 will always only yield 60 raw hammers.

My point was your calculation was no different in spirit to the 'calculation' I did in my very first post. You are just adding up all the hammers from your production over all turns of the cycle. However, the 60 hammers from the whip you distribute over the turns by considering them to come from the food. It's trivial that using the ratio matches up with 60 hammers here (not in the derogatory sense).

You're also right that my example used exactly the right amount of food per cycle. But that doesn't matter. Whether you put the food in on this cycle or that cycle, any food that is "invested" into a population bound for the whip is worth a certain amount of hammers.

No, that's where your wrong. If you have more surplus food than you can whip in ten turns, you either have to deal with unhappy citizen or slow your growth. Both reduce the production value of the food surplus that you would estimate with the ratio....sometimes by a lot. What happens if you add any more food to your cycle? What are you considering to be your food surplus for the city?

Vale mentioned earlier tiles aren't "magical machines that take as input food and give as output hammers".

I don't think Vale's comment really got at the heart of why Dave's 'rules' are wrong. I have a post above that explains why viewing tile outputs this way isn't useful. The problem is you are considering the tiles in isolation. Dave's rules work when you can't switch any tiles after whipping. Oyzar most recently gave a counterexample of these rules, and it's not hard to find others.

If you want to use the ratio to estimate production in a city where you use large enough whips so that the unhappiness wears off before you grow back, you probably wont be too far off, especially if you aren't whipping away production tiles. That is not a general way to think about the production from food though.

Edit-
Let me put it this way...the food that goes into the food bar you can indeed recover as hammers at the ratio. But this is different than looking at a city and estimating that a 6 food surplus will give you ~12 hammers if you whip optimally. It is also different than thinking working farms rather than forests is necessarily giving you more production. It is also different than thinking that if I'm making a given amount of production with a whipping cycle, I can necessarily increase what I make (in future turns of course) by adding more food to the cycle.

 

[OTAKUjbski]

I'm starting to think we may have two different goals in mind. I'm not really trying to prove or even disprove anything. I want to find a quick, simple method for determining if a city can or will benefit from whipping. I'm not so much concerned about how much a city will gain from whipping and especially not concerned about whether that value meets up with previous assumptions or not.

All I want to know is "how do I easily determine if a city will benefit from whipping?"

My point was your calculation was no different in spirit to the 'calculation' I did in my very first post. You are just adding up all the hammers from your production over all turns of the cycle. However, the 60 hammers from the whip you distribute over the turns by considering them to come from the food. It's trivial that using the ratio matches up with 60 hammers here (not in the derogatory sense).

You're right. The spirit of our posts are nearly identical. However, when I read your original post, the only thing I take away from it is "whipping isn't as effective as most people will naively tell you". I think it's great to know that, but it fails to answer the question which immediately arises in response to that realization: "How do I know then if my city will actually benefit from whipping?"

That's all I want to figure out -- an easy way to answer that question.

The reason I included adding the "trivial" ratio is to show that you can apply the ratio at a per-turn and per-tile level -- which is how most people are already accustomed to making calcuations and decisions in Civ.

I believe finding a way to apply the ratio at this level is more likely to lead to a simpler method for determining if a city will benefit from whipping which doesn't include with X's and Y's and quadratic equations.

No, that's where your wrong. If you have more surplus food than you can whip in ten turns, you either have to deal with unhappy citizen or slow your growth. Both reduce the production value of the food surplus that you would estimate with the ratio....sometimes by a lot.

Well, we're talking two different languages on two fronts here:

"Deal with the unhappy citizen." I don't deny growing into unhappiness is grossly ineffective ... I simply don't care how gross. The hammers-per-food ratio is a baseline value that assumes the player knows what he's doing and is properly managing his happiness levels.

"Slow your growth." This, on the other hand, does not affect the hammer value of the food 'invested' into the whip. In fact, you're expected to slow the growth of the city. If you 'invest' too much food, then you move up to the 5th population point and either have unhappiness (see above) or move up to a completely different hammer-per-food value altogether.

