Bacon sandwiches are better than Burgers

[couerdelion]

Over the course of a number of games I have been looking a little more closely at the options that exist in the early game for trading bread for hammers. Initially, I had the general feeling that resources like cattle, copper and horses were preferable to those of corn, pigs and sheep from the perspective of the food/hammer balance. I believe this would be common amongst many civ players who tend to be “hammer-junkies”. Subsequent analysis has now shown that my initial gut-feel was in fact wrong and that with the careful use of pop-rushing, a far better result can be obtained through selecting food ahead of hammers. In short, an army fighting on bacon will be stronger than one fed on beef.

The figures here are based on epic speed although the similar results could be obtained at any game-speed. At epic speed, growth occurs at following food levels 33, 36, 39, 42, etc. Pop-rushing will be assumed to produce 45 hammers per unit of population although this number will vary depending on a number of factors which I do not fully understand. Often you can get 60 hammers per population point but by assuming the lower figure I am excluding an additional benefit that the food/pop-rush strategy will bring. Unhappiness from pop-rushing lasts for 15 game-turns

In the analysis I have taken several hypothetical cities. The first city has grassland pigs, the second has grassland cattle while the third has grassland copper. Conveniently they each take 6 turns to improve and for ease of understanding, I will assume that each of them has been improved at the point when the cities have just grown to size 2. Just as a reminder, these tiles will provide 6/0/0, 4/2/0 and 2/4/0 respectively. Apart from each of these resources, I have also assumed that the city can work several 2/1/0 tiles. For simplicity, I will ignore any hammers or commerce from the city tile and the “first-worked” tile and will assume that both provide 2 food so that any food provided by our “resource” is surplus

Finally, I will assume that this city is not significantly constrained by happiness or health penalties. Where happiness limits start to bite, the food/pop-rush strategy will suffer relative to the hammer strategy.

One more thing. I will use the following naming convention

f= food unit contributing to next population growth
h= hammer contributing to total build capacity
p=population point (at size 2, 36f=1p)

Let us first consider our “Copper city” and run this for 15 turns. With surplus food of +2f, it will take 18 turns to grow so will still be size 2. The food/hammer pool will be 30/60. Using my naming convention, we have:

30f + 60h.

Now let’s move to the “Cow city” and run this for the same duration. With surplus food of +4f, this will grow to size 3 in 9 turns and the city will start working another 2/1/0 tile. At this stage the food/hammer pool is 36f+18h = 1p+18h. It will then take a further 10 turns to grow so in the remaining 6 turns of our analysis we will be producing 4f+3h per turn or 24f+18h.

Total return from Cow city = 1p + 18h + 24f + 18h
= 1p + 24f + 36h
We can, if we want, burn that extra population point and our conversion formula is 1p=45h. This will give us a final balance of

24f + 81h

Comparing this will Copper city the net difference is

-6f + 21h

Cow city is a little behind in food but will catch up over 3 turns. By contrast, the hammer advantage of Cow city would take at least 10 turns for Copper City to recover but further pop-rushing could then be used to maintain the advantage of Cow City.

Finally to “Bacon City”

Grows to size 3 in 6 turns. Net balance then is 36f = 1p. Working the new 2/1/0 tile it will be producing +6f + 1h and will grown in a further 7 turns. At this stage, the balance will be:

1p + 42f + 7h
= 2p + 3f + 7h

Now it will be producing +6f + 2h for the remaining 2 turns of our comparison to give a final balance of

2p + 15f + 11h

For comparison with the other two cities, I will burn both units of population to give

15f + 101h

Compared to Cow city, the difference is

-9f + 20h

And the case for Pigs over Cattle is proven.

I will be breaking down the figures further to shown conversion rates from food to hammers which will give some theoretical bases to the claim that food is superior.to hammers for smaller cities. In fact, when granaries get added to the equation, this relationship will be true for cities up to size 10!!!!

[couerdelion]

As promised, I have also produced a food/hammer conversion rate chart to help you make some rough estimates when comparing different improvement options. Note that these are city dependent so will not reflect a civ-wide food-hammer conversion rate.

