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Answered Trader range and number of trades

DeletedUser

Guest
While the "star" will pick up your boosts, it neglects your ideal trading partners, and you NEED somewhere cheap to exchange all of those boosted goods. I'd even argue that chasing active radio button traders who have your missing boosts is the "best" strategy, and that your own boosts will fall into place by happenstance.
I fully agree that it is more important to scout towards active trade partners to discover them and rid yourself of the trader's fee, while gaining a supplier for your non-boosted goods. No argument there really.

HOWEVER, if you happen to come across a situation like myself, where there are perhaps one or two active players in your neighbourhood and they happen to be in ring 10+, then I would not recommend this. In this case it's "best" to gain relics as quickly as possible (which is where the 'star-like' formation is most efficient), until inactive players are replaced or other trade partners start appearing. THEN I would revert back to "chasing" the potential trade partners as you mentioned.

Effectively the 'best' strategy is quite situational and thus a variable one according to one's needs. For example, scouting ring by ring might be 'best' in one's opinion once a player has unlocked AWs as they'll need the various relics and possibly more expansions for their city.

The star-like formation would be what I'd call a default or 'fall-back' strategy as it allows you to gain what you need by default (more boosted relics quickly), at a fairly good cost/distance ratio and you spread out across the world map rapidly in all directions. The later allows you to more easily adjust your scouting direction if a potential undiscovered trade partner appears. The provinces that you leave uncompleted/skip would then allow you to relatively quickly gain expansions or relics/shards for AWs when you happen to need them. Just my opinion though.

On the spiral, it's more elegant to create a new ring by overrunning the 1 o'clock corner, but that's not what actually happens. Each ring starts at 12 o'clock, and when the ring closes at 11:59, there's a jog and a new ring is started, again, at 12 o'clock. You can verify that pattern with a close look at us3: genevadugger, or by looking at the top edge on any Elvenar world map, at exactly 12 o'clock where you'll find the start of the most recent ring.

I looked into this on Winyandor and the entirety of the world map's edges are straight. Could it be that the ring was completed fully and then the system started filling in the holes for the deleted inactive players within the current map before expanding further outwards? Will change the spiral if you feel I should. :D

EDIT: This what you mean with the spiral?

spiral12oclcock.png
 
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DeletedUser

Guest
Nicely done.

There's a bit more to the replacement algorithm than
  • Maximum map size (I'm guessing that this may be why you're seeing a complete outer ring.)
  • Maximum deletions per day (There doesn't seem to be a maximum on immigrants per day)
  • Cities are added at the end of a clockwise flat-topped hexagonal spiral, if no interior vacancies are available
  • Each new ring starts at 12 o'clock
  • The same spiral is used when cities are vacated
  • The same spiral is used when vacancies are filled EXCEPT that there's a 48 hour minimum dwell. (Hopefully the developers are reserving themselves a window that they can use for moving isolated cities.)
  • Days since last login (at least 30 days, and it's currently 70 days on us3)
  • Premium sponsored (more than 200 diamonds)
  • Has reached Chapter III
The developers have not chosen to share their algorithm, so while we have some suspicions, we don't yet have enough data to say anything more that's definitive.

My main concern is that we lack a means of archiving Premium and Chapter III cities, and then retrieving them if the owner happens to show up again. The same archive/retrieve capability would also enable the ability to shift (archive/retrieve) an active, but isolated city. I've discussed the tradeoffs in https://us.forum.elvenar.com/index.php?threads/nine-near-neighbors.1248/ with a particular focus on techniques that would preserve the integrity of discovered Relics and Neighbors, while still providing a method by which we can avoid ending up with a map that looks like a doily once a world stops growing.
 
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DeletedUser

Guest
First off, I'm starting to wonder whether this thread needs to be moved into the 'Discussions' forum... While the topics here are still related to the initial questions raised in the OP, we've "come a long way" so to speak. (Another "fun and lively discussion in [the] team chat" perhaps?) :p

Secondly, thank you Katwijk. :)

Got to admit the effort you put into your threads (or even posts) is rather astonishing. Would be one huge step in the right direction if the devs do implement a feature to adjust player's cities within the world map, while still entertaining the interest amongst the players to go out and explore the map 'strategically' (the most important point to me personally , out of the three main you mention in the former version of that thread). Really love the idea about having to rediscover provinces once you've moved (at an appropriately 'lower' cost), in addition to having (some) new neighbours. Makes having a fellowship more interesting too, as those players would have to be chosen even more carefully (no point in having fellowship members who are in your neighbourhood/very close to you - from an efficiency perspective).

