# In-depth look on early-game food value and market boom abuse (theoretical evaluation)

Background:

I recently had a look into the cuman boom vs the malay boom. As I changed the builds to placing less farms and started market abuse, both became much faster and stronger. But opposed to the malay boom, the cuman boom had some limits with this strat. So I wondered about the early-game value of food, how much is it “worth” to buy from the market, so you could actually develop a booming strat for the cumans abusing it optimal so the castle time is not so far behind as it used to be without damaging the eco.

Problem:
How can you evaluate that. As the opposing strat to the market abuse is placing farms, which add a upfront investment and the food income is even worse than the other ressources. So there are 2 factors which should be evalueated:
A) Higher Value of Food
B) General loss of “value” of all ressources. 100 food at 5 min in the game are more valueable than 10 min into the game

To make it easy, I made a simple mathematical approach: For B) I assume a exponential decrease, looking for a “half-worth period” of the available ressources.

In Dark age it is somewhat easy, because the only 2 “eco investments” you can do there are vils and farms. So you have 2 different investments and 2 variants to find.
If I calculate this correctly I get a “half-worth period” of <= 4 mins and a food value factor of <= 1.78. If these would be changed abiove 4 mins and 1.78 factor it would automatically render farms better than vils, which for sure can’t be true.

In feudal it’s basically the same. With all upgrades in the variables would both be a bit higher, But I will come to this later, why this doesn’t matter for the boom approach. Of course only for the boom, if there is much fighting going on, this changes everything.

The real interesting thing is coming with Castle age and extra TCs. As extra TCs “pay back” their Investment in about 10 mins, this is the new value for the “half-worth period” (as the investment is given back the total worth of both timestamps would stay the same). With this taken into account and the new gather rates in castle age come into play, the “value factor” of Food raises to 2.01 whilst booming. But once you add military to this, the value will decrease drastically. So I actually think it’s better to never buy up to this number (201 G / 100 F) at the Market.
Also because of the value factor will fall anyway when the boom stops, this makes all farms less valueable than they might look whilst booming. The classical over-boom effect.

With these factors we can look into eco upgrades, farms and the market.
Always remember: These factors are only valid for a full boom without any disruption, in a practical game at least the real food factor will always be below the mentioned factors.

With the dark age factors, I calculated about 16 foresters to be worth upgrading double bit axe (16! foresters in feudal) and 22 farms until horsecollar pays of. So neither of these upgrades are actually worth it until you got castle age. With the Castle age factors double bit axe only takes 8 foresters and bow saw 13. So both are actually worth getting in early castle.
Farm Upgrades work even better: Horsecollar pays of after 7 farms, Heavy Plow after 9. But only if the factor stays at 2.01, which is rarely the case because the boom will occasionally stop. So here the theory can be a bit deceiving. But I think with like 12 farms both should already have paid of.

Anyhow, with these results in mind, it makes no sense to make any eco upgrades or farms in feudal (until aging up). Early farms can pay of, because the value they will give will raise during their lifetime, but feudal farms just delay your uptime because you could just abuse the market and get a faster uptime without damaging your eco in the aftermath. Here is how this works:

Dark/Feudal: 1300 F can be bought for 1987 G until exceeding 178F/100G For an total advantage of 184 F over placed farms. This is the pure advantage, much like the lithuanian food bonus. If the opponent goes for the same strat, the advantage needs to be halved, so it would be 92 F.
Early Castle Boom: 1900 can be bought for 2525 G until exceeding 201F/100G For an total advantage of 344 F over placed farms. If the opponent goes for the same strat, the advantage needs to be halved, so it would be 172 F.
As you can see 1900 F is a lot to work with, easily exceeding what you would usually have farmed when reaching castle for most games. Even 900 F (half the total amount) is a very high number, high enough to buy you to castle. But you need to be careful. If your opponent abuses the market earlier he can get an edge above you and if you don’t get the transition to the farm eco in early castle you will have big probs with your eco balance.
But for booming maps like arena/hifeout/fortress the no eco market abuse can easily pay off.

If we look at the special case of Saracens, the abuse potential is even bigger: 3100 F for 4705 G means a total advantage of 759 F over a pure farm eco. Even if the oponent is as fast as you in market abuse you would still get an advantage of 437 F over the farm boom until that, 265 more than the 172 F advantage the opponent gets via the abuse. I think it’s obvious why the saracens abuse is so powerful, the pure booming advantage is more than twice the other nations could get out of it.