For simplicity, you should assume that, where the conversion rate is greater than 1.00, each extra food is worth more than an extra hammer.

Size Food/Hammer
1 1.36
2 1.25
3 1.15
4 1.07
5 1.00
6 0.94
7 0.88
8 0.83
9 0.79
10 0.75
11 0.71
12 0.68
13 0.65
14 0.63
15 0.60
16 0.58
17 0.56
18 0.54
19 0.52


With a granary, multiply the above numbers by 200%
With a forge, multiply the above by 80%
With a factory, blah blah (you get the drift)

[smbakeresq]

Interesting work, I always intuitivly knew that population growth was at least as important as production. I think this proves it, although I read your post without checking the calculations.

Thanks

[fed1943]

Good math work,Coeurdelion,thanks.
I always thought:food first(not the same that more or less strong).
An humble sugestion:not anymore 3 cities now,just one;pig,cow and bronze;what's cost/payof in research and improve?what to do first,second and last?(I know,it's impossible to see bronze without BW,but...).
Best regards,

[couerdelion]

Originally posted by fed1943
Good math work,Coeurdelion,thanks.
I always thought:food first(not the same that more or less strong).
An humble sugestion:not anymore 3 cities now,just one;pig,cow and bronze;what's cost/payof in research and improve?what to do first,second and last?(I know,it's impossible to see bronze without BW,but...).
Best regards,

Now this is a different question and I guess you're really saying that you have a capital with pigs, cows and some invisible copper and want to know whether to go for Animal Husbandry or Bronze first and what to improve first.

I think, if I were given this then I would probably research animal husbandry first and then through mining to bronze. I would also probably “pasteurise” the cows first and not the pigs but this is simply because I would not have the slavery option at this stage and would almost certainly end up with some unhappy citizens (if they’re unhappy then so am I).

All in all, with this scenario, I would act contrary to the way I have previously mentioned but this is not really an inconsistency but rather that my initial conditions for the analysis were not set (I do not already have slavery). I’ve I do have slavery then the numbers tell me that, all things being equal, I should be building sties before stables.

I should also point out one other big caveat which will affect my improvement order.

1) If I do not have iron or copper already then that tile gets mined. There would be no question in my mind as to the correctness of this decision since the ability to build axemen dramatically improves the security of all existing structures and improvements
If I am running up against health limits in larger cities and I already have pigs then I would get the cattle up first. The decision is a Civ-wide one and these are really the only ones consider.

[Shaka II]

Very nice work Couerdelion. I have a few questions.

- You mentioned 45 hammers or 60 hammers per pop point. If this is correct, then it would be nice to know what the conditions are for the different conversion rates.

- It doesn't look like you figured in the effect of unhappiness on this. if you pop rush 1 pop, that causes 1 person not to work in that city for 15 turns, yes? If you pop rush 2 pop, I'm not sure how that is handled, 1 unhappy person for 30 turns? This effect needs to be considered before we can evaluate a food/hammer ratio, unlike the conversion in cash buy rushing.

- Does pop rushing hurt in the end, since bigger cities generate more commerce and production? The sooner one gets their cities up to 10 or 12, the more commerce and production they will be generating. In order to build cottages into hamlets and villages, they need to be worked. I think this is difficult to answer, especially since the city pop cap is usually reached in the ancient era at around 6 or so, until more resources or health and happiness buildings are made to allow further growth. Intuitively, it would seem that there's an opportunity to pop rush a bit when this early pop cap is looming. Might as well get rid of the unhappy workers then.

- Another way to look at is the cow city may not look so good in the short term, but once it is allowed to grow to a certain size, it out produces the pig city, which has food, but no production, other than what it's already spent by pop rushing. Does the tortoise beat the hare?

- I like to have at least one big farm with +5 food to support my early mines and cottages, and some smaller +3 food farms or flood plains to balance the remaining cottages and mines.

[Velociryx]

Somebody got a link to the CivFanatics thread? It answers this question...has to do with hammer overflow, and a pecularity with the way Civ4 handles it. Can net you HUGE bonuses of hammers if timed correctly (MM)

-=Vel=-

[Hermann the Lombard]

Shaka, I can give you a very partial answer. The number of hammers varies with the game speed, presumably varies with level of difficulty, and also with distance from the city.