What happens if you add any more food to your cycle?

In a majority of cases, increasing the amount of +food available during the whip cycle will increase the overall effectiveness of the whip cycle (This is not to be confused with increasing the effectiveness of the whip itself!).

Staying at the same city and whip size (and therefore keeping the same hammer-per-food value), more +food will increase the overall effectiveness of the whip for the reasons you've already pointed out. The amount of food you can invest in the whip at any particular city and whip size is a set, unchanging amount. Having more +food simply means you can more quickly meet that requirement and stagnate (or even starve) your city to increase raw production while waiting on the initial unhappiness to wear off.

This is my definition of a "whip cycle" -- the turns between the first whip and when the next whip can occur without stacking/compounding the whipping penalty. At Normal Speed, that number of turns will always be at least 10 for me but may be more give the amount of +food available and the size of the whip.​

Cases where too much +food doesn't increase the effectiveness appear to be those in which the city doesn't have good production tiles and/or is dependent upon too many food tiles to generate the maximum +food level (such as tons of Flood Plains).

What are you considering to be your food surplus for the city?

I may not understand the question, so forgive me if my answer is ambiguous or just plain wrong.

For my particular city, the food surplus was +6 at population 1 (working the Pigs), +8 at population 2 (Pigs & Flood Plains Farm) and +9 at population 3+ (Pigs, Flood Plains Farm & Grassland Farm).

However, the amount of +food available to the city doesn't affect the hammer-per-food value, so this doesn't really apply to my hammer-per-food ratios and how they apply to a tile's "whipping HPT". The only thing the amount of +food affects is how long you have to stay at the lower post-whip populations and how quickly you can "charge" the whip to begin working the city's high raw production tiles while waiting for the end of the whip cycle.

I don't think Vale's comment really got at the heart of why Dave's 'rules' are wrong. I have a post above that explains why viewing tile outputs this way isn't useful. The problem is you are considering the tiles in isolation. Dave's rules work when you can't switch any tiles after whipping. Oyzar most recently gave a counterexample of these rules, and it's not hard to find others.

I'm not trying to prove DaveMcW's rules, so I have no further comments related to his posted ideas.

If you want to use the ratio to estimate production in a city where you use large enough whips so that the unhappiness wears off before you grow back, you probably wont be too far off, especially if you aren't whipping away production tiles. That is not a general way to think about the production from food though.

The hammers-per-food value is not affected by what tiles you whip. Whether you whip a Plains Hill Copper Mine or a Tundra Hill, the amount of food required to grow the population points you whipped and the amount of hammers you gained from those population points does not change.

What whipping away production tiles does definitely affect is whether or not it's worth it to whip at all, because if you're whipping away too many good production tiles, then you're probably better off not whipping at all and sticking to "conventional" production methods.

Again, the hammers-per-food ratio ONLY changes if the size of the whip or the size of the city changes or if you get careless and allow your city to grow into and remain in unhappiness prior to the cracking of the whip.

Edit-
Let me put it this way...the food that goes into the food bar you can indeed recover as hammers at the ratio. But this is different than looking at a city and estimating that a 6 food surplus will give you ~12 hammers if you whip optimally.

6 food surplus = 12 hammers?

I hope that isn't how what I'm saying is being interpreted, because it isn't what I'm trying to say at all. In fact, that statement doesn't even make sense to me.

The amount of surplus food ultimately isn't what determines whether a city can benefit from the whip or not -- it's more the city's production tiles that determine that. For example, just +2 food in one city could be a whipping-godsend if that city has nothing but water tiles ... whereas +6 food may mean nothing (where whipping is concerned) to a city with Grassland Hill Mines and a Plains Hill Copper mine.

It is also different than thinking working farms rather than forests is necessarily giving you more production.

If you're in the process of growing a city for the whip and have to choose between a Grassland Farm and a Grassland Forest, working the Farm for +1 food will very likely generate more hammers via the whip than the Forest will in raw production.