But here’s the point: If this becomes “the play”, Saracens actually wouldn’t benefit the most. But Civs with the faster uptimes like lith, mongols, khmer or malay get the biggest advantage because they can build the market way before the opponent and take the best deals for their gold way earlier than the saracens (others). If Saracens only buy after the other civs already bought til 201 F / 100 G their advantage shrinks to 116 F. So the best counterplay against the Saracen Market abuse is to abuse it even before the Saracen player can abuse it as much as he wants to.

All the values I postet here are just for an orientation, in a real game they should be in general lower, because military is involved. The More military is involved, the less valueable food will become to be bought from the market. Keep this in your mind when trying to go for an strategy involving the market abuse. It can also sometime pay off to even exceeding the 201F/100G value occasionally, because non-idled TCs are still the most important ressource in booming.
But don’t make builds which would involve higher exchange rates. This is basically the edge of the market abuse potential for booming.

Also certain civs are different because their farming bonus:
Chinese
Teutons
(Sicilians)
Slavs
mayans
(khmer => faster uptime can even be better for more market abuse potential)

I didn’t have calculated the food values for these civs, but all should have slightly lower food values and therefore less market abuse potential compared to their other booming strats.

I haven’t played with this abuse yet, because I need to change a lot of my early game for this: earlier hunt, only a few buildings, no early farms, no feudal upgrades… It seems just wrong. I don’t even know how many vills would be the right amount to go up to fc with that strat, because it also depends if the opponent abuses the market, too. But I think I will occasionally try this in closed map at some time, where it could get me the edge in aging up and booming.
Possible strat could look like this: no mill but mining camp ff, market abuse, getting mill + certain eco upgrades on the way up to castle, full boom.

I think with certain civs like malay you could maybe even almost equal the cuman boom with the market abuse boom. Because the cuman player can’t get away with just market abuse then, he has to get the eco upgrades and farms early, where they don’t pay of as fast as in an fc boom.

In the aftermath the food value of 2 explains how valueable free food is. So for example the 400 free food of tatars is basically equal with +400 free ressources of any other kind. The Lithuanian 150 F from the start is equal with 300. The Mayans +15% even exceed the tatars bonus in this aspect because of the faster gather rate of deer and pork.

I will work on some builds how to make the best use of the market for booming. But as I don’t play boomy maps that freequent it may take a while until I can come up with it. I just wanted to share my research result, maybe someone else can find a way to use it in boomy maps or teamgames (may be difficult to abuse the market there ;)). The question is, if the 344 F advantage is worth learning completely new builds which are very vulnerable to any kind of disruption, go way into castle age and are also highly out-of-the-box. It’s not like how the sicilian first crusade abuse was almost impossible to beat in the boomy maps before the nerf.

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skipping them entirely is not practical

also you lose too much efficiency moving vils to gold and then moving them off of it later

the upgrades aren’t good because of their cost. the upgrades are good because you are bottlenecked by the number of TCs and the feudal upgrades can pay for themselves before you are no longer bottlenecked

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You get the upgrades in a bit later, it’s not like they are completely missing.
You alse benefit indirectly from making the farm upgrades before placing any of them.

But anyhow, these side-effects are indirectly included in the form of calculation, the calculation tells you at which moment which investment is the best ecowise. The problem is just with more complex things like tcs because for them I need to set up a complete “build” to calculate.

The thing is also that you get your upgrades when you need them. Until you click up to castle you don’t have as many lumberjacks because you don’t need wood for upgrades + farms. The clear fokus switch actually comes in handy.

what is the exact definition of food value factor?
I’d like to point out that in real game, dark age food shouldn’t be more valuable than other resources cuz you can take natural resources. Shepherds and forager gather around 19~20 f/vm (food per villager-minute) and lumberjacks gather around 21 w/vm, not to mention a great deal of food are from boars of <=680food total gathered at 28 f/vm if i’m not mistaken.

As for the HWP(half-worth period), a villager costs 50f, which is equivalent of 2.5 vm. Doesn’t that mean HWP in dark age is 2.5 minutes instead of 4 minutes?

Can you show details of how food factor rate is calculated?

And also, can you demonstrate your boom with market abuse to show how strong it is by uploading a recorded file?

It actually means how much gold 1 food is worth at that state of the game.