As for the maximum map size - do you reckon we've reached that on the 'new' world of Winyandor already (currently there are 37926 ranked players, my guess is approx. 40000 if all vacancies were filled)? Personally I'd find that disturbing simply because a new world would be opened relatively soon (two months at most is my guess judging by the current development of 'immigrants') and the issue of inactive neighbours just ends up getting spread across even more worlds. Admittedly the devs don't have any other option than to open a new world if that were the case though.

Will consider turning the information we've collected in this thread into a comprehensive (visual) guide for the world map. In regards to that: anything else we'd need to cover? Currently we have covered relic distribution, trader range (limitation of 200 players), counting rings/distances, (briefly) scouting strategies, as well as the placement pattern of new players around the map and vacancies within. (Did I miss something?)

Oh, and before I forget. Other members are welcome to join in on this thread at any time! :D
 

DeletedUser

Guest
The Dec YouTube promo included a pretty broad hint that we'll be getting some sort of Provincial Combat Tournament. You should probably wait to see what that's all about before you put any more effort into a map related guide.

No matter how carefully I look, I can't find a jog at 12 o'clock on the en2 map. I'd like to believe that the spiral expands simply by overrunning a corner, because that makes the graphs a lot prettier, but us2: genevadugger is a very awkward counter-example.

The outer ring on the en2 map has about 110 cities per edge, and it's NOT complete. Here's what I found.
  • 1 o'clock is rika
  • 3 o'clock is Benfullar
  • 5 o'clock is NicolaWright
  • 7 o'clock is acced
    • 8 o'clock is paulineP at the END of the current spirial
  • 9 o'clock is cassaleigh (probably in the previous ring)
  • 11 o'clock is Gazooka0645 (probably in the previous ring)
I'm NOT happy. :confused:

en1 is also flat across the top, from 11 oclock Xinelve to 1 o'clock Cliggy.
 
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DeletedUser

Guest
The Dec YouTube promo included a pretty broad hint that we'll be getting some sort of Provincial Combat Tournament. You should probably wait to see what that's all about before you put any more effort into a map related guide.
Yes, that's a good point. Although I'm hoping it's not going to be a strictly combat related feature. That said, I do believe it will be the first major update/expansion to enter the game (out of the three that were shown) due to the comparatively more amount of information we got through the short preview (a wild guess at best really, but could mean we'll learn more in the next two episodes).

No matter how carefully I look, I can't find a jog at 12 o'clock on the en2 map. I'd like to believe that the spiral expands simply by overrunning a corner, because that makes the graphs a lot prettier, but us2: genevadugger is a very awkward counter-example.
Hmm... I'll re-upload the previous spiral then as an alternative possibility, as I had edited my former post by replacing that spiral with the 12 o'clock version.

P.S.: From a logical perspective I would think the spiral should overrun the 1 o'clock corner as this leaves only six players on the outer ring (at the corners) with 3 direct neighbours (instead of 4). The 12 o'clock version leaves 7 players with only 3 direct neighbours, as the player at 12 o'clock won't have a neighbour directly to the left.
 
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DeletedUser

Guest
If you want to dive into the deep end of the pool, check out http://www.gamasutra.com/blogs/HermanTulleken/20140912/225495/20_Fun_Grid_Facts_Hex_Grids.php, especially
  • Fun grid fact #17 Complex numbers can be used instead of vectors for hex coordinates
  • Fun grid fact #20: Hex grids can be used for fake 3D cubes
A cubic transform is far more efficient than mucking about with hexagonal arrays, and there's some decent math to support cubic arrays. The take away is that it's NOT AT ALL LIKELY that Trader Distances, Scouting Costs, and Combat Difficulty are determined using a "simple" pointy-top hexagonal ring, nor is that model a very good fit for the sparse data that I've been able to glean from my most distant traders. There are just too many exceptions.

Cubic.png

A diamond, similar to the above Fun grid fact
#20 triangle but with a plus and minus z axis
so that the home sector is in the middle, seems
to be a much better fit, and 200 trading partners
could be modeled simply by limiting
=SQRT(SUMSQ(x,y,z) to 25 or so cities in each
direction, constrained such that positive x+y+z
must always equal 25 or so to preserve our
orthogonal cut, plus a similar space where
negative -x-y-z always sums to -25 or so.

