Whipping + Granaries

[vicawoo]

Ok, so settlers give a base 4 food/hammers per turn, workers can chop at 5 hammers per turn or make mines at +2 per turn. So whipping hammers per turn:

Assuming food/hammers is interchangeable (we can convert forested terrain types and workers/settlers use either), we see what bonus whipping allows:
one pop whip = 30 hammers - (20 + 2(n-1)) food - hammers lost due to having to regrow.

So over 10 turns, that is (10 - 2(n-1) - hammers lost to regrowth)/10, so < 1 hammer per turn.
2 pop whips are (60 - (20 + 2(n-1) + 20 + 2(n-2)) - hammers to regrowth), or (20-2(2n-3)-hammers to regrowth), or 2 hammers per turn - (4n-6+hammers to regrow)/10. So at best, you're getting 2 hammers/turn from 2 pop whips.

With a granary, your food is halved, 1 pop whips are capped at 2 hammers/turn and 2 pop whips are capped at 4 hammers/turn, so you're gaining the difference between granary whips and non-granary whips, so your granary gives your 2 pop whips about 2 hammers/turn. Actually, it's
((20 + 2(n-1) + 20 + 2(n-2)) + hammers lost to regrowth without a granary - (10+n-2+10+n-2 + hammers to regrow with a granary))/10= (20+2n-3+hammers to regrow with a granary)/10, making the assumption that you're halving your time to regrow with a granary. Hence, you gain 2+(2n-3+hammers to regrow)/10, at size 4 that could be almost 3 hammers/turn.

Putting that aside, let's assume 3 hammers per turn bonus for a granary. Workers can chop for 5/turn and gain a +1 to +4 bonus for a mine or improvement. Settlers give an initial 4/turn, at the cost of some commerce. Under a different criteria, a granary will pay for itself in 20 turns, so your next worker or settler may be 20 turns later.

Some limitations: whipping might be suboptimal without a granary, in which case we should be comparing granary whipping with no bonus, as opposed to negative bonus no granary whipping. When your cities have a happy cap of 3, whipping means losing 10 turns of that 3rd pop, and that 3rd pop has to compare that granary bonus, and sparing you the details, that is 1 to 4 fhammers per turn for the population versus 4-(2*4-3+2*(turns growing from 3 to 4))/10, so you could be getting a mere 0.5 fhammers/turn compared to working a mine with a 3rd citizen.
You also get some immediate bonuses by having that whipped unit that many turns faster, but that's hard to account for.

Sorry for the messiness of this post, but basically guess granaries give 3 hammers/turn, whipping and hence granaries are a poor idea if you're giving up a high yield tile, and in a 3 happy cap city the granary probably isn't even worth it if you can work a size 3 mine.

I'd say go worker/settler unless your next worker isn't projected to improve more than 2-3 spots in the immediate future and you don't want to chop, then if you have a high happy cap (such as your capital) and only 2-3 special resource tiles in that city, granary.

 

[sylvanllewelyn]

Here's one little flaw about this game: slavery is the earliest civic change available for most games, but it's also one of the most complicated. Putting one of the most complicated civics right in the beginning of a game will turn down many people that are trying this game in their friend's place.

There are no "rule of thumb" for using it; my personal favourite is growing my cities to unhapiness than whip a huge chunk of it away for courthouses. I'm also known to whip out the Oracle that got me courthouses in the first place. For both examples, even if there's a long-term loss in hammers in the following 10 turns, I get economic benefits NOW.

 

[Sabertooth]

vicawoo:

Would you mind repeating that in English?

 

[vale]

I've posted this idea before in a long lost thread, but it is relevant to the discussion here.

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).

 

[UncleJJ]

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).

You seem to be simply adding food and hammers together here, and hence assume that 1 food = 1 hammer. That assumption is true if you are building a settler or worker but is not true in a comprehensive analysis that involves whipping and hammer production from mines to produce units and buildings.

The sort of analyse I use assumes the potential hammer value of food varies considerably with city size. For instance a grassland farm would be producing 3 food for a net +1 food, and through Slavery at size 5 food can be converted to hammers at a rate of 1 food = 2 hammers, so it would effectively produce a net 2 hammers of useful output. Conversely a plains hill would produce 4 hammers but consume 2 food which is also worth 4 hammers, so it produces no net output. So in terms of productivity I would rate a grassland farm far more highly than a plains hill at city size 5.

Would you care to explain what you mean and when you would use your assumption, as I might be misunderstanding you? Incidently, did we discuss this before several months ago? If so I would appreciate a link to that thread if you or anyone else has it. There's no point in us repeating ourselves when this has been "solved" before.