It is complicated: I use a spreadsheet to calculate the “life-time income” of vils and farms and adjust both factors that way that both somewhat optional investments (villagers and farms) get a paypack of exactly their initial investment. The way the calculation works is, that there is only one solution. It would be possible to calculate them, but the maths would be very difficult. All other investments would give you a netto negative payback.
There is no real alternative because both farms and vils don’t deliver a constant flow of ressources and farms expire at one point. So from the raw value of the farm + farmer must be substracted the value a lumberjack would give you during that timespan to get the farm value alone.

So if Vils and farms are set equally we get these values: HWP 4 mins, FV(Food value) of 1.78. Of course if you don’t see farms as an equal investment in dark age, the HWP and FV both shrink a bit.

Sorry I can’t explain it better, but the calculation is quite complicated to explain, but it’s a scientific approach. I wanted to share understandable results, not to explain how the math behind it works, it is quite complicated.

I need to find a good buildorder with a booming civ. I made one sub-optimal build with malay were I build like 4 very early farms to try the effect and made 30+2 pop fc (no loom) with them, leading into 3 tc boom immediately. But I think there is good optimization potential.
The thing is, for that build I made weird decisions like only having 5 on sheep while collecting the wood for very early farms to get the best out of them and lured the boar whilst aging up. With this amount of crazy play there are so many options how to play this, that I wanted to share the Idea instead. I don’t want to give a direction but rather explaining the goal. As I don’t play the boomy maps frequently I’m also torn about try going further into this, because in aggressive maps it’s basically useless to try a strat like this.
Why can I do a strat like this with malay? Because Malay can have the longest dark age for a FC. So you can delay the boar to make the early farms even earlier to get most of the food out of them before even aging up to castle. That was the Idea behind this attempt.
When I saw the result I just wondered how far you could get with an insane strat like this with malay or cumans, so I set up the calculations for the market abuse, so everytime I or somebody else tries a strat like this he could see in the market prices after he balanced his eco in castle if there is even more abuse potential. That’s actually the Idea behind it, to give all them who want to try this an orientation, if they could try to optimize their boom via the market abuse.

With a comparable strat with cumans (there I used 8 (too much in the aftermath) feudal farms with a 20 pop ff, I was able to transition into a 4 tc boom with a castle uptime of 18:20. I stopped at 22:20 with 83 vils (+wheelbarrow+1/3 of handcart researched) from five tcs because I don’t think it’s worth ever to make more than 5. At some point you want to transition into military. I abused the market in this play up to 181 G / 100 F, quite close to the optimum.

Both aren’t real builds, they were just some key ideas how I wanted to abuse the lifespan of farms and the market to get the best booming results. I’m also not somebody who makes buildorders usually, I’m not used to that concept. I try to adjjust the eco while I’m playing.
Sometimes I use buildorders from other people and try to opimize them, but rarely make some on my own, I don’t even know how I should begin with.

To make the “builds” above working I stopped the game at several times to consider how the game will develop and p.e. how much wood I will need in the near future to keep rolling. But what I made is for sure still far away from optimal, I don’t think it’s even worth showing the builds here, because they could misguide others who want to try it themselves. Not that they are particulary bad, but I think there is huge opimization potential.

The play which didn’t worked out was the cuman boom without any farms. This was too much for the market to handle.

If there’s somebody out there who wants to try a strat like this, I hope the raw Food Value Factors of 1.78 in Dark/Feudal and 2.01 in early Castle can help him optimzing his builds, together with the information that the data shows: if you go for this market abuse strat, it’s not worth getting the eco upgrades before clicking up to castle or place any feudal farms with almost any other civ (some bonusses can change this) than cumans. But in Castle they get very valueable soon, according to the maths.

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I propose a calculation framework if you are interested to see. It’s inspired by your approach and it’s not that complicated in my opinion. Here’s the thing:
Dark age food factor calculation :
let x = FV in dark age

• Invest into one vil to take gold
cost : 50 food = 50x gold
reward in N minutes : 21N gold

• Invest into one farm to take food
cost : 60 wood and 1 villager work time for N minutes = (60+21N) gold
reward in N minutes : 19N food = 19Nx gold

By definition of FV, both investments are equally profitable, thus the cost-reward ratio should be the same, thus

50x / 21N = (60+21N) / 19Nx

Let’s calculate x in function of N :
50x*19Nx = (60+21N)*21N
950x^2 = (60+21N)*21
we get the food ratio x = sqrt((60+21N)*21/950)

