Whipping cycles

[Quechua]

Key words, 'almost' guarantee, and 'don't feel like taking the time to prove'

Here's my quick estimate.

42 ~ 61. We have to spend 3 unhappy turns for 6~9. We lose at least 13 pop turns for 19.5.

90 - 61 - 9 - 19.5 = .5 more than stagnant, so it's actually a little worse than 2-pop whip.

Nice catch

 

[cabert]

Wow, that's a lot of spreadsheets.

A few comments :
- a granary doesn't double the hammer value of food. What does it do? It stores half the food from size N and restores it when you grow to size N+1.
So you food bar isn't exactly half full (1F missing, for each level) when you grow (not taking into account overflow food here, because it has nothing to do with the granary). It's not much, but if you spend so much time on spreadsheets, you might just as well do it right.
- What's the cost of an unhappy you store for later whipping? He's eating 2 food. Well, big deal. If you count food eactly to avoid the growth, you end up using less efficient tiles, which is costing more! I can testify I sometimes grow 2 or 3 pop over the happy limit for whipping large items. My favourite is whipping 6 universities 1 turn after I discover education .
- here is a subject noone mentionned (or I didn't see it, sorry for fast reading) : under which condition can it be worth "stacking" unhappies from the whip? I do it in a few situations : war preparations, "happy whipping" = whipping happiness buildings in food heavy cities, GT rush = whipping units under HR for overflow towards the globe theater.

 

[OTAKUjbski]

Because I always have something to say about everything:

- a granary doesn't double the hammer value of food. What does it do? It stores half the food from size N and restores it when you grow to size N+1.
So you food bar isn't exactly half full (1F missing, for each level) when you grow (not taking into account overflow food here, because it has nothing to do with the granary). It's not much, but if you spend so much time on spreadsheets, you might just as well do it right.

I think I typed this but forgot to retype it after I lost my post to computer malfunction. I'm glad you brought this up, because this was one point of confusion it took me a while to comprehend:


Starting from population 1 with a Granary, moving up to pop 2 costs a total of 22 food. 11 food is stored in the Granary.

At population 2, it costs 24 - 11 = 13 food to move up to 3. 12 food is stored in the Granary.

At population 3, it costs 26 - 12 = 14 food to move up to 4. 13 food is stored in the Granary.

So ...

Without a Granary, population 3 & 4 cost a total of 24 + 26 = 50 food.

So the hammers-per-food ratio without a Granary is 60 / 50 = 1.2.​

And with a Granary, population 3 & 4 cost a total of 13 + 14 = 27 food.

So the hammers-per-food ratio with a Granary is 60 / 27 = 2.22.​

Right?

Wrong!

At first, all my numbers were wrong, and I couldn't figure out why. In practice, the hammers-per-food value with a Granary was always double the non-Granary value. But on paper, it was always less.

Then it hit me ... it's something I can only think to call 'food recycling':

Because of the larger Granary size at higher population levels, you get an amount of food equal to the size of the whip 'recycled' back into the city when you whip.

For example, 13 food is stored in the Granary at population 4. So after a 2-size whip, pop 2 starts with 13 food in the Granary instead of just 11.

60 / ( 27 - 2 ) = 2.4 ... exactly double the non-Granary value!

Likewise, 15 food is stored in the Granary at population 6. So after a 3-size whip, pop 3 starts with 15 instead of 12.

15 - 12 = 3 ... the exact size of the whip.

In a whipping cycle, each population level [essentially] costs exactly 1 less food (at Normal speed) because of 'food recycling'.

- What's the cost of an unhappy you store for later whipping? He's eating 2 food. Well, big deal. If you count food eactly to avoid the growth, you end up using less efficient tiles, which is costing more! I can testify I sometimes grow 2 or 3 pop over the happy limit for whipping large items. My favourite is whipping 6 universities 1 turn after I discover education .

The amount of production lost from food consumed by unhappy citizens depends on how long the city has to feed those unhappy citizens and thus is dependent upon how much +food the city has. Low +food means a lot of turns and a lot of lost production. High +food means few turns and less lost production.

For either method, you'd need to know how many turns the city is in unhappiness, because that'll determine how much extra food it takes to get to the target whipping population.

However, "conventional wisdom" doesn't apply, because whipping isn't being utilized to increase productivity -- it's being used to "front load" the production schedule.

To me, this is no different than pre-chopping a forest, which is invaluable not because of any difference in production but because of when it grants that production.

