Dormant hammers/food/beakers/GPP

[krikav]

Something I have been thinking alot about lately, is the factor that hammers/beakers/GPP or what have you, that are parcially invested in some project, is quite useless. It's when you reach the tipping point you get the utility.
Not sure how to formulate this into a theory/model yet, and I'm not sure if it's usefull either... But the idea boils down into something like this:
The first hammer you put into a settler is worth nothing in the present. You have just turned that hammer into a piece of parcially built settler that won't see daylight for quite some time. You will get the utility for that hammer later, compared to hammers you put into that settler later on.

If we compare slowbuilding a settler with F+P 10 with a chop-assisted approach, (same production, F+P =10).

In the first case, we invest 10 per turn, and the first 10 we invest have to lie dormant in a parcially built settler for a whopping 10 turns before we get a benefit from those 10 F+P.
T0: 10
T1: 10
T2: 10
T3: 10
T4: 10
T5: 10
T6: 10
T7: 10
T8: 10
T9: 10
T10: The 100 hammers become alive when a settler sees the light of day.

We start to build a settler and a worker chops two forests.
In this chop-assisted aproach, we get something like this:
T0: 10
T1: 10+20
T2: 10
T3: 10
T4: 10
T5: 10+20
T6: The 100 hammers become alive when a settler sees the light of day.

Now, i'm far from certain how to calculate discount on something in civ4... But if we work from the standard settler (which cost 100F+H) invested in a city that works a forested grassland yields 4 F+H per turn, we also get some commerce. So perhaps it's okay to say that we have a interest rate of 5% per turn? This might be grossly in error, but let's use it for theorycrafting.


This means that 10F+H that is at a turn lying dormant in a parcially built settler has an opportunity cost of 0.5F+H, since those hammers are not doing anything at that turn.

I'm far from certain, but I think that this helps explain why chopping and whipping (and also GA-assisted GP-bulbing).

 

[krikav]

A practical example that helps see the point:
When you build something, you should first let your workers do other productive work, such as farming and cottaging. Only 4 turns prior to completion of that build should you divert your workers to chopping.
This improves your empire first, and the improvements you did can be utilized by your cities while the workers chop.

For the build in question, it does not matter at all if the chop landed in the build at the tail end or the head end. But for the empire as a whole, if the worker makes a farm before chopping or after chopping makes all the difference.

 

[sampsa]

But if we work from the standard settler (which cost 100F+H) invested in a city that works a forested grassland yields 4 F+H per turn, we also get some commerce. So perhaps it's okay to say that we have a interest rate of 5% per turn? This might be grossly in error, but let's use it for theorycrafting.

I don't understand. A forested grassland doesn't yield commerce. Where does 4 F+H per turn come from?

 

[krikav]

I don't understand. A forested grassland doesn't yield commerce. Where does 4 F+H per turn come from?

A settler is 100H, it can create a city which yields 2F 1H 1C at minimum. In 99% of the times, you do have _some_ tile yielding 3 F+H, the example I used was a forested grassland (2F 1H).
The citizen that works that tile consumes 2F to gain 2F+1H (netting 1H), so the total yield of a "naked" city T0 in most settings is 4 F+H.

i.e, for a 100H investment, you get 4H per turn in return. Since there are alot of better cities most of the time, and the fact that you also get commerce, made me do the assumption that the yield is really closer to 5H.

So a 100H investment give you 5% return per turn.

 

[sampsa]

Ah yes, you mean the net gains from settling 2nd city earlier? Yep, rarely it creates less than 2+2 while varies a bit, depending also on maintenance distance and connection, but usually is at least -neutral.

 

[krikav]

Yes, and I use this as a very crude generalisation, that the normal situation in civ4, is that on any given investment, you should expect to get 5% in return.

5% growth means that the available hammers double every 14 turns, and this correspond roughly with what I see in games.
If this is projected and if we assume that one has 1 city, 1 worker, 1 warrior and perhaps 1 pop at T20 (abit optimistic perhaps), then you have two such cities at T34.
You should have a 4-city empire by T48. And by T62 you should either have a 8city empire, or less if you have some infrastructure or an army.

 

[sampsa]

I think completely ignoring commerce, this 14T to double sounds about right. However, cities 5-8 are getting so expensive that it's impossible to ignore commerce and the phase of vertical growth comes.