It fits your calculation when replacing N with 4, we get x = 1.78

I even plotted a graph of food-value in function of N (number of minutes before evaluation)

When N is little, the farm is just build / the vil is just born, the reward is similarly little thus the cost 60wood and 50food resp. should evaluate the same thus around 1.2

When N is great, the farm takes away a vils time which could have been used to take gold, and yields some food. It costs a lot but rewards with less food than gold (in pure number comparison)

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Nice analysis. I think your approach is also comparable, but easier to explain and calculate. At least in Dark + Feudal age. Considering the goal to achieve the fastest uptimes (powerspikes) your calc should even be superior to mine in that period. I don’t know if it’s also as easy if you add the extra TCs in the equasion later on.

While you answered, I had a deeper look into the effect of TCs and how they change the factors in castle age. My assumpiton before with a HWP of 10 minutes was completely wrong:

I actually re-evaluated the TC. Instead of just taking the 10 mins, I added up the value of the vils you get from them over time. I chose that about 25 vils per TC (5-TC boom) is a good estimation for the last TC.
With that in mind I adjusted the FV and HWP so that TC==Vil==Farm (in Value/investment) during that booming.

I was quite surprised to see: The HWP changes to 353 secs then, just below 6 mins. But the Food Value doesn’t shrink that much: 1.905 is the FV I get with this, much more precise approach.
Interestling these new factors are quite close to the dark age factors of 300 s and FV = 1.78. So it actually seems, these factors don’t change much during the ages while booming.

But interestlingly, the new factors influence eco upgrades: DBA: >=13 lumberjacks, Bow Saw: >= 22 lumberjacks. Horsecolar starts paying of after 13 farms, Heavy Plow after 19. Of course these numbers are only valid while booming. When aging up, as you don’t have the opportunity to make vils, it might be worth upgrading even with s lower amount of workers.

Wheelbarrow is interesting, because the stats say, you should mainly look at your farm eco: If you have 37 farms it is worth getting it. If you don’t have any farms, you would need 155 vils to make it worth. A more useful example, if you have like 50 vils and 25 farms, it’s worth it, but if you would have 70 vils and only 15 farms you should prefer getting farms before getting it. Hand Cart is worth it at a sum of vils+farms of 180, so basically in the End of the boom.
To calculate both I added the value lost by not creating vils to the raw cost of the TC upgrades. So if you stop booming, they are worth getting anyways, Only whilst booming it needs that high amount of vils to pay of the investment compared to just adding more vils. ANd of yourse if you are housed.

Additional Information: If you place a TC, always get at least 10 vils out of it. Otherwise it’s not worth the Investment. Every vil after that will give you a positive value from the extra TC.

Sicilian TCs are best build with only 1 builder. It saves about 80 standard ressources all things considered compared to a standard 5 builder tc (it’s not OP, 80 res/TC isn’t that much, it’s even less than the britons cheaper tcs)

The cuman feudal TC can be build with various numbers of vills, I think ff and 8 builders how I made it in my test is fine because you don’t want to relocate your whole eco. But boomwise it would absolutely be fine to make it with 7 or 10, it wouldn’t have a big impact. And yes, I included the walking time to this evaluation. It’s actually interesting that the result of my calc is the best amount would be 8 or 9, exactly the number which is “meta”.

In the next posts I will try to show some graphs which explain how my calculation works, without going to far in details. I’m not good in this, but I will try my best.

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That clearly has a problem. From in game knowledge we know that wheelbarrow is worth it when you have more than 17 farms roughly. Even without farms, “155 vils” sounds very wrong intuitively.

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Yeah I have a slightly wrong estimation here, I see. I assume that the number of farms and vills doesn’t change. But for Sure it does. But as this can’t be predicted exactly, maybe an amount of like 20 farms / 50 vills is enough to get it. But I can’t really give a clear answer. For sure, the bigger the boom the earlier you can research wheelbarrow.

I know, but this is the pure vil count without any farmers. As you can approximate every farm takes away about 4-5 vills from that number… So if you have 20 farms, you only need a vil count of about 60-70 to make it a good investment. It’s very likely to have these numbers right when you boom.

I recently tried a ff archer buildorder with early farms, but I couldn’t optimize the berries/wood to have a good fc uptime there to use all free food. It’s just too many things to optimize with that at once. The dark age was fine, but I couldn’t find a good continueation in feudal. I will try a no farm ff archers into fc buildorder next. It should be much easier, quite close to how pros play saracens archers.

