How do Lombards work?

Age of Empires III: DE III - Discussion
1

I’ve decided to clarify a bit how lombards work, as they’re often misunderstood, which often goes hand in hand with a lack of understanding of how they work.

(For those who won’t read, there is a conclusion at the end with interest rate)

First of all, you need to know that Lombards, without the conversion speed card, already see their conversion speed increased for each Lombard you’ve built.

Secondly, Lombards without Usury card already earn you profits based on the types of resources you invest. So they don’t just convert your resources.

For example :

r.b. = resources benefit.
U. = with activated Usury card

On a base of 10,000 total resources / Single resource invested :

Food invested: 1000

Food : 9 000 → 9 000 [U. : 9 000]
Wood : 10 000 → 10 500 (+500) [U. : 10 550 (+550)]
Gold: 10 000 → 10 500 (+500) [U.: 10 550 (+550)]

Return on resource investment: 0 [U.: Wood, Gold (+100 r.b.)]
Interest rate: 0% [U.: 10~12%]

Wood invested: 1000

Food: 10,000 → 10,750 (+750) [U.: 10,835 (+835)]
Wood: 9,000 → 9,000 [U.: 9,000]
Gold : 10 000 → 10 500 (+500) [U. : 10 555 (+555)]

Return on resource investment: Food, (+250 r.b.) [U. : Food, Gold (+390 r.b.)]
Interest rate: 24~25% [U.: 38~39%]

Gold invested: 1000

Food: 10,000 → 10,750 (+750) [U.: 10,750 (+750)]
Wood: 10,000 -->10,500 (+500) [U.: 10,500 (+500)]
Gold: 9,000 → 9,000 [U.: 9,000]

Return on investment resources: Food (+250 r.b.) [U. : Food (+250 r.b.)]
Interest rate: 24~25% [U.: 24~25%]

In summary interest rates :

Food: 0% / U. : 12%
Wood : 24% / U. : 38%
Gold : 24% / U. : 24%

Without the Usury card, all profits go to food. With the Usury card, on an investment in wood, around 15% of the profit goes in gold. For the rest, profits are paid out in food, when it’s not food that’s invested.

Contrary to what I’ve read on the forum, there’s no particular synergy when several types of resource are invested at the same time, such as wood and gold, or food, wood and gold.

As the example shows:

(To obtain the interest rate on two types of resource, add up the interest rates of the resources involved, then divide by 2: Food + Wood = (0 + 24) / 2 = 12. Divide by 3 when all three resources are invested. The rate may vary from one percentage to another).

On the base of 10,000 total resources / Two resources invested :
Food invested: 500. Wood : 500 (1000)

Food : 9 500 → 9 875 [U. : 9 915]
Wood : 9 500 → 9 750 [U. : 9 780]
Gold : 10 000 → 10 500 (+500) [U. : 10 550 (+550)]

Return on investment resources: Food, Wood (+125 r.b.) [U.: Food, Wood, Gold (+250 r.b.)]
Interest rate: 12~12.5% [U.: 24~25%]

Food invested: 500 Gold: 500 (1000)

Food : 9 500 → 9 875 [U.: 9 875]
Wood: 10,000 → 10,500 (+500) [U.: 10,530 (+530)]
Gold: 9 500 → 9 750 [U.: 9 780]

Return on investment : Food, Gold (+125 r.b.) [U. : Food, Wood, Gold (+185 r.b.)
Interest rate: 12.5% [U.: 18.5%]

Wood invested: 500 Gold: 500 (1000)

Food : 10 000 → 10 750 (+750) [U. : 10 790 (+790)]
Wood : 9 500 → 9 750 [U. : 9 750]
Gold: 9 500 → 9 750 [U.: 9 780]

Return on investment : Food, Wood, Gold (+250 r.b.) [U. : Food, Wood, Gold (+320 r.b.)]
Interest rate: 25% [U.: 32%]

On a base of 10,000 total resources / Three resources invested:

Food invested: 500. Wood: 500 Gold: 500 (1500)

Food : 9 500 → 10 250 (+250) [U. : 10 290 (+290)]
Wood: 9 500 → 10 000 [U.: 10 030 (+30)]
Gold : 9 500 → 10 000 [U. : 10 060 (+60)]

Return on resource investment: Food (+250 r.b.) [U.: Food, Wood, Gold (+380 r.b.)]
Interest rate: 16.5% [U. 25%]

There are no combinations depending on the type of resources invested at the same time.

