How would having Closed Loop Trade Nodes adversely affect gameplay

[yerm]

That would make sense from a movement of goods standpoint, but as it stands it would make rich trader nations poor and nations dependent on goods from these trading nations rich.

I disagree. If you put ALL end nodes inland I think you'll actually have a better result, as nobody can dump light ships on it to monopolize, while the nodes like channel feeding Rhineland, or Venice feeding Wien, or Bordeaux feeding Champagne... they can all be stuffed with light ships who should, theoretically, and if numbers are corrected (probably re-weaken caravans) allow those nations to still gobble up most of the money from trade. It just won't be as easy/mindless to do, and shouldn't take THAT much away from the trading powers.

 

[gall]

It could be done, but i doubt it can be done efficiently.
Do x times:
Calculate at every trade region one of following:

1. One way would be storing in RAM for any trade node (trade node of production X, value of trade Y, crossed Z nods) records and increase trade value only of these with lowest Z and lowest Z+1 for each region of origin in each trade node. It would require way more RAM and CPU as today system.
2. Other way slightly more complicated would be using (trade region of production X, value of trade Y, max distance from point of origin recorded) and don't increase trade value if trade value delivered to CoT have greater or equal maximal distance from origin recorded.

If your programmers have nothing to do:
Let us note x (in R_+^n, where R_+ is set of non negative real numbers) as vector of trade value produced in each trade node, n is of course number or trade nodes. We need to define another vector (in R_+^n) z, which is value of trade collected in each trade node. All trade mechanics (where and how big share is transferred or collected in each node) will be written in matrix (dimension 2n x n) A. a_i,j for i<n+1 is (0<a_i,j<1*trade value increase) share of trade value in trade node j transferred to trade node i. a_(i-n),i for i>n is (0<a_(i-n),i<1) share of trade value collected in trade node i.
pr_(1,..,n) is projection of first n coefficients of vector (or first n rows of matrix), e.g. pr_(1,..,n)(x,z)=x.
In this language loops, which crash the game are eigenvalues of matrix pr_(1,..,n)A higher then one. To be sure that everything is ok lower treshold from 1 to 1-d, where d is 1% or something. What can be done? Find highest eigen value h of this matrix (there are proper algorithms to do this, but this take time), if h>1-d calculate eigenvector v and take A-(h-(1-d))*(v,0,..,0) as new A. Find highest eigenvalue...
Calculating sum of all z would be (pr_(n+1,..,2n)A)(Id- pr_(1,..,n)A)^(-1) x. You are probably already using it.
Da, i know every one will say tl;dr including devs ;D.

 

[yerm]

However fully bidirectional trade would not. Will you ever enable it e.g. for modding purposes only?

Fully bidirectional trade could be made to work, and probably even be simpler than current trade, but they'd be redoing the whole thing. You'd have to separate out goods/money and power/collection. Certain buildings (manufactories) and ideas would increase how much trade is in the pool, things like ships would increase how much it is moving and where, and then other factors (buildings, province modifiers, and maybe ships again) would separately collect. In this way you would have trade moving in a possible infinite loop because it never inflates ever, while collection is working off of this separate system.

Since trade currently ties the two together, with the goods directly producing a trade value which is moved, and transferring increases and collection decreases that actual trade-good-generated value itself, any infinite trade connection would necessarily be an infinite loop and crash even, I assume, a mod. I suppose a mod could nuke all manner of trade power generation from all sources and make it work, maybe, depending on how the initial goods into trade value works.

 

[newtlord]

How about the ability to "tax" the outgoing trade, as long as you control the (major) province(s) the centre of trade is in?

Really, gaining money from outgoing trade is something that ought to be in the game anyway. In game, goods leaving (say) one of the Indian trade nodes is bad news for any nation located there, whereas, in reality, many realms in the area gained far greater wealth from Europeans buying and taking their goods than they would have if trade had remained local.

 

[DanubianCossak]

So When the ROTW revamp happened quite a few patches ago now many of us thought we saw the Indus Trade Node lead back into Kashmir meaning the Indian Trade Nodes would have been able to transfer power to each other in a closed loop if a power had the merchants and power to pull it off.

If say Paradox did do this change, and say did it for India and another closed loop in China lets say, Would this be a detriment to gameplay? Cause in my mind it would make sense for an Isolationist Empire that focused on internal trade, but I don't know if this could be somehow bloated and abused to lead to a broken game, Discuss?