In my example (whipping at 4-pop for 2), that +1 food is worth 2.4 hammers, which is more than the 1 hammer the Grassland Forest grants.

However, if you are already at the intended population size (4 in my example), then you've already met the required 'investment' and can work whatever tiles you want for the best raw production (such as how I worked high hammer tiles for just +1 food at population 4 while waiting for the end of the whip cycle).

Any additional food once the 'investment level' has been met does not help the current cycle. It will help the next cycle if you choose to whip again later; but for the time being, you've met this cycle's requirement and can stop worrying about food and growing.

It is also different than thinking that if I'm making a given amount of production with a whipping cycle, I can necessarily increase what I make (in future turns of course) by adding more food to the cycle.

As I think we've both pointed out, the only thing more food does for the whipping cycle is allow the city to more quickly meet the 'investment level' and revert to "normal production".

What enough +food more could mean to the city is the ability to grow one turn into unhappiness in order to whip for a larger amount (such as when your happiness limit is 5 and you grow 1 turn into population 6 in order to whip for 3 ... such as in MyOtherName's example from page 1).

However, I think you're right that making the initial assumption more food in the cycle equals more production can be very deceptive. There are more factors than simply how much +food the city has.


I'm sleepy ...


-- my 2

 

[Quechua]

Ok, fair enough. Maybe I had confused what you were saying with some other people in this thread who were speaking in similar language. You are only speaking about food going into the food bar, I am talking about food in tiles before we actually decide the optimal production path. As long as you don't confuse the two there's no problem.

If you want to find out when whipping is better than normal production, first consider the total hammers you will produce after 10 turns in your stagnant production configuration. Unless you can't avoid it, I think it's hard to find an example where it's best to whip in a longer cycle.

Also note the food necessary to grow back. If your city is 'nice', like in your example and in my first Pig Pen example, you can get the food necessary by switching plains mines to grassland mines etc, and you wind up costing yourself an equal amount of hammers at 1:1. If you can't do this, the analysis can get a little more complicated.

Now, we're also going to be losing some population we had in the stagnant configuration so that also costs us (losing a mine costs you 2, forest 1, etc), and if we have to have unhappy citizens that costs us (-2 for each unhappy population turn). If the costs are greater than the hammers from the whip, you shouldn't whip.

There are a lot of posts with examples using this style of analysis (Krikkitone in particular did a lot of them).

 

[OTAKUjbski]

You are only speaking about food going into the food bar, I am talking about food in tiles before we actually decide the optimal production path. As long as you don't confuse the two there's no problem.

Maybe I'm just still groggy from last night, but you clarify what you mean by "food in tiles before we actually decide the optimal production path"?

I should probably ask: what is your goal in all of this? (I think we might have the same goal just with different approaches.)

If you want to find out when whipping is better than normal production, first consider the total hammers you will produce after 10 turns in your stagnant production configuration. Unless you can't avoid it, I think it's hard to find an example where it's best to whip in a longer cycle.

MyOtherName's example extended the whipping cycle to 12 turns, and he was able to get a better average hammers-per-turn payout from whipping by doing so.

The reason he was able to extend the whipping cycle to gain more production was because the available production was low in comparison to the amount of +food present. If the Pig Pen city used in his example had less +food or better production tiles, extending the whipping cycle probably would not have been as beneficial (if even at all).

Also note the food necessary to grow back. If your city is 'nice', like in your example and in my first Pig Pen example, you can get the food necessary by switching plains mines to grassland mines etc, and you wind up costing yourself an equal amount of hammers at 1:1. If you can't do this, the analysis can get a little more complicated.

But what does that 1 food you gained by losing the 1 hammer gain you (or does it even)?

That's the question the hammers-per-food ratio answers ... and it answers it immediately.

