[SPOILERS] William discovers a source of horse. FDR of Mongolia

[WilliamLP]

Interesting discussion here by the way, I'm really enjoying it. Even if some of what Suttree and Seven is saying is surely passing over my head. But I love the culture of over-analysis that exists here!

I sometimes am the stubborn guy who won't accept (yet) the thing at step 1 which is needed to be given to talk about steps 2 and further. 10% of the time that leads to something interesting. 90% of the time it's just rehashing things when it would have been wiser to just listen to people more experienced than me.

The questions I'm interested in, since the whole premise of this kind of talk hinges around them:

1. Can growth in Civ 4 be usefully modeled by a compounding interest model? The thread by Seven that someone pointed me to on this topic is absolutely one of the best insights I've ever seen about the game, to have the idea to equate an ongoing return with a fixed present cost.

It seems like in the early game, the curves are certainly increasing at an accelerating rate. Somewhere the reasoning has to break down though, since the game has a finite time limit, and very few games go long past Industrialism, so using a formula that has part of an integral past there is worth questioning. Also, once all land is occupied, I wonder if outputs start to flatten out to linear and even decelerate. Eventually every tile is going to be worked and all output-increasing techs and buildings will be in place.

Does this have an important effect on models? (I.e. are there better models, which are still simpler than analyzing the full complexity of the game, and useful?)

2. Do beakers, production, and food and growth follow the same shape of curve at all? Food, for instance, should probably level out earlier once you're working every tile. (With bumps for, e.g. Biology and SP, if (big "if"!) I ever get there.) Can taking into account a difference lead to a better model? (E.g. my perhaps the rate of return I need for a forge to be valuable is different than that for a library.)

Anyway, I'm hoping to keep thinking about this kind of thing until Jowy starts massing chariots on turn 40 in his capital which ends up being 8 tiles from mine because we both spent our first turn moving toward each other.

[Ceiliazul]

It seems like in the early game, the curves are certainly increasing at an accelerating rate. Somewhere the reasoning has to break down though, since the game has a finite time limit, and very few games go long past Industrialism, so using a formula that has part of an integral past there is worth questioning. Also, once all land is occupied, I wonder if outputs start to flatten out to linear and even decelerate. Eventually every tile is going to be worked and all output-increasing techs and buildings will be in place.

Does this have an important effect on models? (I.e. are there better models, which are still simpler than analyzing the full complexity of the game, and useful?)

2. Do beakers, production, and food and growth follow the same shape of curve at all? Food, for instance, should probably level out earlier once you're working every tile. (With bumps for, e.g. Biology and SP, if (big "if"!) I ever get there.) Can taking into account a difference lead to a better model? (E.g. my perhaps the rate of return I need for a forge to be valuable is different than that for a library.)

Anyway, I'm hoping to keep thinking about this kind of thing until Jowy starts massing chariots on turn 40 in his capital which ends up being 8 tiles from mine because we both spent our first turn moving toward each other.

Yes the growth can continue into and past the industrial age. If you want to win, you *better* keep growing. When working all tiles, with all core multipliers built, the growth curve may require annexation of other lands. Turns out that cavalry/tanks are output increasing builds too!

That's not actually glib. If you fall off the growth curve even late in the game, you're going to lose to the guy who kept growing. This answers your question about more complex models too: even basic models are quickly overshadowed by military factors beyond your knowledge and control... so putting tons of effort into a complex model is probably not worth it.

[suttree]

...so I don't know where I misinterpreted you (or failed to interpret you completely).

We seemed to disagree about this:

If a point of commerce is taken to be worth 3/5 of a hammer, then spending hammers to build wealth to get tech is 3/5 efficient* and does not necessarily meet the baseline standard.

That is,

Suttree: You always have a hammer investment that tracks the average growth rate because you can build wealth.
Seven: Building wealth (subject to *) is an investment with return less than the average growth rate because 1c=3/5h.

We "disagreed" because I want to derive/use the 3/5/8 valuation differently. And I thought the difference was interesting.

Seven: If I reallocate labour from a farm and a gh mine to two cottages, the economy has neither grown nor shrunk.
Suttree: Reallocating resources from hammers to commerce grows the economy when the marginal commerce return of a hammer is small and shrinks the economy when the marginal commerce return of a hammer is large.