Even though whipping is very likely less productive in a situation like this, the tactical advantage whipping gives far outweighs the tangible, calculable costs.

- here is a subject noone mentionned (or I didn't see it, sorry for fast reading) : under which condition can it be worth "stacking" unhappies from the whip? I do it in a few situations : war preparations, "happy whipping" = whipping happiness buildings in food heavy cities, GT rush = whipping units under HR for overflow towards the globe theater.

That's definitely worth mentioning.

Whipping a happiness building or unit [under HR] essentially negates the stagnation period while waiting for the whipping penalty to wear off, so as soon as you can get back to the "happy cap", you're right back where you started.

Thanks ...

 

[Elandal]

Would this be a good time to ask "How good is Sacrificial Altar?"

 

[KrikkitTwo]

Sacrificial Altar makes it almost Always worthwhile to whip
(you only lose 5 population turns from whipping, so a tile needs to have 6 hammers to eliminate even a 1 pop whip advantage)... basically whip is limted by food rather than Happy.

 

[UncleJJ]

OTAKUjbski, I agree with almost all you've written here. Your arguments and the discussion have clarified some of my own ideas about whipping. It seems to me that you have conclusively proved this method of looking at the productivity of food component of individual tiles available to the city can instruct how and when (or even if) a city should be whipped. I can see that in the case of severely limited happiness the methods proposed by other members do work and allow calculation to be made. However, I am not sure I understand how these other methods can be applied to circumstances where the whipping cycle is not "closed" in the sense that the city is the same size before and after the whipping cycle. If the city grows or is reduced in size how do these other methods calculate the hammers produced? How do these other methods work to calculate the productivity in a situation where there is no happiness cap but the city is limited by the tiles it works (perhaps sharing some with other cities)?

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

I am astounded that you could think this. Perhaps you mean specifically in the city you had just studied prior to making the comment - which had several grassland hills available and a low happiness cap. That city was close to being a production city and they are seldom whipped. But as a generalised statement this is not true. The primary benefit of Slavery is that it can turn food into hammers in a more efficient way than most other methods in the early and middle game. In some cases it is just about the only way to produce significant hammers in a city.

Consider an Ice city founded in the arctic. Take an example where it has 1 fish and 1 clam tile available (both coastal) and say 10 other coastal tiles, 5 ice tiles (useless) and some ocean tiles. That city can be founded and made productive in a reasonable time using Slavery despite having only one hammer from the city tile. It can generate its own fishing boats ( x 2), a granary and lighthouse for maximising its food production and a courthouse (maintenance + EPs) and library (culture + beaker bonus). This won't be your best city by any stretch of the imagination but it can be used to help draft or whip an army or fleet and can run several specialists once set up. Later in the game it can pump out lots of EPs. Why settle such a city anyway? To stop other civs grabbing the spot, perhaps. Or it might be your only source of the fish or clam resource and so be beneficial to your empire in that sense. Whatever the reason, I select this example since it is only viable to settle the site using Slavery - unless you are willing to waste a huge amount of gold on buying hammers with US. The example is extreme but that just proves the point more clearly. The use of Slavery in this situation is all about vastly increasing the productivity of the city and that is its primary purpose. There are many less extreme examples where a combination of high food and Slavery makes an otherwise weak city low on hammers into a useful one. Once developed the excess food in the city can either be turned into hammers for units or used to run specialists.

Consider another example during a domination push where a captured city is made useful much faster by using Slavery. Although during the war it will have WW and motherland and perhaps B&SotF unhappiness which will severely limit its happiness. - Slavery is a way to balance the happiness available with the prevailing conditions. which change as culture eventually quells the Motherland problem and as the empire switches into and out of war. The varying happiness cap makes growing and maintaining the city, according to a prearranged plan, rather difficult. In this situation I often build up -4 or -5 unhappiness from Slavery as several whips are made as fast as possible if a high food surplus is available. As cabert has mentioned a convenient trick under these conditions is to whip in infrastructure such as temples, forges and markets that not only give a benefit but also raises the city’s happiness. A similar effect can be accomplished under HR by whipping units.

How would the various methods proposed by Quechua, vale, Dave McW, krikkitone and maybe others, deal with these situations? Can they calculate the most productive tiles to work or the best city size to make the whip at? Are these other methods limited to working in a closed cycle and assume that there is no net gain or loss in food?