Since I knew in my example one food was worth 2.4 hammers, it was easy for me to see a Grassland Hill Mine was worth 1.4 hammers more, since that food gained was going toward completing the whip cycle. Thus, making the switch was a simple decision made immediately.

I think we're both arriving at the same conclusion, though. To me, I just find it easier to make the comparison at the hammer-per-turn level.

Now, we're also going to be losing some population we had in the stagnant configuration so that also costs us (losing a mine costs you 2, forest 1, etc), and if we have to have unhappy citizens that costs us (-2 for each unhappy population turn). If the costs are greater than the hammers from the whip, you shouldn't whip.

This is another step I think I can 'skip' (it's actually just simplified) by using the hammers-per-food value/ratio.

Referring to my example from before, I knew my target hammers-per-turn was 14.0, because that's how much 'normal', non-whipping production I had at population 5.

While growing the city back at population 2 and 3, both amounts of +food resulted in a hammer-per-turn value greater than my non-whipping production (20.2 & 22.6 HPT respectively).

That was my first indicator whipping had promise. Even if it took the city all 10 turns to grow back to population 4, it was going to generate more hammers from whipping than from not whipping.​

However, it was clear I had "too much" +food, so I knew I'd be sitting at population 4 for a while completing the whip cycle. As it turned out, I was able to sit at +1 food and make 12 hammers at population 4 without growing the city. At 2.4 hammers per food, those turns spent at population 4 completing the whip cycle were worth 14.4 hammers per turn (still more than the non-whipping HPT).

That was my second (and final) indicator whipping would benefit the city. At all three population levels, I was making more whipping hammers-per-turn. At that point, it didn't matter exactly how many hammers I would gain per whipping cycle -- I just knew it was worth doing.​

And that was the question I wanted to answer ... "is it beneficial to whip this city?"

There are a lot of posts with examples using this style of analysis (Krikkitone in particular did a lot of them).

No offense to either you or Krikkitone, but those examples always feel over-complicated to me.


Let's do this ... give me a sample city. It can be any population with any tiles, and I'll use my 'method' to answer the question "should this city benefit from whipping?" Likewise, you can use yours (put it in a spoiler tag, plz) to do the same thing.

I'm entirely certain we'll both arrive at the same conclusion, but I'd like to see if my method really is as simple as I'm making it out to be.

 

[Quechua]

MyOtherName's example extended the whipping cycle to 12 turns, and he was able to get a better average hammers-per-turn payout from whipping by doing so.

The reason he was able to extend the whipping cycle to gain more production was because the available production was low in comparison to the amount of +food present. If the Pig Pen city used in his example had less +food or better production tiles, extending the whipping cycle probably would not have been as beneficial (if even at all).

Not exactly. When you work out his method without making the granary error you do get a higher number than ~13, but that's because he's 3-pop whipping. Vicawoo did this example in 10-turns and got a higher number, though he also makes a mistake. I did the example myself (and didn't post it) using 2 unhappy citizens and got 14.4 if I recall. I wouldn't be surprised if I also made some math error too though.

Let's do this ... give me a sample city. It can be any population with any tiles, and I'll use my 'method' to answer the question "should this city benefit from whipping?" Likewise, you can use yours (put it in a spoiler tag, plz) to do the same thing.

I'm not convinced at all that the ratio is useful for this, so I'd be happy if you came up with a simpler way than me.

The city has only grassland mines and grassland farms. I'm 2-pop whipping at size 4, cap 5.

Spoiler :

Since we're only switching between 2 tiles, I'll use an exchange of 2~3 instead of the usual 1:1, which also works. It takes 25 to recover costing us 37.5. Each lost pop, either farm or mine, costs us 1.5. We're at 2 for 1 turn, 3 for 2, for 14 lost population-turns. So 60 - 37.5 - 14*1.5 = 1.5 more than non-whipping. The 1.5 means we either end the cycle with +1 or -1,+3.

 

[OTAKUjbski]

I'm not convinced at all that the ratio is useful for this, so I'd be happy if you came up with a simpler way than me.