I want my economic model to be such that option A is a "better" than option B iff the value I assign to A is greater than the value I assign to B. If, in the model, I do my best to approximate the best option (maximize marginal return) then my economy will track the average growth rate.

We agree: 3/5/8 approximates the opportunity cost of food vs. hammers vs. commerce.
Suttree adds: 3/5/8 also seems to approximate the relative marginal return of food vs. hammers vs. commerce (but not always)

So we agree:

...building wealth is a red flag, because maybe you could have gotten better total yield by making more cottages and fewer mines, or whatever.

But this makes the most sense if you have in the back of your mind some valuation for commerce as compared to hammers where, to start, you could have known that more cottages and fewer mines were considered a better total yield than any other allocation of cottages and mines that satisfies 3/5/8.

The valuation that matters in making decisions is the marginal return on hammers vs the marginal return on commerce on a given turn and in the near future. Sometimes I can look ahead and make a good guess about what that will be. In the long term, I can't, so I use 3/5/8. Both because I will have some flexibility to substitute and because the game is balanced such that even if I'm locked in to an allocation, 3/5/8 isn't going to be a bad approximation of the value of commerce/hammers/food on any given turn.

I think the above is useful because it more precisely captures the way I actually makes strictly economic decisions in the game. I project the available investments. That projection tells me how valuable the various factors of production will be. I manage my cities to maximize the factors of production with the greatest return. That is, (1) I have a variable factors of production f/h/c (2) I have variable products that define prices f$/h$/c$ (3) I maximize income. A fixed f$/h$/c$=3/5/8 valuation squishes (1) and (2).

So I don't think we "disagree" about anything, but I was at least "talking" about things differently. And I thought that the difference was interesting.

[WilliamLP]

From the lofty intellectual spheres of Civ growth philosophy to the depths of my decisions in this game:




My people aren't going hungry, that's for sure! Yet another fanstastic food tile (6/0/1) was revealed. The red border is vision after the border pop so no need to scout there. I'll probably move to the "3" next and circle clockwise. Only a few more turns are left where the scout can wander without fear of animals.

There are a few possible sites north of Mr. Ed which would far from the worst second or third city locations ever. The plains hill 2E of the wheat is also interesting.

(Bears and lions didn't exist yet in 4000 BC... Didn't you know?)

[WilliamLP]

So the question of worker-worker-settler vs worker-settler-worker.

I can look at my first build (worker-worker-settler):

Side by side with (worker-settler-worker). There might be ways to tweak these to get better discrete math effects and save a turn on something somewhere.

They diverge on T26. The second build:

• Finishes the settler 5 turns earlier (EOT33 instead of EOT38).
  
• Second worker is 11 turns slower (T41 instead of T30).
  
• Warriors #2 and #3 are 3 and 4 turns slower. (T36, T42 vs T33, T38).
  
• The fourth food is available 3 turns later (T37 vs T34).
  
• Growth to size 4 is 4 turns later (T37 vs T33).
  
• As of turn 42, hammers are down by 20, but that's because I chopped in the first plan. Still, the first plan has the extra worker turns to do it so perhaps it counts. The first build puts more food-hammers into growth vs hammers (a good thing).
  
• As of turn 42, capital is 5/28 food at size 4, down from 3/30 at size 5. So second build is down by 26.
  
• Commerce is 3 down. (4 lost because of growth to size 4 later, but one gained because I revolted in a lower commerce turn).
  

So is 5 turns on the first settler worth all this? It can be quantified. With an example to settle on the plains hill working a 2/1/1 tile, a turn is worth 2F, 3H, 3C. (2 commerce worked + 2 trade routes - 1 maintenance). It also gets 1 turn to work the wheat before the capital grows, or it can keep working it freeing the capital to whip perhaps.

Quick and dirty, multiplying the per turn values by five:

• positive = 10F + 3F (work the improved corn once in the new city), 15H, 15C
  
• negative = 11 worker turns (this could include 40H of chops or not), 26F (in capital), 0 hammers (ignoring chops), 3 commerce. 7 warrior-turns (not useless).
  

So the net difference is essentially 11 worker turns and 26 food in the capital vs 12 commerce, 15 hammers, and 13 food in a new city. (Plus I suspect it's possible to shuffle that around with better micro.) I think especially because of the worker turns, the slower settler wins here.

