Bacon sandwiches are better than Burgers

[Blake]

I basically agree with nbarclay, avoiding food surpluses is a good thing - it is best for example to tie up workers on plains cottages to stop the city growing beyond happy limits.

The utility of poprushing is precisely when the city is terminally low on hammers but has an abundance of food, so pop-rushing is the only way to get infrastructure in a timely fashion.

Now that said, a food rich start is still much, much, much stronger than a food poor start, I like grassland pigs more than grassland cattle.

If we take for example, a wide expanse of grassland, with a lot of grassland hills, and one resource.
A cow resource gives 2 food surplus and lets you work 2 hills, the three workers provide 8 hammers.
A pig gives 4 food surplus and lets you work 4 hills, a total of 12 hammers. And in the same way, grassland hills are stronger than plains hills, and grassland is generally stronger than plains.

Furthermore, the coverted (for me) 6 food tiles, allow a size 3 city to create 2 scientists and continue to grow at a respectable rate. If 2 cities have 6 food tiles I can create 4 scientists and generate enough great scientists to do some good things with. In comparison a start without the high food tiles will either kill the growth of the scientist cities (making the GS's come at a heavy price, kinda defeating the purpose of them), or they'll have to grow to size 4-5 first, slowing the whole thing down.

I saw somewhere someone said that "The difference between a food-rich and food-poor start is basically an entire difficulty level" and I'm inclined to agree.

[Tau Ceti]

Pop rushing appears to be quite buggy on non-normal game speeds. For details, see here: http://forums.civfanatics.com/showth...68#post3544368

[nbarclay]

Originally posted by rewster1
It's actually 30 hammers per pop point sacrificed, pretty much regardless of the amount of food that went into making that pop.

That depends on the game speed. The original poster in this thread was using data based on epic speed (or at least how epic speed is supposed to work), and much of the subsequent discussion is based on that same speed.

[nbarclay]

Originally posted by Alkis2
From what I read, it seems that the best period to pop rush is when your cities are still small. Therefore you do that at size 2-3 and then you let them grow. By that time you will have Monarchy and aqueducts, and more resourses, so everything is in order.

Pop rushing when a city is small has a lower cost to replace lost food, but the cost in lost opportunities to work tiles tends to be vastly higher. A pop point lost to a rush build in a small city will generally affect a city's size, and hence its productivity, for most of the time until the city grows big enough for food and happiness to reach equilibrium, which can be a whole lot longer than the duration that unhappiness reduces the size of a maxed-out city.

By the way, I noticed that my earlier analysis was assuming the absence of a granary. I added an edit to reflect the fact that with a granary (and assuming the assumptions I'm basing my calculations on are correct), pop rushing can be a good investment in general for cities that max out in practical size below size 10. So a combination of a granary and extensive use of pop rushing may be an attractive option in the early game (in a time with small cities and no forges available yet), especially on higher difficulty levels where the population cap is relatively low - at least as long as pop rushing doesn't interfere with using tiles that yield more than one extra hammer per food lost.

[Shaka II]

The reason that pop rushing is better for smaller population is that the conversion of food to hammers is fixed, e.g., 1 pop = 45 hammers on epic apparently, regardless of how much food the particular population point cost. A size 3 city required filling up the 36 food bin to go from 2 to 3, while a size 6 city required filling up the 42 food bin to go from 5 to 6, a bit more expensive. But the granary makes the food cost only half, so 18 and 21 respectively for a size 3 and size 6 city. At first glance, it might look like a good deal, even without the granary, but when considering the unhappy worker for 15 turns, one tile less is contributing for 15 turns. And then the penalty on not growing larger to have more worked tiles becoming villages, towns, etc.

Intuitively, I think it's probably the way to go for the early city with little production capability (size 3-6), but lots of food capability to convert, especially with the granary. It also looks like the way to go when city pop caps are in effect with no immediate relief on the horizon.

There do appear to be some quantization effects, which Vel has alluded to and provided a link.

I thought I'd found a perfect city for this, my third, playing as Romans (cheap granaries), but the flood plains city also had hills and plains, eventually becoming my highest production city, site of the Heroic Epic, and a solid financial city to boot. But it had a nice balance of flood plains farms, marble quarry, cottages, mines, and even a pig farm.

It's a fun contest to not pop rush and see if you can grow without hitting the pop cap. It's easier as the Romans naturally, with +2 health/cheap granaries (for more health), and Praetorians to help capture more health and happiness resources. Part of why the Romans are so much fun to play.