It would be horrible for gameplay. Why? Because you would swim in money. The money youd earn you would invest in building provincial improvements, earning even more money, and snowballing you into a situation where the game loses all challenge.

Just play a game as Hansa, or any country that can expand in Lubeck trade node to dominate it. Once you are able to earn ~40 or 50 trade gold per month, its game over. It just stops being any fun.

 

[RyanX]

I disagree. If you put ALL end nodes inland I think you'll actually have a better result, as nobody can dump light ships on it to monopolize, while the nodes like channel feeding Rhineland, or Venice feeding Wien, or Bordeaux feeding Champagne... they can all be stuffed with light ships who should, theoretically, and if numbers are corrected (probably re-weaken caravans) allow those nations to still gobble up most of the money from trade. It just won't be as easy/mindless to do, and shouldn't take THAT much away from the trading powers.

That's true, until every german minor puts their merchant in the Channel to steal trade. Account for "transfers from traders downstream" and caravan power and you can easily have 40% of the trade leaving the Channel and going to Rhineland, while Rhineland was the one who bought the goods, didn't sell them.

 

[yerm]

Right, which is why numbers would need to be corrected such as caravan power =p

 

[RyanX]

Right, which is why numbers would need to be corrected such as caravan power =p

It would be a lot of balancing work for questionable gains, I find.

 

[beckermt]

Exactly, you would collect HALF of the value of the 3 nodes, then the other half would continue BACK INTO the loop, get added to the value of all three nodes again, and incresed by merchants every time it updated (which i asume is now only monthly). Thus your total value of trade would increase by around 60% (i think) every month (the 50% you sent back through, +15% for merchants steering). The total value that you collect half of, would just continue growing every update (month) even though the total trade value of the provinces remained unchanged.

Who controls the other 50%? If they're also steering, then that goes somewhere else. If they're steering AGAINST one of the nodes you control fully, then the amount they steer reduces the amount you steer. Pretty simple actually. If you bring 10 ducats (100% of node 1) to node 2, where you're collecting, but someone else is bringing 5 ducats from node 2 to node 1, then, at the end, you have 5 ducats moving from node 1 to node 2.

Assume both nodes started with 10 ducats. Node 1 now has 5 ducats (no collectors, it is lost) and node 2 has 15 ducats. If you are the only collector in that node, you loot 15 ducats. Otherwise, the 15 is split amongst the collectors (steerers already had their effect).

Now, in this example, steering into a node someone else controls 100% is, just like in the game now, a terrible idea.

You say that the trade value would grow each month, but it would only be based on the province value, calculated once per month, then modified by you efficiency or whatever.
In the above example, if you had 50% bonus trade efficiency, you'd collect 22.5 instead of 15.

If you had improved steering, then the amount you would steer could be increased. (Let's say 15%.) So, you steer 11.5, the other guy 5, now 6.5 ducats move into node 2. At node 1: 3.5 remain, node 2: 16.5. The total value is the same, but you got more of your money where you wanted it. Exactly the point of steering power (or whatever it' called. )

Now, I suppose you could run into an issue if there's no opposing steerer and you have bonus steering power, but maybe you could have an effective value or a power vs. power set up, so the total amount of money doesn't increase just from steering.

 

[hauptman]

Who controls the other 50%? If they're also steering, then that goes somewhere else. If they're steering AGAINST one of the nodes you control fully, then the amount they steer reduces the amount you steer. Pretty simple actually. If you bring 10 ducats (100% of node 1) to node 2, where you're collecting, but someone else is bringing 5 ducats from node 2 to node 1, then, at the end, you have 5 ducats moving from node 1 to node 2.

Assume both nodes started with 10 ducats. Node 1 now has 5 ducats (no collectors, it is lost) and node 2 has 15 ducats. If you are the only collector in that node, you loot 15 ducats. Otherwise, the 15 is split amongst the collectors (steerers already had their effect).

Now, in this example, steering into a node someone else controls 100% is, just like in the game now, a terrible idea.

You say that the trade value would grow each month, but it would only be based on the province value, calculated once per month, then modified by you efficiency or whatever.
In the above example, if you had 50% bonus trade efficiency, you'd collect 22.5 instead of 15.