What is better to try first: About 5-6 archers, full wall into fc boom or two ranges+bs into delayed fc boom?

I dont get your approach. Shouldn’t the food value be the result of your considerations instead of the start? How do you calculate the value of farm upgrades (considering the value the give you is really weird, beeing only temporary)? Why do you get such increadibly low value for weelbarrow/HC?

I’ll try to explain-

It is. The FV is calculated via the approach.

The approach is that every available ressource losses it’s “worth” over time at a constant ratio. That decrease is expressed by a HWP (Half Worth Period). So if you have for example 200 food in the beginning of the game and do nothing with it for 1 HWP, it basically loses half it’s “worth”. (Of course you lose also the idle time of your tc, which is even more valueable, but just from the theory, it works like this).

So to explain your firs question: I summarize all the future incomes of the investment you did, by taking the timestamps into account when they come in. For a Farm, the first few trips are evalueated almost 10 F each, but a trip after 5 minutes is only worth 5 F at the placement of the farm.
The same is for Lunberjacks.
The only tricky thing is, that a Farm actually needs a villager to be used, so after you summarized all the income value during the lifetime of that farm you have to substract the value a lumberjack or goldminer would have given you during this time.

So with the things exlained above, it should be pretty clear: Since farms “live” longer with the upgrads (and are also more efficient with some upgrades) you get just more food out of them. Of course the value of this later food is much longer and, since the lifetime is longer, the substracted value also raises, this is not linear, but there is still a nice increase of the total value you get from a single farm then.

If youI then just Divide the ressource cost of the upgrades by the increase of value you get from each farm, you get the minimum amount of farms needed to pay back that initial investment.

The same is for all other investments.

Because these upgrades don’t increase working rates much, except for wheelbarrow which increases the farmers working rate. Hand Carts doesn’t increase farming much because the food refreshing rate of the farms is already almost reached by wheelbarrow.
Additional to this both take time in the TCs where you could possibly make vills, so I had to add the value you would get from making that vills to the cost of these upgrades. A castle age lunberjack with bow saw would give ressources worth of 84 w (inclusive the initial loss of 50 F + housing space) over his lifetime. As wheelbarrow takes the same time as 3 vils to be researched I had to add these 3 * 84 W to the initial investment cost. Making it a Investment totally worth 700 g all things considered (with a f/g ratio (FV) of 1.905). 250 of this comes from the 3 vils you could have produced in the same time, 60 comes from the 75 secs you have to wait for it and the remaining 390 are mainly the quite high food investment (175f 50 w).
In comparison, every farmer gets an additional value of 19 w with wheelbarrow, but a lumberjack only a value of 4.5 w, its only a 2-3% increase in value.

In total my calculations aren’t that far away from the “common knowledge”. Normally you say about 17 farms with 50 vills is a good time to get it. My calcs say about 22 farms + 60 vills. Maybe because I took the delay and slightly higher initial ressources also into account. But I can’t tell precisely. I don’t think it makes a big difference in a real game though.

Is this explanation enough?

edit: I just saw, the extra 3 ressources to carry for each trip have an impact in my calculations. Since I don’t use gather rates, rather evalueate every “trip” the first few carries after wheelbarrow come later, this delay after researching wheelbarrow reduces the value you get for each working villager. This is I think why Hand Cart is so “bad” in my calc. these extra 7 ressources per trip take away a big chunk of the increase of working efficiency.

Actually FYI, for a realistic setting of two layers of farms around the town center, wheelbarrow increases farm rate by about 15% (from 18 food/vil-min to 20 food/vil-min) and hand cart increases farm rate by about 13% (from 20 to 23 food/vil-min).
For other resources it’s like 3%-5% increase of gather rate.

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Well, I didn’t reach that state in my test with 5 tcs +mill. It’s enough for up to 48 single-layer farms (depending on placement about 35-40 is more reasonable).
But you’re right in later states of the boom you might have some of these farms, too.

But this is highly dependent on the game, I don’t know how I could include this in my theoretical evalueation. It’s more a practical advice if you have some outer layer farms it might be worth it to get the upgrades earlier.

Also I would like to share a thought of how resource devalues overtime. Your approach assumes it does exponentially. I am wondering whether it would make more sense for it to do inverse-quadratically.