The city has only grassland mines and grassland farms. I'm 2-pop whipping at size 4, cap 5.

Spoiler :

Since we're only switching between 2 tiles, I'll use an exchange of 2~3 instead of the usual 1:1, which also works. It takes 25 to recover costing us 37.5. Each lost pop, either farm or mine, costs us 1.5. We're at 2 for 1 turn, 3 for 2, for 14 lost population-turns. So 60 - 37.5 - 14*1.5 = 1.5 more than non-whipping. The 1.5 means we either end the cycle with +1 or -1,+3.

My initial reaction is that this city will not benefit from whipping. Why? Grassland Hills. Even at 2.4 hammers per food, a Grassland Hill Mine costs 2.4 but gains 3 (net gain of 0.6). The net gain from whipping should be 0 or negative to expect any whipping benefit.

But let's see ...

(This post has a lot of text but only because I want to be clear on each thought process and calculation. The "short" version I do is only a few lines but makes no sense if you don't understand what the numbers mean or how I arrived at them. The "short version" is the text I've kept to the right.)

At pop 5, I'll have to switch between working:

City Center	+2F	1P
Grassland Farm	+1F	0P
Grassland Farm	+1F	0P
Grassland Hill Mine	-1F	3P
Grassland Hill Mine	-1F	3P
Grassland Hill Mine	-1F	3P
TOTAL@5	+1F	10P

-and-

City Center	+2F	1P
Grassland Farm	+1F	0P
Grassland Hill Mine	-1F	3P
Grassland Hill Mine	-1F	3P
Grassland Hill Mine	-1F	3P
Grassland Hill Mine	-1F	3P
TOTAL@5	-1F	13P

( 10 + 13 ) / 2 = 11.5 non-whipping HPT (this is the target)​

Whipping at 4 for 2 = 2.4 hammers-per-food.

At population 2: 10.6 whipping HPT​

City Center	+2F	1P
Grassland Farm	+1F	0P
Grassland Farm	+1F	0P
TOTAL@2	+4F	1P

4 * 2.4 + 1 = 10.6 whipping HPT

At population 3: 13 whipping HPT​

City Center	+2F	1P
Grassland Farm	+1F	0P
Grassland Farm	+1F	0P
Grassland Farm	+1F	0P
TOTAL@3	+5F	1P

5 * 2.4 + 1 = 13 whipping HPT

At population 4: 15.4 max whipping HPT​

City Center	+2F	1P
Grassland Farm	+1F	0P
Grassland Farm	+1F	0P
Grassland Farm	+1F	0P
Grassland Farm	+1F	0P
TOTAL@4	+6F	1P

6 * 2.4 + 1 = 15.4 whipping HPT

But since I know I can't maintain +6F the whole time, I need to consider a couple more options:

At population 4: 13.6, 11.8 & 10.0 HPT​

City Center	+2F	1P
Grassland Farm	+1F	0P
Grassland Farm	+1F	0P
Grassland Farm	+1F	0P
Grassland Hill Mine	-1F	3P
TOTAL@4	+4F	4P

4 * 2.4 + 4 = 13.6 whipping HPT

City Center	+2F	1P
Grassland Farm	+1F	0P
Grassland Farm	+1F	0P
Grassland Hill Mine	-1F	3P
Grassland Hill Mine	-1F	3P
TOTAL@4	+2F	4P

2 * 2.4 + 7 = 11.8 whipping HPT

City Center	+2F	1P
Grassland Farm	+1F	0P
Grassland Hill Mine	-1F	3P
Grassland Hill Mine	-1F	3P
Grassland Hill Mine	-1F	3P
TOTAL@4	+0F	4P

0 * 2.4 + 10 = 10.0 whipping HPT

So far, it doesn't look good at all. 10.6 HPT for one turn at pop 2 and 10.0 HPT at pop 4 for what is likely 5 or 6 turns looks real bad.