For our half space triangle we're looking for
100 cities plus 200 relic sectors. It's geometrically
convenient to think of the triangle as half of a
600 cell square, and the square root of 600 is 24.49.
25^2 is 625 sectors, which would be 208 trade partners.

I can't really say anything definitive about scouting costs and combat difficulty, because I'm saving my expensive discoveries for future chapters, but I strongly suspect that the correct model will be rhomboidal, rather than hexagonal. Sometime in the next few days I'll go into a virgin world and carefully observe the scouting costs to validate the rhomboidal distance model.

3x3grid.png


Note that the rhomboidal rings are similar to the flat-topped hexagonal rings, 45 degrees rather than 30 degrees, except that the horizontal sides are extended to form a peak, rather than going vertically, so if somebody has collected data for scouting costs and combat difficulty, the peaks at 9 o'clock and 3 o'clock should be cheaper than would be predicted by the various hexagonal models.
 
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DeletedUser

Guest
I moved a post from a few days ago, because I now have more data, and an interesting discovery.
I have some EXCELLENT news. The us3 outer ring got to genevadugger, at 12 o'clock, and DID NOT jog to the next ring. So the counterexample was an anomaly that we can, henceforth, ignore. This means that we can, thank goodness, stay with the pretty model wherein the spiral expands by overrunning a corner.

I got the odd jog again on the us3 map near 12 o'clock, Sarah Dragon at the moment, but this time I'm watching it more closely, and I've noted that the Tiink is at the "real" end of the Ring 252 spiral, on the 1:45 radial. What's happening is that the flat-top of the global hexagon does NOT fill clockwise from 11 o'clock to 1 o'clock, as one would expect, but rather it backfills counterclockwise from 1 o'clock back to 11 o'clock.

This MAY be a bug that only effects the top edge of the global map, in which case I'll write it up, but it may also be that half of the edges are back filling and we just never noticed before. In either case the map is being extended a spiral edge at a time, and the only question is whether it's a clockwise monotonic sequence or if it jumps back and forth. Once an edge has been completed the results are equivalent.
 
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DeletedUser

Guest
That's indeed an interesting observation Katwijk. Thanks for sharing. :)

Looking at the en2 map, it's still flat-topped and I haven't spotted an indent anywhere yet, so I'm assuming the system is still too busy filling in vacancies through deleted inactive players. Might take a while before we see a new ring develop there.

As for the aforementioned rhomboidal cubes/rings, I cannot confirm that theory for the rings in relation to scouting costs. To quote my previous post:
I've looked at rings 6-8 specifically and the costs to scout these provinces are definitely in a pointed-topped [hexagonal] pattern and include player cities as "null relic sectors". (The visual found in the official Wiki that you've linked in a previous post, Katwijk, follows the same principal.)
 

DeletedUser

Guest
I created a new city, en2 > Katwijk if you want to take a look. I'm very carefully acquiring each ring by starting at 12 o'clock and working clockwise. Every 3rd ring will have a city at 12 o'clock so the first relic sector will be at 1 o'clock.

If my rhomboidal distance model is correct, then the observed data will be tightly constrained.
  • ALL of the unscouted costs in the current ring will always be the same
  • ALL of the unscouted costs in next ring(s) will always be the same, but they will differ from the unscouted costs in the current ring by a fixed amount that is attributable to the base cost for the ring
  • ALL of the unscouted costs in any ring will always increase by an identical amount as I acquire sectors in any ring.
Rhomboid640.png


Once I've isolated the base cost for each ring, then I'll have two number series that I can use to back into formulas for:
  • The base cost for each ring, which I expect to be 100 times the square of the ring distance
  • The separate incremental cost for the total number of acquired sectors, which I expect to be 100 times n^1.05, rounded down to a multiple of 5 coins.
Note that the rhomboidal model covers exactly the same sectors as the pointy-topped hexagonal model, until you approach the cities at either 3 o'clock or 9 o'clock in the current ring, where the rhomboidal model predicts lower costs than the pointy-topped hexagonal model.
 