 

[vale]

If you want to see the original post it was in the context of whipping cycles. If you are only interested in raw hammers produced during a cycle (or the corresponding stagnation) food and hammers are equivalent for pure production assuming you have the necessary means to convert between them (food deficit tiles if you are stagnating or the whip if you don't. Food is superior in the whip cycle because in addition to contributing to the overall productivity, it speeds along the regrowth and minimizes the lost population turns. But I certainly don't believe food is superior enough to make a grassland farm superior to a plains hill mine in most instances.

When you are stagnating, your total production is exactly total food produced + total hammers produced - total food consumed. So wow, how nicely does that lend itself to being exactly what I said? What is each tile contributing and consuming? It is contributing its food value, its hammer value and consuming 2 food (assuming we are healthy). And in a whip cycle while it is not quite as obvious, the same thing holds. If it is a true cycle, you are producing a specific amount of food over 10 turns to return to the start point, call it F food. So over the course of the whip cycle the hammers produced not from the whip will be:
total food produced + total hammers produced - total food consumed - F. The exactly same idea except this time that F food is being converted into H hammers every whip cycle as a bonus to the production.

The idea that food and hammer = production is not a new one, and it is not from me. It works here and you can use this idea to analyze the overall effectiveness of whipping for individual cities quite easily. It actually lends itself perfectly to the analysis of whip cycles.

Whipping Cycles

 

[vicawoo]

vicawoo:

Would you mind repeating that in English?

Ok. Messy math blah blah blah. Results.

Whipping best case scenario: x hammers per turn, where x is the number of pop whipped.
With granary, 2x hammers per turn.
Realistic nice case, 2 pop whips yield 3 hammers per turn.
Happy cap of 3 case, 2.5 hammers per turn - yield per turn of 3rd worked resource.

Don't whip if you're working all special resources, and hence don't build a granary.
Build workers over granaries if they can make multiple decent improvements. Settlers are slightly worse (4 per turn) unless you can make over 2 fhammers/turn in improvements (2 mines or a special resource). Chopping is better in the short run.

 

[Ibian]

This all has a mathematical answer. As with most answers of that type, it tends to be simple.

 

[vicawoo]

You seem to be simply adding food and hammers together here, and hence assume that 1 food = 1 hammer. That assumption is true if you are building a settler or worker but is not true in a comprehensive analysis that involves whipping and hammer production from mines to produce units and buildings.

The sort of analyse I use assumes the potential hammer value of food varies considerably with city size. For instance a grassland farm would be producing 3 food for a net +1 food, and through Slavery at size 5 food can be converted to hammers at a rate of 1 food = 2 hammers, so it would effectively produce a net 2 hammers of useful output. Conversely a plains hill would produce 4 hammers but consume 2 food which is also worth 4 hammers, so it produces no net output. So in terms of productivity I would rate a grassland farm far more highly than a plains hill at city size 5.

Would you care to explain what you mean and when you would use your assumption, as I might be misunderstanding you? Incidently, did we discuss this before several months ago? If so I would appreciate a link to that thread if you or anyone else has it. There's no point in us repeating ourselves when this has been "solved" before.

I've thought about this, and for the purposes of workers and settlers, food = hammers. It's easier to just treat whipping as a source of extra hammers. The only drawback is that you might see food growth as an investment in additional hammers, whereas hammers cannot do this.

 

[futurehermit]

Man I opened Pandora's Box with this thread

 

[vicawoo]

Man I opened Pandora's Box with this thread

I don't get why people are so averse to applying basic algebra to solve problems, math to most people is like fire to frankenstein. It's like having to concentrate and focus a little, is, well, it reminds me of Chris Rock's stand-up about people loving to not know in the ghetto.

 

[siggboy]

I don't get why people are so averse to applying basic algebra to solve problems, math to most people is like fire to frankenstein. It's like having to concentrate and focus a little, is, well, it reminds me of Chris Rock's stand-up about people loving to not know in the ghetto.

The question is if we want to apply maths while we're playing, all the time. The "bean counting" that was talked about is doing just that. I don't want to count single hammers, overflow and production bonuses to synchronize my whipping perfectly. Too much effort in a game of 750 turns.

I'm happy if the basic algebra supplies me with rules of thumb that are "good enough" to work for me at my chosen difficulty level.

In another thread DaveMcW made the assertion that West Point (which gives +4 XP to units) increases your fighting power by 25%, and he went from there to look at how many hammers worth of units would have to be built to compensate for that edge in fighting power. I believe that many players have these kinds of rules of thumb without actually going all the way to validating them (by creating a mathematical model), and I also believe that some of these rules are counterproductive because they are way too inaccurate. (Probably you can tell that I don't think much of Dave's 25% rule in that regard ;-).