Now let’s move on to resource conversion speed, which doesn’t wait for the Advanced Lombards card to convert faster.

As shown in the example:

Based of a maximum of 1000 total resources:

(!) Food, wood and gold have their own queue of conversion rate, which means that between investing 1000 food or 1000 food, 1000 wood and 1000 gold, the conversion rate will be identical.

1 lombard: 8.40 min
2 lombards: 4.20 min (-50%)
3 lombards : 2.52 min (-33%)
4 lombards: 2.12 min (-24%)
5 Lombards: 1.48 min (-19%)

Just as an indication, on a maximum of 250 total resources (divide by 4):

1 Lombard: 2.10 min
2 lombards: 1.05 min
3 lombards : 0.43 sec
4 lombard : 0.33 sec
5 Lombards: 0.27 sec

With the Advanced Lombards card, simply divide by 2:

On a maximum of 1000 total resources:

1 Lombard: 4.20 min
2 Lombards: 2.10 min
3 lombards: 1.25 min
4 lombard : 1.06 min
5 lombard : 54 sec

Just as an indication, on a maximum of 250 total resources:

1 lombard : 1.05 min
2 lombards : 32.5 sec
3 lombards : 21.2 sec
4 lombards : 16.5 sec
5 lombards : 13.5 sec

Conclusion and thoughts:

Lombards, without the shipping of cards that enhance them, can already bring you profits and increase their conversion speed. However, these profits will, for the most part, be transformed into food. The only exception: with the Usury card activated, when you invest in wood, around 15% of your profits will be transformed into gold, the rest into food. Also for conversion speed, we can say that 3 to 4 Lombards are already sufficient to get an interesting conversion speed. The Advanced Lombards card is thus a very interesting card with its +100% conversion speed, but requires more macro from the player. I therefore believe that, if you invest in Lombards occasionally to convert resources for emergency situations, or to boost your economy etc., the Advanced Lombards card can be very interesting. Unlike, if you regularly invest in Lombards as a continuous trickle of resources, the Advanced Lombards card get less useful, because the time you save in the very rapid conversion of your resources will be lost between each reinvestment on your part (Lombards on standby) to try to maintain a continuous flow of resources, in addition to the macro that this can require.

In my opinion, the Usury card is only useful if you make Lombards your primary/secondary food source. Although without Usury, this is already a viable strategy, since your interest rate is converted into food.

In conclusion, I think Lombards are still very interesting at the beginning/middle of the game for the tax-free conversion of resources, the experience flow thanks to Offices card and the food benefits they bring. Beyond that point, Lombards become much less interesting, although they can be very useful if you make them your main/secondary supplier of food, with a 38% interest rate in wood (with Usury).

Here again Interest rates of each resources with and without Usury Card:

Food: 0% / U. : 12%
Wood : 24% / U. : 38%
Gold : 24% / U. : 24%

If there are some mistakes, please tell me.

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4

huh the fact that it was thought that lombards dont generate profits pre-usury was so ingraned its written in the wiki

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But from your numbers and I just checked it does generate food profits, probably due to the fact that the food rate is higher and the lombards generate res by decreasing stored res over time.

This actually changes how comaprable lombards are to a factory (which is kinda the trade off that italy has by losing one factory) and also makes it a lot more complex

though i think the ursury numbers might need some closer look, this might be a lot more complex then we might be thinking

I just tested 1000 food invested and i got these instead with ursury
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5

Thanks for that write-up - very informative!