[nbarclay]

The "fifteen turns" figure (give or take depending on game speed) only comes into play if a city is bumping up against its happiness size limit. Otherwise, the penalty of not being able to work as many tiles due to the loss of a pop point lasts not just fifteen turns, but the entire time until the city reaches its maximum size. The penalty won't come into play every single turn of that period because the fact that cities grow faster when they're smaller helps a little in catching up in size. But it will affect most of the turns for what can, unless the city has a staggering food surplus, be a very long time.

Pop rushing to finish a granary when a city is small might make a huge amount of sense because the granary can help the city grow faster to replace the lost population, and there may be times when using a pop rush to finish a lighthouse sooner has similar logic. But otherwise, if the city has decent tiles to work to make growth worthwhile, I can't see how pop rushing when the city is small instead of waiting until it gets bigger (and therefore can work more tiles) could make sense as anything but an emergency measure.

Actually, there may be one other exception: hyper-food cities (i.e. cities with multiple food bonuses and virtually no low-food tiles to absorb the surplus). If a hyper-food city (HFC) waits until it hits maximum size to start pop rushing, it can run into trouble from being able to grow a lot faster than the happiness penalty allows it to use up its excess growth in pop rushing. If the civ needs more settlers or workers, building them in a HFC can be a great way to make use of the HFC's food surplus while at the same time controlling the city's growth. But if a HFC won't be able to control its growth by building settlers or workers, pop rushing early so the unhappiness will have time to dissipate before the city reaches its maximum size may be better than the alternatives - especially in the early stages of the game when there is little opportunity to leverage excess food into specialists.

[fed1943]

ShakaII:I think it is almost,but not exactly,as you said.
The city needs 36 food stored to grow;gets it and grows;without granary remains with 0 food,with granary remains with 18 food,the half it had,but not the half needed to grow again.
Best regards,

[Shaka II]

Originally posted by nbarclay
The "fifteen turns" figure (give or take depending on game speed) only comes into play if a city is bumping up against its happiness size limit. Otherwise, the penalty of not being able to work as many tiles due to the loss of a pop point lasts not just fifteen turns, but the entire time until the city reaches its maximum size. The penalty won't come into play every single turn of that period because the fact that cities grow faster when they're smaller helps a little in catching up in size. But it will affect most of the turns for what can, unless the city has a staggering food surplus, be a very long time.

I realize that now. The addition of 1 more unhappy worker doesn't hurt you unless you're at the pop cap. But, if you build things that only cost 1 pop, like swordsmen and axemen, then it adds up to make you hit the pop cap sooner. Probably things like settlers, or a library are the better choices.

Also, it appears that there are some quantization effects, i.e., what happens when what you build is not an integral number of the 45 hammers? I did some experimentation with my marathon game (which uses 90 hammers per pop) and for integral numbers of the pop/hammer ratio, it looks good, if you wait a turn to avoid the first turn penalty. Building things that are not integral costs of the pop/hammer ratio appears to have certain quantization conditions. I tried building a temple, which is about 2.5 pop in hammers, again waiting 1 turn. The overflow was handled correctly, but it cost 3 pop with no partial compensation, either in food or hammers. Repeating the temple, but building partially to within 2 pop led to good results again. But, to do a partial build, you need production, not food.

I think a temple is a good buy, especially if the pop cap is in effect. But also, building things that cost at least 2 pop is better since the unhappiness adds and presumably you're growing at a faster rate than 1 pop per 15 turns in this super high food city.

Probably the best use would be a settler pump for a large or huge map would be a good application. In a standard pangea, the AI closes in so fast that I'm pleased to get 4 well placed cities out, occasionally 6, but sometimes only 3. But even if I only get 3, I grow big cities with production to capture more, and pop rushing doesn't seem to have a place. Not until the end game anyway, when I pop rush theatres in.

fed1943 - You're right, I over simplified it. The effect on food per pop is doubled.

[Yosho]

Actually, there may be one other exception: hyper-food cities (i.e. cities with multiple food bonuses and virtually no low-food tiles to absorb the surplus). If a hyper-food city (HFC) waits until it hits maximum size to start pop rushing, it can run into trouble from being able to grow a lot faster than the happiness penalty allows it to use up its excess growth in pop rushing. If the civ needs more settlers or workers, building them in a HFC can be a great way to make use of the HFC's food surplus while at the same time controlling the city's growth. But if a HFC won't be able to control its growth by building settlers or workers, pop rushing early so the unhappiness will have time to dissipate before the city reaches its maximum size may be better than the alternatives - especially in the early stages of the game when there is little opportunity to leverage excess food into specialists.

It also makes sense to pop-rush a culture building, if the fat cross will give you much better squares to work; one extra farmed rice square is probably worth two plains squares.