Assuming you have only one TC. Your number of vils increase linearly, so is your resource gather rate. Thus the resources gathered should increase quadratically.

Now let’s consider upgrades and more TCs. They change the slope of resource gather rate in function of time but they don’t change the fact that it stays linear. So the general trend of quadratic increase still holds.

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It is surely a possible approach, but makes calc much harder.
The cool thing about exponential decrease is if you calculated a process over a time period you can yust copy paste it in any other time period - just multiply it with the de- or increase regarding to the time difference. This allows me to calc even comlicated things like the TC, which would be terrible to evalueate with any other form of decrease.

So it’s basically a pragmatic approach.

If you have the TCs available you have all possibilities to make a “natural growth”, so once Castle age is Reached my approach should be correct.

Okay, i think i see the issue now. Your approach assumes there is something to invest into, but if we exclude military, there really isn’t. The first time in the game you are bottlenecked by food is the second you try to click up to castle (assuming FC into boom; scout rush is another story ofc).
As an in-game example: Say we replace the lith bonus; their starting food is normal, but they get x food when building the first market. How big an x do you need to make this new bonus as strong as the old one (assuming just booming to castle, no military)? The answer your approach gives is about 600. This is clearly wrong. Its actually just 150 food (+some small amount to factor in the lower amount of force drop off early on). Thats because it doesn’t matter at all when you get your food, as long as you get it in time to click up to castle.

Since farms “live” longer with the upgrads (and are also more efficient with some upgrades) you get just more food out of them.

Yes but…you dont seed all the farms right after researching horse collar. You seed them over the rest of the game. Its a very specific timing thing with sharp drop-offs, which your model just doesn’t account for.

I think this really sums up the problem of the approach you took: Those limitations are huge, no matter how much you downplay them. The first half of the game boom, you only have 1 TC. Later you get 3-4, but this doesn’t really help: You can convert the harvest of about 30 farms into more vills, anything more will be bottlenecked by TC time once again. Your approach of continous devaluation would be fine if the game was about booming to 10k vills on x TCs, but it seems to run into problems once we use more realistic numbers.

Wouldn’t call it Issue. But there are indeed thngs to invest into: The ages,

And this is also when your starting food gets scarce. But even if we assume, that all ressources until that aren’t losing any worth, we have 2 things to consider:

1. The Farm still costed 60 w, building time and working time
2. the remaining food of the farm has an initial dropoff after clicking up and then falls down in worth exponentially in the boom.

If we Ignore 2) for the moment and placed a theoretical farm with the 9th vill to get all out of it until aging up, we have to give the food from this farm still a FV of 1.36 to make it a good investment for reaching that powerspike.
If we include 2) and take a more realistic 7 vills + loom + feudal before aging up to castle. in whitch all food is worth “the same” and ignoring the dropoff after clicking caslte, we need to evalueate food 1.39 g already. If we assume a 25 % dropoff after clicking castle, we get a FV of >= 1.41.
But here comes the key part: Building these early farms delay both your castle and your feudal uptimes. In a closed map you have enough free food to get up without or just minimal market abuse, so there is no benefit in getting these farms, you reach that powerspike anyhow. In open maps you don’t want to delay your powerspikes of feudal and castle, because both would make you vulnerable.
So the assumpiton to have res generally drop of in worth is even guilty IF you calculate with these powerspikes.In the real game you sometimes just need to react to your opponent, so not having ressources available or having a later uptime because you placed farms in dark age can cost you the game.
The constant decrease I assume is in the aftermath almost equal with a powerspike dropoff. If you just average the ressource value until that powerspike you get a comparable dropoff as if you calculated with that powerspike from tha beginning instead. So my 353 sec HWP is in the end equal to a 37.5 % dropoff after clicking castle.
Of course you could argue, this dropoff is estimated too high, but then the question is, why do we evalueate the castle times so high, if having the ressources to get it isn’t worth more than later? It’s because the castle age allows you to boom with an exponential growth. Since it is also not every time easy to predict the exact uptime, the exponential decrease of ressource worth allows to estimate the value of these investments even though you can’t predict the exact uptimes - if your uptime is different to the estimation you made in the beginning, the calculation wirh the powerspikes becomes meaingless. So for example if you invest in horsecollar and 6 farms in feudal, this leads to a much later castle uptime which would also increase the theoretical value of the farms because the dropoff point would be later, you would get an even bigger theoretical value for the farms, leading you to the assumption that feudal farms are even more worth than vills. But as we all know: The best strat for booming is actually to get castle age as soon as you possibly can (without damaging your eco like the khmer up does).
So the exponential decrease solves these kind of problems you would run into with the inconsistancy of the game. Like if you get lamed or don’t find all your sheep, find some extra free food or not luring deer.
I know, it isn’t optimal, but I think it is actually the best general assumption we can possibly make if we don’t know exactly how the game plays out.