If I had to make a quick decision in a game based on the information I already have, I'd say no.​

But let's work it out and see what happens. If there is a gain, I expect it to be minimal. I'll start the cycle at population 4 with 22 of 28 food (given the city, this is exactly 1 turn from pop 5).

TURN	POP	+FPT	HAVE	NEED	PROD	TOTAL_PROD
0	2	4	22	24	61	0
1	3	5	14	26	1	61
2	3	5	19	26	1	62
3	3	5	24	26	1	63
4	4	6	16	28	1	64
5	4	0	22	28	10	65
6	4	0	22	28	10	75
7	4	0	22	28	10	85
8	4	0	22	28	10	95
9	4	0	22	28	10	105
						115

115 / 10 = 11.5 hammers per turn, which is exactly what we'd make not whipping.

If the Grassland Farms were riverside, or if we had Flood Plains Cottages to work in lieu of the Farms, then we'd gain no production but a little commerce.

But, there's another option (and likely the one you used). Whipping is better when done with the food bar full. So I'll start the next exercise at population 4 with 27 of 28 food in the bar.

TURN	POP	+FPT	HAVE	NEED	PROD	TOTAL_PROD
0	2	4	27	24	61	0
1	3	5	19	26	1	61
2	3	5	24	26	1	62
3	4	6	16	28	1	63
4	4	4	22	28	4	64
5	4	0	26	28	10	68
6	4	0	26	28	10	78
7	4	0	26	28	10	88
8	4	0	26	28	10	98
9	4	0	26	28	10	108
10	2	4	26	24	61	118
11	3	5	18	26	1	179
12	3	5	23	26	1	180
13	4	6	15	28	1	181
14	4	6	21	28	1	182
15	4	0	27	28	10	183
16	4	0	27	28	10	193
17	4	0	27	28	10	203
18	4	0	27	28	10	213
19	4	0	27	28	10	223
						233

233 / 20 = 11.65. That's just a 0.15 HPT gain over non-whipping.

0.15 * 10 = +1.5 hammers per cycle.

Sure enough, we both arrived at the same numbers.​

EDIT: Could you check this example for accuracy? I extended the whipping cycle to 12 turns in order to whip at 6 population for 3 points, and it appears I squeezed out an extra 0.15 hammers per turn (or another +1.5 hammers per 10 turns).

Spoiler the turn by turn of it all :

TURN	POP	+FPT	HAVE	NEED	PROD	TOTAL_PROD
0	3	5	16	26	91	0
1	3	5	21	26	1	91
2	4	6	13	28	1	92
3	4	6	19	28	1	93
4	4	6	25	28	1	94
5	5	0	17	30	10	95
6	5	0	17	30	10	105
7	5	0	17	30	10	115
8	5	0	17	30	10	125
9	5	0	17	30	1	135
10	5	7	17	30	1	136
11	5	7	24	30	4	137
						141

141 / 12 = 11.75 hammers-per-turn

That's 0.25 HPT better than non-whipping at population 5 and 0.15 HPT better than whipping at population 4 for 2 on a 10 turn cycle.

I'd like to point out for practical purposes, though, that it would take 23 of these cycles to catch up to non-whipping production, because the beginning of this cycle is 6 turns after the beginning of the non-whipping cycle (which equates to 69 hammers behind).

However, I think your 2F ~3P only works if switching between two types of tiles ... and even then only if you're switching between Grassland Farms and Grassland Hill Mines. I'm curious to see how you make the conversions when using a variety of tiles.

That being the case, even though I don't completely understand your math, it certainly took up less space on the screen.

Can you do that same math for me given only the following tiles (again, happiness limit at 5 whipping at 4 for 2):

Grassland Pigs
Flood Plains Farm
Grassland Farm
Grassland Forest
Grassland Hill Mine
Grassland
Plains Forest
Plains Hill Mine
Plains Hill Mine​

These are the same tiles from my last lengthy example, so I already know my answer. I just want to know how your method approaches the issue, because it's starting to look just as simple as mine.