If you had improved steering, then the amount you would steer could be increased. (Let's say 15%.) So, you steer 11.5, the other guy 5, now 6.5 ducats move into node 2. At node 1: 3.5 remain, node 2: 16.5. The total value is the same, but you got more of your money where you wanted it. Exactly the point of steering power (or whatever it' called. )

Now, I suppose you could run into an issue if there's no opposing steerer and you have bonus steering power, but maybe you could have an effective value or a power vs. power set up, so the total amount of money doesn't increase just from steering.

Ok for an example... Let's say you are Brandenburg, and you want to use Hansa for you loop of infinate money... when Lubeck > Channel > Rhine > Lubeck.

Choose Lubeck, as Hansa collection point and your main trade port, that you steer away from. In the lubeck node you allow Hansa his 1 province (the capital). He has little trade power, so collects very little.

Then in the channel, you collect here, and Own EVERY province. Now since you are not collecting in your home node, you take a trade power debuff, so only collect 50% (purely example).

Now in the rhine... you FEED the hansa Huge amounts of land. His power propagates up stream to the channel (pulling that other 50%) and he sends everything back to Lubeck, add infinitum.


Would be pretty easy to set up... and explode the game with infinate money.

 

[Shadowstrike]

Hypothetically speaking, what would be the impact of removing "bonus" trade created by steering? There would be no incentive to steer through as many nodes as possible (which is kind of weird to start with), but this might in turn make distant trading less lucrative (which would discourage Portugal and the Netherlands from pushing into the Far East). One might imagine that trade bonuses could then take the form of multipliers when collecting (which wouldn't have the issue with the infinite loops).

 

[Torulf]

http://en.wikipedia.org/wiki/Infinite_loop

you can just simulate that all uncollected tradegods sinks when it reach Bermuda

 

[User29]

Bummer, I figured since it would still be connected to everything else it would be okay, but if even thinking about it crashes the game, I guess that's that. Just that Indus into Samarkand direction, going RIGHT THROUGH Kashmir, always irks me

 

[TheMeInTeam]

Fully bidirectional trade could be made to work, and probably even be simpler than current trade, but they'd be redoing the whole thing. You'd have to separate out goods/money and power/collection. Certain buildings (manufactories) and ideas would increase how much trade is in the pool, things like ships would increase how much it is moving and where, and then other factors (buildings, province modifiers, and maybe ships again) would separately collect. In this way you would have trade moving in a possible infinite loop because it never inflates ever, while collection is working off of this separate system.

Since trade currently ties the two together, with the goods directly producing a trade value which is moved, and transferring increases and collection decreases that actual trade-good-generated value itself, any infinite trade connection would necessarily be an infinite loop and crash even, I assume, a mod. I suppose a mod could nuke all manner of trade power generation from all sources and make it work, maybe, depending on how the initial goods into trade value works.

You could probably mirror the trade paths in reverse and have it operate as a completely independent trade layer from the current direction (IE outgoing/reverse value independent from incoming value). It sounds like a lot of processor burden for not much real change to how the game is played though. I don't think EU IV really needs to be hammering in serious changes to trade at this point, it's not a perfect model but it's far enough ahead of the things that work poorly and will be for quite some time, even if each patch they fix a few weak links at once.

 

[zdlugasz]

Fully bidirectional trade could be made to work, and probably even be simpler than current trade, but they'd be redoing the whole thing. You'd have to separate out goods/money and power/collection. Certain buildings (manufactories) and ideas would increase how much trade is in the pool, things like ships would increase how much it is moving and where, and then other factors (buildings, province modifiers, and maybe ships again) would separately collect. In this way you would have trade moving in a possible infinite loop because it never inflates ever, while collection is working off of this separate system.

Since trade currently ties the two together, with the goods directly producing a trade value which is moved, and transferring increases and collection decreases that actual trade-good-generated value itself, any infinite trade connection would necessarily be an infinite loop and crash even, I assume, a mod. I suppose a mod could nuke all manner of trade power generation from all sources and make it work, maybe, depending on how the initial goods into trade value works.

Either I do not understand or you misunderstood.

System theoretically already is (almost) bidirectional, but you can not assign merchant to steer "back" and IIRC the malus for steering back was supposed to be sth. like fixed 80%.
If they allowed merchants to steer in any direction (possibly allow for trade power propagation "backward", but thats not mandatory) and make malus for steering back moddable/variable then we would have fully bidirectional trade.
Example: China dominates Malacca (land power and ships) and forces 70% of non-chinese trade to move back to China.
The problem is trivial (algorithmically speaking) and remembering devs's words/notes I think it is already solved (=implemented). Simply speaking "backward" connection from B to A does not consider trade value which came to B from A - simple, and no loop whatsoever.