In the End I would like to say, that I don’t got here the way “let’s calculate this theoretically, it must work in the game” but because I figured out when booming with malay and cumans, that my boom was much faster and better with the market abuse than without. This is how I came here and tried to calculate “how far” we could go with the market abuse to improve the boom, rather than damaging it.
And if there is also some practical usage for open maps, if there are buildorders how you can make pe ff archers into fc with it, which are superior to the commonly used strategies. But since we don’t know exactly how the FV changes with the addition of military this might be an unfullfillable dream. On the other hand, having less farms makes your eco more flexible, too. So even in open maps it could indirectly pay of, because you can transition into more archers/military after fc with less on food. So this strat could pay of via the options it enables when reaching castle and the induced outplay potential alone, but that’s hard to evalueate.

But for closed maps I already had a quite good run with cumans using this strat. The market abuse allowed me do get a much earlier castle time and still be able to immediately add 2 more tcs, boom with them, transition into an almost pure lumberjack/farm eco and the 5th TC shortly after.

I also made a calculation which is the lower limit of the FV. If I set the value feedback of the fams to 1, so they are basically “neutral” I get a FV of 1.54. So in the End, for all strats in castle age, the real FV should be somewhere in between these two: 1.54 < FV < 1.905. A lower value would make farms a bad investment, a higher value would lead to a netto res loss when using the market to buy food.
The HWP or value decrease has almost no influence in this, it is mainly calculated by the interaction of tcs and vils.

To be honest, i have a rough time getting your point. You write a lot and throw in lots of numbers, but you dont really show how you get to those numbers which makes them mere statments.

Your framwork yields clearly nonsensical results (i gave two examples already; for the farm upgrades, your result doesn’t even have the right unit as the value of researching farm upgrades decreases with every farm placed), and before those are fixed its very difficult to draw any conclusions - because if some of the results are wrong, why would we assume the others are correct?

I clearly saif after x Farms, so every farm which is placed AFTER the upgrade counts towards that number.

I collect you feedback to think about which graphs would be helping to explain. The thing is, it is not easy to explain the maths behind it, because they are complicated. I can only show graphs with show the results and make it understandable what is happening there, everything else would be far to compicated to explain here.

Is there a guide how I can embed graphs here?

Here is why the exponential decrease is the only one which can work as an approximation:
All other decreases would mply a time-dependancy, so the same investment would be valued differently, just because it was made earlier or later. Here an example how this would look like, if we would set the value of a vil at the beginning of the game == 0 after 50 minutes gametime with a) an exponential and b) a quadratic decrease.
In the exponential the reduced investment cost would place the new vil right on the payback line of the older one, while the quadratic (or any polynomial except of course e^0) decrease will underestimate the initial investment, so it seems like the new vil would have a much better payback than the old one.

Orange Line: Villager produced at the beginning of the game
Blue Line: Villager produced 150 s into the game

This would lead to a misconception that it woud be better to delay investments like vils, farms or eco upgrades to get the most out of them, just from the mathematical approach.

Because of that a polynomial decrease would also underestimate the value of a farm because farms lifespan is in the period where the polynomial evalueation of income is in average always worse than exponential ones with the same integral.

With polynomial decreases we also have the problem with additional factors which must be chosen by us: We must chose which part of the graph we use, because x^-a (a>0) is undefined at 0 and falls rapidly between 0 and 1, so we must ignore that part at least. Also a itself is hard to approximate because it must be at least k + 2 if k is the highest polynomial payback we can achieve with any strategy in the game, otherwise the value of that strat would divergate. Since we don’t know the value of k yet we also don’t know how big a must be at least.
But for the example of a towncenter, k is 2, so a must be at least 4, but once we build new tcs with the income of the first, that complete strat would be evalueated as diverging, so we can’t compare it with any other strat. Which would be the goal of any evalueation to get comparable values.

So in my conclusion, a exponential decrease is actually the only viable one to approximate different investments in the game, just because it is absolutely impossible to calculate with any other decrease.