[couerdelion]

A few additional points

I deliberately avoided the situation with happiness restrictions because this is obviously going to affect the analysis. On the whole the calculations work well for a new city in an established civilisation 3+ happy resources.

One thing that has not been considered is that the decision to pop-rush is an OPTION. If you look at it in this way then food beats hammers IF we choose to turn the food into hammers through population rushing. In other words, we CAN better cows with pigs if we want to.

What I have not done is to compare a city with pop-rushing with the same city not pup-rushing. Here we do run into problems not just of comparative happiness but also of lost production in tiles not worked while the city regrows.

The figures though can be very interesting in comparing which tiles to work. With a granary and forge, at size two, food is worth 2.00 hammers. This means that a 3/0/0 tile will produce the same production as a 2/2/0, 1/4/0 or 0/6/0 tile. We can also work with the convention, f (food), h (hammers), p (production). So at size 2 (using my table above)

f = 1.25 * 200% (granary) * p = 2.50p
h = 125% (forge) * p = 1.25p

So if I wish to pop-rush, I am indifferent between a grassland farm and a copper mine on plains hill.

I believe that the hammer, or rather, production gain from pop-rushing does not vary with difficulty level.

[Velociryx]

All of the above is true when looking at the gains to be found from a purely hammer-oriented approach, but I contend that this is not the full picture.

So far, the greater bulk of the discussion here has been on the gain in hammers from a pop-rush, and the opportunity cost in hammers lost due to tiles not worked.

There has been relatively little discussion on the vast amounts of turn advantage that can be created by getting a given building or unit 20-odd turns faster than you otherwise would have. This has been touched on, to be sure, but is one of the major factors in favor of the pop-rush, and as such, deserves a closer look.

Some examples off the top of my head:
* Cultural buildings that are more than a thousand years old = double culture. Obviously, building these when the clock is still jumping ahead quickly (20-40 years per turn) is MUCH more effective than waiting...nod to the pop rush).

* Speed in building an attack force (if you want to catch an opponent unawares, then pop rushing the last few units you'll need for the attack force that nets you 4 new cities can almost certainly undo whatever opportunity cost you face for doing it--with the new cities tiles worked more than making up for the lost tilels worked at home).

* Limited number of items to be built in the build queue. The faster you complete them, the faster you gain ultimate flexibility in that city. This is worth a few lost tiles here and there, and certainly makes a good case for rushing infrastructure as needed.

IMO, looking at hammers gained vs. potential hammers lost due to missing pop points only gives you roughly 1/3 of the picture, and thus, by itself is insufficient to make the case one way or the other.

Definitely worthy of consideration, but I do not believe it is either as simple or as linear as it has been made out to be so far.

$0.02

-=Vel=-

[couerdelion]

Originally posted by Velociryx

$0.02

-=Vel=-

You’re selling yourself too cheaply

With regards to the idea of this being linear approach, I deliberately wanted to simplify things so that I had some theory to use when playing. Most people don't like to worry about more complicated calculation like working out time to grow two pop points.

With some sort of simple conversion scale I can compare the relative value of food, production and commerce rather than select tiles/improvement by a more gut feel approach. To do too much more would be detailed micro-management and I don’t want to have to do things like count the turns since the previous pop-rush.

[couerdelion]

I’ve now read the CivFanatics thread and understand the confusing results you get from population to hammers conversion on rushing.

In short, there are two calculations

1) How many population needed to rush to finish the build. Incidentally this will determine if the poprush is possible
2) How many hammers are gained from the poprush

As it turns out, after stage 1 has been worked out, it appears that the number of hammers gained per population point is only dependent on the number of hammers needed. It is the lowest multiple of 30 which will complete the build.

So when pop-rushing with one citizen, if you can do this when you need 31+ hammers for completion, then you will get 60 hammers. For two population points, you will ONLY get 45 per population if the remaining build requirement is 61-90. If it is 46-60, you’ll get 30/pop while if it is 91-120, you’ll get 60/pop.

What this seems to suggest is that the forge and granary are the two important builds to enable a profitable poprush strategy.

[Hermann the Lombard]

Senior moment question: in pop-rushing, are there leftovers applied to the subsequent build? I assume not but would be delighted to be wrong.

[rewster1]

Leftovers are applied to the next build... if you pop rush a warrior you will actually get two warriors worth of production. But don't pop rush a warrior... that's silly.
The leftovers have any bonuses removed before applying the production to the next item, whereupon it's own specific bonuses are reapplied. So pop rushing a wonder as industrious with stone doesn't let you then build an entire building for free, or other such exploits.