[unamablebuiler]

it also varies vith underlying terrain forrested hill will give more hammers than forrested graslands and plains

[Shaka II]

Originally posted by Hermann the Lombard
Shaka, I can give you a very partial answer. The number of hammers varies with the game speed, presumably varies with level of difficulty, and also with distance from the city.

I was wondering if his 45 or 60 hammers was coming from different speeds, but I think he said epic speed. I don't know if it also varies with difficulty, but it's possible. I think he's playing emperor.

Distance from the city? Not sure what you mean by that. That applies to how many hammers you get from a forest, if it's outside the city. The 45 or 60 hammers is in reference to how many hammers you get for sacrificing 1 pop from the city.

[Hermann the Lombard]

Whoops! Sorry. Brain fart.

[nbarclay]

Under normal circumstances, if my analysis using the figures supplied is correct, pop rushing is not worth it. The normal tradeoff between food and hammers is one for one, yielding a minimum cost of 33 hammer equivalents that must be sacrificed to regrow a lost population point. Then add to that fifteen turns in which the city size limit without happiness problems is one lower, meaning one less tile worked. (If the city is not already bumping up against its size limit, the time in which one tile less is worked as a result of a pop rush can be much, much longer.) If that extra tile would be a grassland forest, that’s another 15 hammers. That adds up to a minimum of 48 hammer equivalents - more at larger city sizes - in order to get 45 hammers from a pop rush.

Assuming my analysis is correct, pop rushing only makes sense in special situations where there are other factors involved. To give three examples (and there are certainly others),

1) When the resources available and other considerations break down in such a way that a city starts to have health problems before it reaches a size where happiness becomes a problem, the danger to public health eats into the advantages that normally come from growing the city as large as happiness permits. Thus, the fact that pop rushing lowers the limit on how big the city can be without happiness problems is not as big a cost as it normally would be - especially if the pop rush is timed to have the city regrow right after the rush.

2) If a city is bumping up against its happiness-based size limit (or is already past it), using a pop rush to finish a building that will improve the city's happiness sooner buys back at least some of the unhappiness penalty that the rush costs, thereby reducing the net cost of the rush. That can be especially attractive if a city is already wasting food from being past its happiness limit (something I try never to allow to happen unless very special circumstances are involved but have been known to have happen occasionally due to micromanagement errors or canceled trade deals).

3) If a city has plenty of food but very little production, it may be worth a loss of shield efficiency in order to get buildings completed in a reasonably timely manner. That is, the gain from getting buildings completed sooner may offset the fact that pop rushing has a higher shields+food cost than normal construction. (That may be especially important in coastal cities where the only tile a sacrificed citizen could have worked is a water tile, since water tiles don't increase in value from being worked longer the way cottages do.)

Edit: The analysis above assumes the absence of a granary. If a granary cuts the food cost for replacing population lost to pop rushing in half, pop rushing can be a good investment for cities with granaries that are maxed out in size until until a civ has enough luxuries and so forth for cities to grow to size 10, as long as the pop rushing doesn't prevent the city from working a tile that gets a better return than one hammer per food lost (for example, a mine or a plains tile with an elephant camp or quarry).

[rewster1]

It's actually 30 hammers per pop point sacrificed, pretty much regardless of the amount of food that went into making that pop. So, if you have a granary, for instance, you've nearly halved food cost to grow a pop and therefore nearly doubled the hammer:food ratio. And that on it's own makes it worth it in many cases.
If you have even one good food resource (seafood, pigs, wheat, corn) you can usually whip basic infrastructure into place more efficiently than you can build it with hammers. Unless of course you have multiple hammer resources...

[fed1943]

Yes,that's.Trade 1 pop.for 30 hammers.Doesn´t lose food;so,the food requeriments for the next grow will be acording the new population number(after poprush done).
Best regards,

[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.

What happens when you sacrifice more than 1 pop point? Do you get all the hammers, 2X or 3X? If yes then it's good because the unhappiness penalty is the same, just 1 unhappines for 10 turns (in normal).