These boards are filled with bean counting arguments, but the community is missing some definite reference work on many of the issues. This could be a spreadsheet with a comprehensive model of, for example, whipping mechanics, and the spreadsheet could then be used to give you a rule of thumb for the scenario that you are interested in.

That's my suggestion to make the (not so basic) algebra work for the community. Threads like this one, on the other hand, are going to be forgotten tomorrow and only a select few are even bothering to dig through the formulae (or rants like this one .

 

[futurehermit]

I don't get why people are so averse to applying basic algebra to solve problems, math to most people is like fire to frankenstein. It's like having to concentrate and focus a little, is, well, it reminds me of Chris Rock's stand-up about people loving to not know in the ghetto.

For me, it's because this is a game. I work hard all day. I don't want to work while I'm playing a game. I want to relax and have fun. Math isn't fun to me.

 

[TheMeInTeam]

A little time investment early in algebra can prevent you from having to really think about this later on though. It will probably save time in the end.

 

[futurehermit]

I am starting to think more about it (hence this thread). But I still probably won't ever really get into the math end of it. As long as I get the gist of it and it works out alright, I don't care really if I am working at 100% efficiency.

 

[Nares]

I don't want to count single hammers, overflow and production bonuses to synchronize my whipping perfectly. Too much effort in a game of 750 turns.

It's really not so bad once you habitualize it.

Most people are just intimidated by it, which is very much in line with the general dumbing down of gaming society, so it's no surprise.

 

[futurehermit]

Civ4 is already complex imo, so I wouldn't say not wanting to do algebra to whip at 100% efficiency is = dumbing down of gaming society. It's not like this is a FPS or something

 

[siggboy]

A game which is supposedly "dumb", "dumbed down" or "being dumbed down all the time", depending on who you talk to, is World of Warcraft. And still, it gives enough food for thought to the hard core player base to produce pictures such as this one:

(And much more esoteric stuff, actually; I don't have the hunter spreadsheet installed anymore, since I got the WoW addiction out of my system, but believe me, it's a monster ;-)

Now, talking about "dumbing down" in the context of Civ IV is completely moot...

 

[Nares]

Civ4 is already complex imo, so I wouldn't say not wanting to do algebra to whip at 100% efficiency is = dumbing down of gaming society.

Civ really isn't that complex.

The number crunching, while being the most complex aspect of civ, isn't even that extreme. If it wasn't basic algebra we were talking about, you might have a point.

But the freedom to choose the level of effort one puts into a challenge lies at the very foundation of what makes America great.

You're content where you are, and that's acceptable. I don't think anyone is going to force you to put in more effort, though they might look down on you in a SG (and with good reason).

At best, people will try to persuade you that the effort isn't nearly as monumental as you think it is. Even DaveMcW likely had some "difficulty" with making calculations when he first started putting in that level of effort. Undoubtedly he hardly even computes a number at this point; it's all internalized. He probably even plays faster than you or I would, with fewer mistakes, because he put in the effort at some point to develop a better grasp of the system.

 

[TheMeInTeam]

Civ really isn't that complex.

The number crunching, while being the most complex aspect of civ, isn't even that extreme. If it wasn't basic algebra we were talking about, you might have a point.

But the freedom to choose the level of effort one puts into a challenge lies at the very foundation of what makes America great.

You're content where you are, and that's acceptable. I don't think anyone is going to force you to put in more effort, though they might look down on you in a SG (and with good reason).

At best, people will try to persuade you that the effort isn't nearly as monumental as you think it is. Even DaveMcW likely had some "difficulty" with making calculations when he first started putting in that level of effort. Undoubtedly he hardly even computes a number at this point; it's all internalized. He probably even plays faster than you or I would, with fewer mistakes, because he put in the effort at some point to develop a better grasp of the system.

This is of great importance when trying to reach high levels in any game. One has to not just think, but actually believe "if it can be done, I can and will learn to do it". Something might seem hard at first like that, but only at first if you truly believe that it will eventually become second nature. Usually, if one bothers they're surprised at how fast it is possible to improve.

Of course, my dual goals are here are a balance between improvement and having fun (basically, being able to at least stand a chance of winning in each game I play). Would I have learned faster if I kept running deity level games the second I got the game over xmas? Most likely. I might have even won a couple by now. I didn't do it that way though, I just kept learning about the game and moving up in difficulty as I went (which leaves me at emperor at the moment, though I'm probably only a few weeks out from consistently braving the immortals university games here, and may go back and play old ones also).

It starts getting pretty chancey though. I hear at deity it's virtually impossible to win every start. That won't stop me from trying though .