Age-up times and economy

[KaanHoca]

First of why I ask this question: There are civilizations like Russia, Portugese also potentially e.g the British, Sweden or Ethiopia
which work diffrently regarding booming, many of them miss strong vill shipments like 3v or 5v at this point, but they have over average economic growth compared to many civilizations with 3 villager shipments like Spain. (I am not considering the strong economic buffs for Age 3 for this example since I'm too lazy to find the perfect example out of so many semi-ff, eco civs)

With portugese if you should find an food treasure, it's actually economically better to idle TC do an 10/10 and make use of 2 TCs faster.

With USA it is economically better if doing an FF to Age-up later and sending 3 Immigrant cards in Age 1 to skip age 2, since the civ can get 4v and bank in Age 1 for an bigger cost than 2.

And the question is basically: How could I calculate the opportunity cost for idle TC or 700w shipment with eco upgrades like ST easier compared to sending 3v twice and staying longer in Age 1 for example and then aging up with extra economy for 90sec of age up time but I got worse age 2 shipments.

Civs where I struggle atm are: Japan staying in age 1 for doing an shrine boom with HK and also sending shipments like 7LuckyGods (XP-Shrines) then also sending GFA which is completly useless at start for long time but gives good value after coming in. Also Japan Age 2 shipments kind of aren't great either I think, maybe I'm wrong? Would like the opionion about that since 4v, 600w are just 2xAge 1 shipments but 90sec delayed, so why not send 2x 300w for example which come in 90sec and 50sec earlier.

or with Ethiopia you have these 2 intresting strategy features: Abuns, mountain monastaries and Jesuit Influence (200Influence each Homecity card)
so I thought maybe its better to just go Age 2 with 10/10 but quite slow since no age 1 card sent and build 5 abuns faster and also buff the Age 2 shipments with 200Influence which should payoff the economy lost while aging and before. (atl. 1 card more with 200influence and Age 2 value instead of age 1 card and TC idle time.

[callentournies]

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[callentournies]

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[callentournies]

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[richard]

And the question is basically: How could I calculate the opportunity cost for idle TC or 700w shipment with eco upgrades like ST easier compared to sending 3v twice and staying longer in Age 1 for example and then aging up with extra economy for 90sec of age up time but I got worse age 2 shipments.

The opportunity cost of idling TC is a function over time. It is not a constant. (Provided you constantly produce vills from age II onwards)

The ressources you lost cause you idled TC grow linear over time then.

That s because ALL your vills you produce (from age II onwards) will come out later and thus start gathering later.

[Kaiserklein]

Haven't read everything but yeah basically the way a given action impacts your economy can usually be described by a simple function, which depends on the kind of action.

Say you're going for a 13 cdbs age up as France. You'll have one less cdb for 90s while aging, that's a fixed loss of resources of 90 VS (they're cdbs so it's 25% more but w/e). But then if you're shipping 4 cdbs upon age up, you get them about 28s earlier, which is a fixed gain of res (4 x 28 = 112 VS). You also get steel traps 28s earlier which is another fixed gain of res, which depends on how many vils you have on food, but you get the point.
So it's pretty easy to figure out that an idleless 13 age up actually nets you resources (on top of the other benefits, such as having units out earlier or sending your 2nd colonial card earlier cause it's back to back). It's strictly superior to 14, provided it's idleless. Which is btw why people often suck at France, but that's another story.

Now if it's not idleless, it's harder to calculate. Say you idle for 14 seconds for the sake of simplifying, that's half a vil cycle. One way to look at it is you're popping each cdb 14s later, so you're losing 14 VS per vil cycle (= 28 seconds). Another way would be to say you're down half a cdb, so you're losing 0.5 VS per second. It's exactly the same thing, but anyway the point is you're constantly losing VS other time, so it's a linear function, while it was previously just a fixed amount (a constant).
It's the same if 1 vil get raided, it will be a linear amount of res lost over time. While if you lose 1 huss, it will be a constant loss of resources. So "is it worth losing 1 huss for 1 vil" is a question that can't be strictly answered, it depends on how long you have till it pays off.
Same if you queue your 1st vil late... Which almost everyone does because they're not splitting properly on crates (I'll never understand that)

Then there's harder stuff to calculate, like the otto mosque upgrades. Once you tech it, you'll gain say 5 VS (or w/e, doesn't matter) from your next vil popping 5s earlier. But the vil after that will pop 10s earlier, then 15s, etc. That's an arithmetic sequence, so the cumulated loss of VS would be at the nth vil: 5 x n(n + 1) / 2 = 2.5n² + 2.5n, which is a quadratic. In other words, it keeps paying off more and more the longer you wait, unlike a linear function.

Then you have weird stuff like shipments which are "exponentially" (kinda) more expensive over time, meaning XP is less and less valuable. But at the same time your shipments become better as you age up, making XP more valuable for a while. Probably one of the hardest things to calculate.


So like I said, you can do maths to find out whether aging 13 idlelessly actually means less eco (it doesn't). Or even estimate that aging 13 with less than 10 seconds of idle time is usually a good deal in most situations (you'll be down a fraction of a cdb for the rest of the game, but you'll still have more resources early on and more tempo, and a good player knows how to snowball that). Or prove that training sheep or cows from a pen essentially never pays off. Or that eco theory in age 1 as ports pays off after 10 mins or w/e, which is crap.

But at the end of the day, there's just too many parameters for the most part, simply because we aren't playing treaty. In treaty you can essentially craft the perfect boom, because you're aiming at a 40 minutes timing or so, while in sup with military involved, you're aiming at different timings depending on your opponent's civ, the map, what you scout...
So it relies much more on experience than on maths. And out of experience, I can just tell you that staying age 1 longer to shrine boom is terrible haha. Tbf that could probably be calculated as well but I cba. Also civs like jap or ethiopia just have a lot of different options so it's harder to tell overall.


On a side note, that also applies to military, e.g when to tech veterancy, or when to ship combat cards. You can estimate it, but in reality it depends on too many parameters.

[Mitoe]

Callen and Kaiser have good answers. To keep things simpler: as a general rule of thumb with the original 14 civs you should always try to age as fast as possible without idling your TC for longer than 12-15 seconds (about half a vill).

The tempo of getting TPs/markets/wonders/vill shipments sooner (as well as military units out to harrass before opponent has units) is going to compensate you for what you miss out on for several minutes usually.

The only exception to this rule with the original 14 is Dutch, who should only do 14v if they get really good treasures. If you do 14v without good treasures, even without idling the TC, you will get ALL of your banks slower which is just not worth it.