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6

Yes, the strange thing about the conversion calculation is the distribution of profits with and without the Usury card. The fact that most of the profits are converted into food undoubtedly shows that it’s more profitable to convert resources into wood and gold, rather than food (as, I’m sure, most players do).

I think I’ve already explained the complex and strange part of this card in the post. I don’t think that further analysis will bring us anything else of interest.

What can be examined, however, is the viability of a strategy focused on a single food source, based on the benefits obtained from food with the Lombards.

Yes, i get also 12% of interest as well as 10%. It can vary. But what is not very logical is that with the Usury card, you don’t get a 36% of Interests rate (which would be more logical), but 38% minimum rate, which can go up to 40%.

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This has taken me down a rabbit hole of testing and modeling how this actually works and I think i have got it, though the result is a bit startling cause it fundamentally changes how i thought this thing works and the meaning of the card , even the ingame text is kinda of not explaining properly the actual outcomes of the card

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From both of these description, the immediate interpretation is that you are getting 1.25 gold for every 1 food or 1 wood invested.

But any testing shows that is not the case and somehow if you invest in food, you get more in both wood and gold and in total only like 10-12% more, as you have described.

The reason for this is that what it is actually doing is that for every 1 gold that is generated, you only take away 0.8f from the amount invested. This means that what the actual impact of ursury is is to make your investment pile last longer, and therefore generate more res as the res generation last as long as there is resource still invested in the lombard.

This means that ursury increases the amount of time it will take to fully convert food and wood into coin, by about 10%

this also means that the formula for comparing lombards to factory just got a lot more complicated

8

The initial data is a bit confusing…

Why not write it as

Food invested: 1000
Food: 10000 → 9000

…

Thing about ‘profit’ is that you need to consider VS (villager second) and thus their gather rate to check what is really profit. Unupgraded values:
food gather rate = 0.84
wood = 0.5
coin = 0.6

so you have 1000 wood = 2000 VS, 750 f = 893 VS and 500 gold = 833 VS → 2000 VS worth and in return you get 1726 VS worth (also you need to subtract how much it takes to convert the resource).
profit: 1726 (- time to convert) - 2000 = -274 VS (- time to convert)

With Usury:
1000 wood = 2000 VS, 835 f = 994 VS, 555 c = 925 VS → 2000 VS and in return you get 1919 VS (and you have to subtract the time to conversion, so it is a bit worse),
profit: 1919 (- time to convert) - 2000 = -81 VS (- time to convert)

Still not worth. As i keep saying only food has a good worth change in lombards, but wood is always a NO. Coin is situational depending on how many lombards you got (only for > 3 lombards with ADVANCED Lombards).

For eg food
1k food → 1191 VS
gain: 500 wood → 1000 VS + 500 gold → 833 = 1833 VS (- time to convert)
profit: 1833 (- time to convert) - 1191 = 642 VS (- time to convert)
with Usury
gain: 550 wood → 1100 VS + 550 gold → 917 = 2017 VS (- time to convert)
profit: 2017 (- time to convert) - 1191 = 826 VS (- time to convert)

Gold:

1k gold → 1667 VS
gain: 750 food → 893 VS + 500 wood → 1000 VS = 1893 VS ( - time to convert)
profit: 1893 (- time to convert) - 1667 = 226 VS (- time to convert)
with Usury
gain → same
profit → same

The thing, at the end of the day, is that Italy doesn’t have a factory for a measly ~700 VS gain for food converted BUT it doesn’t have any advance MILL gathering boost (like malta) so it is not worth an entire factory (which can make heavy cannons for free)

9

They pretty much never pay for themselves in 1v1, they’re only useful for the cards that deposit resources. It is even worse if you send usury because age 4 cards have a value of 1600 resources, there’s no way your making that back so better to just send 1600f lol.