 

[krikav]

If one accepts this "5% growth is normal" as a crude metric, then it follows that slowbuilding a settler compared to a 2-forest chop assisted settler is losing 27.5 hammers compared to 16.5 hammers, just as a consequence of the fact that slowbuilding locks in the early hammers for such a long period, before the settler is out.

So it's not only a question of if you get your settler out earlier, it's a question of how long your hammers are "stuck" in a build being unproductive before they are released and start to yield benefits.

 

[Bibor]

It's just more beneficial and practical to look at what you are saying from the opposite angle.

Your start your empire with, say 150 worth of hammers (settler + warrior or scout) and for sake of simplicity, say, 50 beakers worth of tech (your starting techs).
Once you settle your first city, your first city is worth exactly 100 hammers, and - ignoring tech for now - but adding the price of a warrior, lets say the founding capital of your empire is 150 hammers.

What you do next is simple, in theory: you increase the value of your empire by generating profit (beakers, hammers, gold, culture etc.) by the means of profit multipliers (tile improvement, city improvements, population etc).
All investments in this game, with the exception of settlers, work as profit multipliers for that initial 100 hammer investment each and every time.

To take your example, delaying the settler. If the settler costs a 100 hammers and is at 90 hammers invested, is it worth delaying the settler by 10 turns and switching to, say, "produce science" instead? The real answer is: it depends.
What if those beakers that you acquire from this city that paused settler production could be used to get an early tech that can be traded for 2 equal value techs from neighbors? The profit from those beakers would triple! If it's a tech worth 500 beakers, you'd be getting 1500 beakers worth of tech, or three techs for the price of one. How much did this city contribute to that tech by "hammering beakers"? lets say 10% of total tech cost or 50 beakers. But it's 150 beakers now. So was it worth it? Again, it depends Civ4 is a great game!

What new cities do is what new stores do to a retail chain - they reap global benefits (like happiness and health multipliers), but take some time to become profitable, especially if you are planning to "hammer in" lots of buildings, which, again, serve as profit multipliers (for example a marketplace multiplies gold income by 1.25 and adds more happy heads that add further % to overall productivity of the city). This is why best players treat food resources as the most important real estate, because if the city can grow to-but-not-above global happy/health caps without further hammer investment, these cities can return their investment much faster. And this is where whipping ties-in as well.

Dear Lord, I just realised how simplified Civ5 mechanics are compared to 4.

EDIT: To answer your further question: yes, if below or at happy cap it's always more beneficial to improve the city that has more profit multipliers (library etc.) and except if settling for a really important resource or blocking off AIs, it's not worth settling the next city until it can work at least 1 improved tile from the moment it's founded.

 

[sampsa]

Bibor, I understand what you say. However, I think krikav's example was from the very early game, before tech trading etc, when the question really is about maximizing food+hammers -output for the most part. Later it becomes much more complicated.

 

[Bibor]

Bibor, I understand what you say. However, I think krikav's example was from the very early game, before tech trading etc, when the question really is about maximizing food+hammers -output for the most part. Later it becomes much more complicated.

For the early game, there are factors that transcend short-term gains like blocking off land or connecting a critical resource (say copper).

In case of copper, the opportunity cost might be scrapped as it is in fact a mandatory move (do I go archery or bronze working? I have bronze, I better connect it, since I didn't research archery). So in that case, for connecting that bronze the "saved up beakers by not researching achery" also need to be taken into account, as well as the beaker cost for connecting the bronze mine via road (the wheel) if not accessible by river.
When blocking off a neighbor it's also imperative that the settler comes out as soon as possible. So these are special circumstances.

When determining the value of a new settlement, as krikav says, "it costs 100 hammers and does nothing", and will continue to do so until:
1. the city is founded
2. its yield transcends it's maintenance loss

However, "speeding up settler production via chops or whips" has its benefit roughly halved if the new city's food tile is not prepared in advance. This also applies to "2nd worked tiles" of importance, like gold, silver or even riverside luxuries for financial leaders.
Thus, not only does the settler has its opportunity cost, but worker costs and worker turns also need to be taken into account. A worker improving the 2nd city's basic 1-3 tiles can't do anything else during that time.
This is why creative leaders are IMO very powerful, as it's often possible to have food tiles for new cities prepared in advance, or at least improved almost as soon as the new city is founded, even if in the outer ring (and thus enabling superior long-term city placement), as well as providing superior science yields via cheap libraries and thus mitigating early city placements that are not adequate for cottaging.