 

[OTAKUjbski]

However, I am not sure I understand how these other methods can be applied to circumstances where the whipping cycle is not "closed" in the sense that the city is the same size before and after the whipping cycle. If the city grows or is reduced in size how do these other methods calculate the hammers produced? How do these other methods work to calculate the productivity in a situation where there is no happiness cap but the city is limited by the tiles it works (perhaps sharing some with other cities)?

I'm sure Quechua can answer that better than I, but I'll put my 2 in as I see it.

Both methods rely a few variables directly based on the available tiles. You first need to know how much +food is available to the city at various city sizes, because you have to know how many turns the city will be at the smaller, post-whip sizes. Then, you need to know what the city's max 'raw', non-whipping HPT is at both the largest size and at the "-1" size.

Both methods also rely partially on the whipping cycle starting and ending with the same amount of food. Quechua's method automagically factors in the assumption. My method doesn't factor it in automagically but also doesn't necessarily need to 'factor' it in since food calculations should start with the food bar full -1 (or at least enough to "skip" the lowest pop size).

I am astounded that you could think this. Perhaps you mean specifically in the city you had just studied prior to making the comment - which had several grassland hills available and a low happiness cap. That city was close to being a production city and they are seldom whipped. But as a generalised statement this is not true. The primary benefit of Slavery is that it can turn food into hammers in a more efficient way than most other methods in the early and middle game. In some cases it is just about the only way to produce significant hammers in a city.

You got me on that one. I was, indeed, talking about "good" production cities.

In an 'okay' production city, whipping will most likely increase productivity.

In a poor production city, whipping will all but certainly increase productivity.


I feel like your war example falls into the same category as Cabert's University example in that it shows the weakness of relying on any method to calculate whipping efficiency. No matter how great the inefficiency might be, it is far outweighed by the tactical advantage of quickly whipping and buildings in a wartorn city or in getting Oxford 15 turns early.

On the same token, I think both of those examples strengthen the accuracy of my original conclusion -- that Whipping is more important for its tactical advantages than it is for its production potential (i.e., it's because of its tactical advantage Whipping is able to offer production to an all-food city).


-- my 2

 

[Quechua]

How would the various methods proposed by Quechua, vale, Dave McW, krikkitone and maybe others, deal with these situations? Can they calculate the most productive tiles to work or the best city size to make the whip at? Are these other methods limited to working in a closed cycle and assume that there is no net gain or loss in food?

We're talking about closed cycles because that's essentially a static situation that lets us isolate the hammers per turn due to our method alone. If we have a captured city with unhappy citizens, and we whip it down to a lower size and don't grow back, we are harvesting the investment put into the population by the previous owner in a one-time deal. It doesn't really make sense to include the hammers from this whip in comparing the hammer outputs of two population states (even though having these hammers now rather than later has significance).

If your goal is to maximize production, and you suddenly get more happiness and want to grow to the higher size, you can analyze your production during the growth in the same way we analyze the production given up growing back during a whip cycle. The main question is whether its better to grow to the new size quicker, giving up some hammers now but starting the new whip cycle sooner. I think I could answer this with pretty much the same methods as a closed whip cycle.

As far as the most productive tiles to work, usually it's best to work the tiles with the highest food+hammers, although you still have to balance the food. If you look at Otaku's example with the pigs, floodplain farm, and other various tiles, you'll notice I did get a whopping 1 hammer more than him. That is only because he chose to work a grassland farm on one turn, while I used a method working the more productive plains mines instead.

 

[Willburn]

An interesting thread. But its not as easy to calculate stuff as to just see the hammer benifits. Whipping has one more strong side, it has lots of production massed at a single point in time. There is a big difference between getting say a libary whipped at turn 8 or produced at turn 10 even if the overall production would have been higher for not whipping (I guess there are examples where this would hold true.) But you would then have to calculate the benifit of getting the libary early to see the total gain. So in short just focusing on how much hammers you get is a wrong way of looking at the game. You should be looking at what gives you what you need fastest.

 

[VoiceOfUnreason]

There is a big difference between getting say a libary whipped at turn 8 or produced at turn 10 even if the overall production would have been higher for not whipping (I guess there are examples where this would hold true.) But you would then have to calculate the benifit of getting the libary early to see the total gain.

See: Does using Slavery hurt my game?.


If you are getting really micro, you may also want to worry about rounding effects of the 25% production multipliers (forge or org rel), where one 30P whip is a lot more than 10 x 3P/turn, etc.

 

[Willburn]

Yep i know (but thanks for the link)