10

Usury is +200 VS assuming you put food. To have a profit, you would have to put 10k food in it (2000 VS ~ 1600 F / 0.84 = 1905 VS [- time to gather the crates])… which requires 11905 VS for it to be worth.

Assuming 99 vills all working in the mill (with some upgrades as mill gathering isn’t 0.84), it isn’t that much 12k VS / 99 V = 120 secs (+ time to convert) = 2 mins + (540 sec / 60) = 11 mins , which of course doesn’t consider that you can’t just put all vills on mills, or just put all the food in lombards.

This ONLY for usury to be worth compared to a 1.6k food shipment.

In a semi - realistic scenario you would require minimum 14 mins (assuming 40 vills on upgraded mills AND advanced lombards AND all food collected to go into the lombard) for it to be worth compare to another 1.6k res shipment.

So yeah in 1vs1, never send it, in Team games, neither if it isn’t a Treaty game 60+ mins :stuck_out_tongue:

1 Like
11

You also have the cost of advanced lombards card to pay off as well and of course it is hard to quantify the opportunity cost of having all the res tied up in lombards instead of being units in the fight.

They should just give italy their second factory, they are like worst treaty civ anyway which is the only possible scenario where lombards are even ok, they perform even worse in 1v1 and never come close to replacing a factory.

12

I dont think profit for lombards should be taken in terms of villager seconds, especially using natural res values since the direct trade off for italy is not having a second factory, its a mid to lategame comparison

From the numbers provided, assuming you keep them top up, the profit rate( ie res you get above the amount you put in) 5 lombards with advanced lombards and ursury is 10.46f/s, 1.083w/s and 2.16g/s and maybe the 1.25xp/s you get from the other card, in addition to the benefit of them being able to be rebuilt, acting as taverns and rebalancing your eco. A factory that is more food heavy is inefficient but it does have its benefits.

In the early game you get value from it either by going Uffizi which means you get slightly more then a TP worth of XP trickle and sending the deposit cards, turning them into unraidable crate vils effectively.

from the numbers 5 usury lombards have about the profit rate of an upgraded factory (atleast in pure res terms) so arguably its the same as sending a factory tbh (and you can keep it top up) but its not the best ways to make these comparisons

13

I am using VS because, unlike the factory producing res from nothing, the lombard needs to have resource put inside it to start “gather”, the res which are gathered by vills. You can’t say lombards produces in ‘profit’ x amount of res/s, when those res were collected by the vills beforehand and converted.

For instance the single factory insn’t just ‘X/s produced’, it is 99 VILLS + ‘X/s’ produced.
While for the lombard this same doesn’t apply.

2 Likes
14

The fact that you have to micro it makes it far worse than a factory.
That alone makes it at most half a factory.

15

If you are taking the net value of res generated (already taking out the amount you input in) then I dont see any reason why that isnt valid.

If you input in 250 of each res and get back say 393f , 262w and 276g from 1 lombard over the course of 138 seconds then you can say the lombard is producing 1.036f/s, 0.086w/s and 0.188g/s on net. You are gaining more of each resource then just the amount you initially put in

this would be resource you are gainning in addition to vils or factories that you have

16

Because you are ignoring that those 250 of each res also have their gathering rate (VS) that is necessary to consider. They don’t exists from nothing to be put inside the lombards, you have to have them in your res pool.

1 Like
17

Yes you will need a seed res but from the example given the lombards generate enough res to be reinvested, would it be correct to attribute every resource that it generates after that to the villager seconds equivalent?

sure you account for that inntial effort to gather the 250 of each res (lets use natural res rate to make it the worse case)

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After the first input of 250 res each you are in the negative, but after the first period you are positive net of villager seconds and since you generate enough res from the lombards to continue depositing, you are generating res that are independent of any more villager seconds.

even in this example I am taking the worse case of you are still taking villager time to gather for the next 250 res to put in, you are have a positive and growing net of villager seconds as you are depositing each time.