I agree with you krikav that improving your existing cities need to come first, I would just add that (pre-) improving 1-3 tiles for your next city is just as important, especially in the early game when (except for the palace) multipliers are scarce and the land provides yields at face value.

EDIT: I'm just basically reporting what I see in Lain's videos, as I'm a far worse player. His meticulous planning to the extent that a workboat reaches a fish half across his empire on the exact same turn as a new city is founded is just one example.

 

[Gumbolt]

That 100 hammers and additional cities settled may stop an Ai having 10-11 cities. By restricting the Ai growth it makes the end game much easier.

Of course if you have early slavery then whipping adds a huge dimension to this. Grow to size 4 with 2 chops and whip! Or size 6 and whip.

I think getting your best resources up and running is key to any start. Have a 2nd city with a farmed corn resource is huge. Growth and whipping wise. We saw in Cookbook advantage of 2nd/3rd city to whip settlers from size 4-2. Once you have libraries they cities could add 6-7+ science a turn without rep..

Your initial figures do not account for overflow from previous builds. Using overflow from a previous build can reduce settler build time. You could infact chop into a build knowing it will overflow into a settler.

 

[krikav]

I do appreciate the discussion. But I think that the theme I tried to present isn't really clear.

Say that you play in the early game and first put 90 hammers into a settler for your third city, and then change your mind and start some other build.
Compare this with the same situation, but where you have only put 10 hammers into the settler.
Which hurt your game more?


And also, say that you think that building a settler direcly after your initial worker is a good idea, and you put 10 hammers into that settler at T13-T14, you then change your mind and want to grow to pop2 first.
Now you can resume your build of that settler after you reach pop2, or if you reach pop3. (In both cases the settler takes 9 more turns to finish.)
In which of those does your game suffer more from those early 10 hammers?
From this perspective I think its obvious that it is the one where you waited until pop3. Since those 10 hammers that was initially invested has been lying dormant for more turns before finally becomming something concrete.


Still not clear? Another example.
Say you have a playstyle where you want to give your empires scientists some variation, so that you each turn change tech rotating through all available techs all the time.
Such that when you play greece, you finish agriculture when you have also put 100 beakers each into TW, Mining, Myst, Archery and sailing.
Now, you are hurting your game immensly, not because you are wasting beakers since those beakers aren't technically lost. But because your beakers are lying dormant in techs that are only half-finished, instead of reaching agriculture earlier, thereby unleashing a benefit to your empire.

 

[Fippy]

It's quiet interesting that mixing build orders, i.e. switching between settler and warrior early,
can actually result in getting your settler 1t sooner.
Just ask Gumbo about my sgotm micro madness

While your worker improves food, settler might be the better build on a few turns (not on more than 2t i think), even if completed at higher city size.

An example:
16/22 food stored, and you wait for 6f wet corn being improved.
Next turn your worker will have the farm completed, and your growth increases from +3 to +6.
If you switch to settler now, we lose 3 food but gain some settler hammers, new pop reached will still happen on the same turn thou.
Those "sneaked in" settler hammers might be enuf to speed his completion up by 1t.

 

[krikav]

@Fippy Absolutely, such early micro is very important, if something is really madness it's rather to dismiss such considerations as madness.

In the example you present, what you are doing is that you redirect hammers that would end up in a warrior (or barracks) to the settler instead, since you will only spend one turn growing while building, instead of two.
This might or might not be desired, depending on if you are close to completion of the warrior, or if you really need the warrior.

To try to shoehorn this example into what I'm trying to discuss here... The 16/22 food you have in your bar at that turn, is completely useless to you. You get no benefit from that food what so ever.
Only only get the benefit of an extra pop/citizen once you reach 22F. So I call those 16 food dormant or stagnant.

A horrid mistake one can do, is to from your situation start building the settler while at pop1 and 16/22 food.

I think proper play/micro circulates alot around minimizing stagnant beakers/hammers/food/GPP.

 

[Gumbolt]

I think what Mylene is suggest is when food is at 16/22 and you grow in 2 turns at 3f surplus you might as well invest those hammers for one turn into settler and grow on +6 food. The question is would this speed up the settler by 1 turn. Same goes for warrior. Sometimes completing warrior with OF can speed up a settler by 1 turn. This is where Mylene's micro reaches another level. Others will also do the same for food in granaries and when to whip so your granaries are full.