My analysis is probably filled with fallacies, mistakes, and egregious notions.

Also an EOT 38 settler will be behind the RB meta. (I believe most people will play for the faster one.)

[WilliamLP]

That's not actually glib. If you fall off the growth curve even late in the game, you're going to lose to the guy who kept growing. This answers your question about more complex models too: even basic models are quickly overshadowed by military factors beyond your knowledge and control... so putting tons of effort into a complex model is probably not worth it.

But whether it's worth it depends on whether someone finds the modeling more fun than the actual game or not, right?

Civ is a pretty awesome meeting point of the strategy and big picture with the detail oriented parts. It's certainly what makes the game appealing to me. People with strengths on both sides seem to find their games to shine in.

But yeah, I'm not really looking for complex models but maybe places where simple models could still be simple but made better. (I fully appreciate that you can easily make everything in the game that gets boosted by 25% an exact multiple of 4 so that you win in discrete math while getting trounced in the actual game!)

[suttree]

[random]
What about starting the second worker immediately at size 2 (holding the warrior on the queue)
[/random]

I don't know when you get BW....

[WilliamLP]

[random]
What about starting the second worker immediately at size 2 (holding the warrior on the queue)
[/random]

I don't know when you get BW....

The earliest I can get BW is EOT24 since huge speed is slow. It's 85 beakers for mining and then base 207 for BW which is effectively 175 getting +2 prereq bonus for 32 turns. (If I save a bit of BW until after I'm making 15 beakers per turn, then I get a whopping 3 prereq bonus... I might be able to save a whole two or three commerce this way! )

I tried the second worker immediately but wasn't that impressed with the result. It only comes out on turn 28 instead of turn 30 at size 3, and whipping feels like a non-starter to me. (On turn 27 the second worker is 57/60 done but there's no flexibility at all to squeeze hammers out of this start.) I didn't play too much with chopping with the first worker, since that feels like a strat for India only since they get better returns over time from chops.

I also don't know if I'd really feel good about delaying a warrior for that long.

I know some players get good results out of early game BW and whip plays. I think I should look at a couple such starts and figure out if and why they're really better.

Turn 3:




There's really nice food up here, plus ivory for happiness. It's too far for a reasonable second city site though.

The next scout move could be S-SE (very conservative) or NE-SE hoping there isn't a forest 2E1S of the sheep which would slow the scout down moving south. NE-NE feels too aggressive, given that in a landlocked start I really want to see what is in every direction, and soon.

Two players have already found hut techs. These could shift the balance dramatically in this game! Getting Bronze and saving 16 turns of early research for free would be simply massive. It would mean I could be many turns ahead on a run for HBR or snowballing with earlier Pottery. I think just for this chance it makes sense to get Mining first even not going directly to Bronze afterwards. (Because I think I'd rather start farming the corn as soon as possible and concede to learning where the copper is later than otherwise.)

Going by demos last turn, I think most people have land starts. The average land tiles per player was over 8. I'm really curious what this map looks like in the big picture, because there mysteriously must be quite a lot of water somewhere. But if cities aren't on the coast, where is it?

Since there are only 130-something land tiles per player (less than a 12x12 square) some of the land I see, e.g. perhaps the elephant, should be contested. I wouldn't be surprised to meet a contact or two on any given turn now.

[WilliamLP]

The wimpy scouting path:




There's my first hut. I'm putting a turn into Agriculture just in case I'd pop Mining from it. (It just smooths out risk to a microscopic degree - I'd be less happy to pop Agriculture than otherwise to balance, but still really really happy.) And I'm convinced I don't need an immediate bronze opening. And I'm also interested in hilarious counter C&D measures, like researching both Mining and Agri to within 1 turn of completion just to confuse the heck out of people.

It will be interesting to see if anyone is going religion first! With this start, it wouldn't be completely insane to go for that with a Hunting + Myst civ.

[WilliamLP]

Turn 5:

The hut had 38 gold. I'll take it, though a second scout would have been more fun.




So many farm animals to hunt. Barb animals should start appearing now so the scout has to be careful.

The plains hill 2W of the scout is looking like a fine option for a second city. Production bonus, immediate trade connection, good food, and it can be quite productive without a border pop.

Still no contacts to attack me and put this slow start to the test.