I would argue in that in the better and more I think representative case you are in effect just using the the lombard’s own generated res to reinvest and therefore subsequent investments are independent of VS but even in the worse case you are still making positive gains

18

I am saying the reasons for using VS, indeed then you can offset by saying the lombards also generated the res, so lets put that back and so forth but then you have to consider also the time frame that you can effectively USE the resources… at the end, you are converting to use it.

1 Like
19

yes and im saying you are still in the end generating net resources from the profits as though it was a factory after the initial investment and you can attribute a rate to it as though it was a factory

its not the toggleable choice of a factory but you are still getting an x/s of res which are enough to be put to use, assuming 5 maxed out lombards (advanced lombards & ####### ### a profit of 10f/s , 1w/s and 2 g/s ( if you get the xp card as well then you also get xp) but it is as though you have a factory that is generating these res for you as long as you remember to keep atleast 250 of each res inside

21

If you read the rest of the post, you saw that I also write in this way for two types of invested resources, which saved me from writing this:
Food: 10,000 → 9,500 → 9,875 [U . : 9,915]
Wood: 10,000 → 9,500 → 9,750 [U . : 9,780]
Gold: 10,000 → 10,500 (+500) [U . : 10,550 (+550)]

Which is not less confusing…

You’re partly right, but completely wrong, because your formula ignores Lombard profits with which they can reinvest. It can’t be used to calculate a real profit from benefits, even less to compare it to the villagers’ gather rate. Your formula could be valid for a maximum of 499 foods in the Lombards. Because, at 500, your lombards can be self-sufficient thanks to the profits they generate (they can even be self-sufficient without resources invested thanks to the cards). That said, you’re partly right because that players tend to over-invest resources in their lombards, either because they want to invest as many resources as possible to be comfortable afterwards, or because they don’t know they’re making profits while converting their resources, or because, knowing this, (and here is the crux to the problem) they have no way of knowing their return on investment. I insist on this point, because if they could know their return on investment, then they would be aware of their net profitability, and therefore of the effectiveness of lombards (especially at ages 2 and 3).

Once again, you’re partly right, but completely wrong. If the player overinvests in wood in Lombards, then your formula could be considered (although it needs to be put into perspective for obvious reasons), as he would be investing in resources that are slower to gather: with your reasoning, food would indeed be more interesting for an investment in Lombards. But if you reinvest your profits, it’s no longer food that’s more interesting, but gold and wood - especially wood with the Usury card! Because it’s with these two resources that you’ll accumulate the most benefits, and with those (food’s benefits) you’ll be able to convert them into gold and wood, in other words, to generate profits in gold and wood - it’s a virtuous circle.

And this is where the biggest problem with Lombard comes in, and one on which we can only agree: once you’ve invested a first time, a second time, a third time etc. in Lombard, you no longer know which of the profits or net resources gathered by your villagers you’re going to reinvest. Lombards don’t currently allow you to control your spending, by reinvesting only your profits. This is precisely where changes need to be made.

I agree about the micro. That it’s too pesant while we have no idea of the return on investment. But I’m against the idea of adding a second factory in Italy. The idea of the Lombards is not to replace the factory, because it doesn’t have the same use and the industrial revolution in Italy came really late (so let’s stop comparing them with the factory), but to be an interesting economic lever until age 3. So in age 4 it obviously won’t replace a second factory, but will still serve as a complement. An interesting combination would be (if you have already enough heavy canon) to produce wood with your factory, and invest the wood in your Lombards with the Usury card (to be tested).

Are you sure about this?
Because I think I’ve identified the problem (which I guess is a bug) with the Usury card.