 

[krikav]

That is indeed what Fippy suggests. Let's also say the city has a 1H city center.
The two alternatives you have is to build settler one turn, and then grow to pop2 building warrior with 6F. This is likely correct most of the time.

The alternative is to continue build warrior this turn, and get a 19/22 food bar, and another hammer into the warrior.
Next turn you will end up with 19+6= 25/22 food (or rather 3/24 at pop2) and yet another hammer into the warrior.

First alternative is: No food in the bank, 1 extra hammer in warrior and 4 extra hammers in settler.
Second is: 3 food in the bank, 2 extra hammers in warrior and 0 extra in settler.

The 3 food in the bank I say is almost completely worthless, so what you can choose between is 2 more hammes in a warrior, or 4 extra hammers in the settler.
If the 2 extra hammers is the differance between getting your first warrior out, and you really need him for fogbust or defense, that might be best.
If there is no need for the warrior, or it won't complete, and you get the settler out a turn earlier due to the extra 4 hammers invested, that is likely the way to go.

 

[Gumbolt]

Of course you can micro tiles too. Your logic assumes you will only run tile x. So growth and hammers can be tweaked. All higher level players will micro cities most turns.

Benefits of an earlier settler can snowball. 1 turn here and faster city 2 can lead to faster city 3/4. Pends what you really value. If your waiting for a warrior escort and settler has to sit there your logic is right. On deity level some will fog bust second city sites anyway.

 

[krikav]

Yes, it depends on what you value, what is needed at the time.
I'll just continue trying to explain, since the topic I'm trying to discuss really is something different than a general discussion of the utility of getting your settlers out earlier.


If we are at this fictional turn from Fippys example, and we have 16/22 food in the bank, and we have a worker that will turn a 3F resource into a 6F resource next turn. A 1H city center and a warrior at 13/15 built.
Call this "Scenario1"
Now we can consider working the 3F resource for one turn, and then the 6F resource for one turn, and end up with:
Pop2, 3/24 Food and a built warrior.
Call this 1a)

This might be what we need. OR it could be better to build a settler for one turn and only then grow to pop2 with the warrior. Our result would then be:
Pop2, 0/24 Food, a warrior pre-built at 14/15 and a settler pre-built at 4/100.
Call this 1b)

What is best obviously depends on the situation.
However, the thinking and philosophy I'm trying to hint at in this thread is the relative value of these hammers.

Say that all things are equal from this previous example, except that we have no hammers invested in a warrior.
This we call Scenario2.

The same aproach as in scenario1 would result in:
2a)
Pop2, 3/24 Food and a warrior at 2/15

2b)
Pop2, 0/24 Food, a warrior at 1/15 and a settler at 4/100.


Now I hope we can agree, that using aproach "a" is more sensible and likely to be the better aproach if we find ourselves in scenario1, compared to scenario 2.
In 1a, we release the dormant hammers previously invested in the warrior.
So the value of the two hammers is in this scenario much higher, compared to the value of these hammers in 2a!

 

[Bibor]

I don't think that you can put what you're describing into a formula, because what you're describing is how we play this game: determining when to build and what.

There are only two types of actions in civ4:
1) actions you want completed as soon as possible
2) actions you want completed at an exact moment

Both have a built-in loss. Actions you want as soon as possible prevent you from doing something else during that time as well as having a cost of possibly not being fully utilized for a time.
Actions that you want at an exact moment, on the other hand, can prevent you from capitalizing on an opportunity you can't predict will happen, at least not with certainty. For example getting out a settler at a perfect turn, just for the spot to be taken by an AI.

You deal with this by transforming the inherent weakness of the first type into an advantage, by sacrificing past and current gains for future profit. The Lib race, cavalry rushes, beeline to Aesthetics are perfect examples.
And you use the second type of actions to create the best possible base for "first type" actions. Examples would be unit and build order micro, optimal diplomacy etc.

I don't think it's valuable to think about tiny elements of the "loss segment" as something to be prevented. I think it these kinds of losses be embraced, acknowledged and compensated by profits on actions that inherently carry profits.

Or, to put it into another perspective, a single "bad roll barb" can kill your warrior, even if you do everything right. And then you have to whip another warrior, efficiency be damned. Now you can count all your fogbusting warriors as hammer investments and nothing else. Or you can treat them as expenditures that buy time for your cities to pop borders and reduce the fog, for workers to work in safety, and for other, stronger units to be created at more optimal later turns.