 

[sub-woofer]

http://en.wikipedia.org/wiki/Infinite_loop

As a matter of fact, it could be quite easily implemented without infinite loops. Disclaimer: I'm not by any means advising for trade nodes loops. I think it would be a waste of time and budget that you could spend on some more interesting things (events for Brittany! more interesting navies! a big party for all the talented Paradox staff!). But, from purely mathematical point of view, that's a system of equations that almost always has a "sane" solution.

For a simple example, imagine a trade node cycle, consisting of 5 nodes with 50% trade being collected in every node and 50% sent forward. Now imagine one ducat starting in one of the nodes. Only 1/32th of the ducat survives the whole cycle and gets back, only 1/1024th survives two cycles etc. - in fact, exactly 0 ducats travel infinitely, all of it gets collected at some point.

In fact, if there is no cycle with 100% trade sent forward (which would really be an unsolvable situation), by solving a (not really complicated) system of linear equations you can quite easily compute collected amounts for all merchants. The situation is not exactly alike, but quite similar to a Markov chain: http://en.wikipedia.org/wiki/Markov_chain.

Sorry to bother. Just couldn't resist.

 

[TheMeInTeam]

As a matter of fact, it could be quite easily implemented without infinite loops. Disclaimer: I'm not by any means advising for trade nodes loops. I think it would be a waste of time and budget that you could spend on some more interesting things (events for Brittany! more interesting navies! a big party for all the talented Paradox staff!). But, from purely mathematical point of view, that's a system of equations that almost always has a "sane" solution.

For a simple example, imagine a trade node cycle, consisting of 5 nodes with 50% trade being collected in every node and 50% sent forward. Now imagine one ducat starting in one of the nodes. Only 1/32th of the ducat survives the whole cycle and gets back, only 1/1024th survives two cycles etc. - in fact, exactly 0 ducats travel infinitely, all of it gets collected at some point.

In fact, if there is no cycle with 100% trade sent forward (which would really be an unsolvable situation), by solving a (not really complicated) system of linear equations you can quite easily compute collected amounts for all merchants. The situation is not exactly alike, but quite similar to a Markov chain: http://en.wikipedia.org/wiki/Markov_chain.

Sorry to bother. Just couldn't resist.

They want the design to include extra value per node to encourage long trade routes such as the Indies --> Sevilla. Therefore, each hop adds value from nothing, which is what's causing the infinite loop. If it were a scenario where each month a static % of trade from one place was collected elsewhere based on trade power (such that 1 ducat leaving Malacca would never be more than 1 ducat anywhere else) you wouldn't have an infinite loop problem unless you did funny stuff with power propagation.

But as you say it's not like that would actually make the system any better.

 

[Baronh2o]

Johan's infinite loop reference would be problematic, but only with 100% control of a loop.

A single tag wouldn't even need 100 percent control of the loop. Essentially a circular (loop) trade route would probably crash the game pretty quickly. This is because money is always compounding upon itself regardless of which country is consuming it, providing it, or forwarding it. In essence it's classic programming, it needs a break point to avoid a memory consumption error.

 

[Shadowstrike]

Couldn't encouraging trade steering through multiple nodes be accomplished by a multiplier when/where trade is collected (by tracing the most distant node where any ducats originated from), which would get around the infinite loop problem?

 

[Evil4Zerggin]

http://www.eu4wiki.com/User:Evil4Zerggin/Trade_with_cycles

Determining how much is collected at each node in the presence of cycles is 4 lines in MATLAB:

function [ collected, incoming, outgoing ] = tradeWithCycles( network, collectionShares, localValues )
%TRADEWITHCYCLES
% network: n x n matrix representing the trade network
% localValues: n x 1 vector representing local trade value at each node
% collectionShares: n x 1 vector representing proportion collected at each node
B = diag(collectionShares) / (eye(size(network)) - network);
collected = B * localValues;
incoming = collected ./ collectionShares - localValues;
outgoing = localValues + incoming - collected;
end

Naturally you would have to remove merchant boost to prevent the possibility of infinite trade value. Power propagation might also have to be tweaked since there is no longer a clear "upstream".

Even if you used matrix exponentiation instead of solving the linear system (e.g. if you wanted to be extra-sure not to run into numerical precision issues) it would converge quite quickly---each iteration doubles the path lengths considered.

Of course the devil is always in the implementation and integration.