Going back to my numbers, the Usury card currently gives us the following:
Food : 9 000 → 9 000 [U . : 9 000]
Wood : 10 000 → 10 500 (+500) [U . : 10 550 (+550)]
Gold: 10 000 → 10 500 (+500) [U .: 10 550 (+550)]

Instead of this :
Food : 9 000 → 9 000 [U . : 9 000]
Wood : 10 000 → 10 500 (+500) [U . : 10 550 (+550)]
Gold: 10 000 → 10 500 (+500) [U .: 10 660 (+660)]

This would mean that it generates 20% and not 25% gold profit when you invest food and/or wood. Alternatively, it’s 25% and the net profit should be +625 with the card.

But I’d go for the 25% error specified in the description, because with 20% this is what you’d get when you invest wood with Usury:

Current data (probably bugged):
Food: 10,000 → 10,750 (+750) [U .: 10,835 (+835)]
Wood: 9,000 → 9,000 [U .: 9,000]
Gold : 10 000 → 10 500 (+500) [U . : 10 555 (+555)]

Data with 20%:
Food: 10,000 → 10,750 (+750) [U .: 10,750 (+750)]
Wood: 9,000 → 9,000 [U .: 9,000]
Gold : 10 000 → 10 500 (+500) [U . : 10 600 (+600)]

But here’s the thing: if you count correctly, the rebalancing I did from food to gold left over 40 resources that I didn’t distribute. Because by removing the 40 resources (we’ve seen that it can vary between 30 and 40), we reduce the interest rate on wood from 39-40%, which I found illogical if you remember, to around 36%. Which makes more sense in view of the interest rates! (0,12, 24, 36).

However, I’m not 100% sure of what I’m saying.

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22

You are still not considering that it is taking 138 secs for the resource to convert. And in that time - a factory - production happens. And also that while you indeed have a profit of 170+24+43 for each 250+250+250 resource inputted, if you keep reusing, you will continue to have that profit, you aren’t getting 500 res + 500 res +500 res + the profit the next time, you are still getting (170+24+43) times X, as you need to keep that pool ongoing for it to generate res (so the 250 res is removed from usable resource you have, as i wrote previously).

so for x period the profit in VS remains in VS → 237 VS * X

assuming the period i 1 (138 secs)

1 factory is → 138 * 7.15 = 987-> 1.974 VS (not considering even the heavy cannon which is greater)

1974 / 237 = x = 8.32 * 138 =1148 secs / 60 = 19 mins

The value is here converted just so we can have the same base for the factory to compare.

You will probably say that putting more res = more return but that also means more initial VS that you need to offset from.

1 Like
23

Your initial gathering isn’t happening from the lombard, it is happening from the vills. The lombard needs to reuse its 250 pool that it has generated which means only the difference of the initial and the value / res from the vills can be considered as its profit, which continues to repeat, This for the entirety of the initial pool you need to invest. Any resource you have invested is a minus, and that it is self sustaining can only be done by NOT using that part and reinvesting, which makes the ‘trickle’ not worth.

Again, not considering the original offset. That is why converted to VS, it is easier to reason. You have gathered 500 wood? → generated 700 food → invested in food → generated more wood ?? STILL need to consider that 1) invested resource is removed from your pool 2) invested resource came from the vills at its source 3) it takes time for it to convert which factors, it isn’t happening instantly. If it was an instant exchange, it would be like you wrote.

Lets consider the scenario:

1k wood invested → in your pool (0 food, 0 coin, -1k wood)
return 835 food + 555 coin → (835 food, 555 coin, -1k wood)

  • invest also 1k food now (835 + 165 from you) → ( 670 food, 555 coin, -1k wood)
    → 550 wood + 550 coin → (670 food, 1105, -450 wood)
  • invest also 1k coin (555 + 445)
    ->750 food + 500 wood → (1420food, 600 coin, 50 wood)

so 1k wood + 3 x Period time = 1420 food + 600 coin + 50 wood

( 1690 + 1000 + 100 ) -( 2000 + 414) = 376 profit

in 3x period time, a factory has 5920 VS profit. The above considerations even ignores VS for the reinvesting resource required, as if they were magically made by the lombard itself.

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