 

[OTAKUjbski]

This is off-topic given the numbers and the calculations, but I think it's worth noting in favour of Whipping.

A whipping cycle can begin at the beginning of the food bar.

In practice, this means the early whipping cycle can begin a few turns before the non-whipping cycle.​

The whipping cycle can also begin at the end of the food bar.

In practice, this means the optimal whipping cycle always begins one turn before the non-whipping cycle.​

In both cases, the whipping cycle's production comes sooner and is also "front loaded", which is to say its production comes at once at the beginning of the cycle.

In practice, this means whipping results in units/buildings more quickly, which we all know can mean the difference between getting the jump on your neighbour and not getting the jump.​

I no longer believe whipping's primary benefit is increasing productivity (though it has the potential). I believe the whip's benefit is quicker productivity.

-- my 2

 

[Quechua]

I'll use standard 1:1 ratio. We need 25, costing 25. With the pigs and floodplain farm we can cover that without switching to the lower yield tiles, so no losses this way. Ten turns losing forest, and we spend 1 turn at both 2 and 3, for 16 lost due to population.

60 - 25 - 16 = 19 gained by whipping.

I doubt this calculation took more than 2 min. But then I tried to verify it, which took forever because I kept making arithmetic errors and not seeing where they were. Shows you the usefulness of the quick way.

Verification:

Stagnant config: Pigs, all 3 mines, plains forest. 140 after 10 turns

1) 24/28 -> 24/24 work pigs, floodplain farm. 8,1
2) 20/26 work pigs, floodplain, plains mine. 6,5
3) 13/28 work pigs, floodplain, 2 plains mine. 4,9
4) 17/28 work pigs, all 3 mines for the rest of cycle. 1,12
5) 18/28
....

60+1+5+9+7*12 = 159

 

[Quechua]

EDIT: Could you check this example for accuracy? I extended the whipping cycle to 12 turns in order to whip at 6 population for 3 points, and it appears I squeezed out an extra 0.15 hammers per turn (or another +1.5 hammers per 10 turns).

I checked it worked in practice before I posted it, but the whole point of doing this is so you don't have to do the lengthy turn-by-turn analysis. You're getting more hammers with your 12 turn way because you're doing a 3-pop whip. I can almost guarantee I could do better using unhappy citizens in a 10-turn cycle, but don't feel like taking the time to prove it again.

 

[OTAKUjbski]

I doubt this calculation took more than 2 min. But then I tried to verify it, which took forever because I kept making arithmetic errors and not seeing where they were. Shows you the usefulness of the quick way.

Tell me about it.

It took me a while to wrap my head around how your method works, but now that I understand how your method works, I think both ways are the quick way (yours might even be quicker).

It looks like the 'hardest' part of either method is simply determining how much food is needed to grow the city back and how long you'll be at each population level.

After that, it's even simpler mathematics.

Thanks for humouring me with the example and by working with mine. Now I have two methods for determining a city's whip potential.

 

[vale]

I can almost guarantee I could do better using unhappy citizens in a 10-turn cycle, but don't feel like taking the time to prove it again.

I don't really see it. The best I can do is 147 hammers over 12 turns (12.25 per turn). Options that cycle over 10 turns get hurt badly by the double bladed inefficiency of extra grassland farm turns and unhappy population and without a food resource to boost it, I'm willing to bet its impossible to get 123 hammers over a ten turn whip cycle in this city.

147 hammers over 12 turns is
start at 16/32 food, 3 pop-whip gives 90 hammers brings us to 16/26 food.
work all farms for 2 turns to bring us to 13/28 food and give us 2 hammers.
work 2 mines and 2 farms for 7 turns to bring us to 27/28 food and give us 49 hammers.
work all farms for 2 turns to bring us to 26/30 food and give us 2 hammers.
work 4 farms and a mine for 1 turn to bring us to 16/32 food and give us 4 hammers.

90+2+49+2+4=147.