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DeletedUser

Guest
It'll be interesting to see what your studies show. Here's a visual that I believe to be self-explanatory as to why I can't see the rhomboidal distance model being correct:

scouting-costs_mapped.png

P.S.: I did view your city, prior to your post, lol. Must have been when you literally just created it? It had nothing built save for the default buildings. :D
 
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DeletedUser

Guest
That's some pretty fine graphics work, and it's a solid case for the pointy topped hexagon model.

As you acquire sectors the unscouted "next sector" costs always go up, everywhere, each time you acquire a sector. So your numbers are presumably the costs that you're seeing RIGHT NOW those unscouted sectors?

Have you been tracking the incremental costs as you explore sectors in each ring and, if so, do you recall those numbers?
 
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DeletedUser

Guest
That's some pretty fine graphics work, and it's a solid case for the pointy topped hexagon model.
Thank you. :)
So your numbers are presumably the costs that you see RIGHT NOW those sectors?
Precisely. They have increased to 200k, 270k and ring 8 provinces remain at 410k oddly enough. (Wondering whether I misread ring 8's costs earlier to be honest, but I'm very certain it was 410k before too. EDIT: This was not a mistake. It happened again, this time the increment skipped ring 6 and 7, but 8 and 9 increased by 10k.)
Have you been tracking the incremental costs as you explore sectors in the same ring and, if so, do you recall those numbers?
Unfortunately I haven't been tracking them until very recently. For ring 6 the costs increased from 140k to 200k in 10k steps for every further province I scouted in either that ring or ring 7. Equally I can remember the costs for ring 7 increasing in 10k steps from (210k - 270k). As for ring 8, I'm not certain at all. EDIT: I now know that the costs do not increase every time after scouting the next province.

Here the numbers I can confirm are 100% accurate at this time:

Total Number of provinces scouted/completed: 85 (Rings 1-5 are complete)
Scouting costs ring 6: 200k (17 of 24 provinces scouted/completed)
Scouting costs ring 7: 270k (7 of 30 provinces scouted/completed)
Scouting costs ring 8: 410k (1 of 30 provinces scouted/completed)
Scouting costs ring 9: 670k (0 of 36 provinces scouted/completed)

As I am currently scouting/completing the rest of ring 6 and then 7 to gain some extra expansions, I'll keep track of the costs and post updates.

------------------------
Update: (Changes are highlighted)

Total Number of provinces scouted/completed: 86 (Rings 1-5 are complete)
Scouting costs ring 6: 200k (18 of 24 provinces scouted/completed)
Scouting costs ring 7: 270k (7 of 30 provinces scouted/completed)
Scouting costs ring 8: 420k (1 of 30 provinces scouted/completed)
Scouting costs ring 9: 680k (0 of 36 provinces scouted/completed)

------------------------
Update: (Changes are highlighted)

Total Number of provinces scouted/completed: 87 (Rings 1-5 are complete)
Scouting costs ring 6: 210k (19 of 24 provinces scouted/completed)
Scouting costs ring 7: 280k (7 of 30 provinces scouted/completed)
Scouting costs ring 8: 420k (1 of 30 provinces scouted/completed)
Scouting costs ring 9: 690k (0 of 36 provinces scouted/completed)
 
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DeletedUser

Guest
I think the progression is probably exponential, and the "skips" are actually just round off error, because I'm seeing similar behavior in the earlier sectors. I'll probably end up speaking Polish by the time I'm done verifying that "Nope, it wasn't a typo."

In the following table I'm showing the actual cost for each ring, paired with the UNscouted costs for the next ring. Once I have enough data, then I'll try to isolate Ring Distance and the Number of Scouted Sectors. I've highlighted a couple of the cells where the progression slopped over into the next multiple of 5, which "looks like" a typo, but it wasn't.

1 shows All of 2 2 shows All of 3
100 na 780 na
200 230 920 1800
300 330 ~ ~
410 430 ~ ~
510 540 ~ ~
630 660 ~ ~
done 780 ~ ~


I also turned in a Text Related Error in Beta,
because it's well nigh impossible to read
dark red numbers on a dark brown background.

Using a lighter red shouldn't be very difficult.
LighterRed.png
 
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DeletedUser219

Guest
I can sort of verify some of those numbers. I have been completing each ring before starting the next. With 4 provinces left, ring 8 is at 600K, ring 9 at 750K, and I can see a few (should be ring 10) at 1M. Don't let me interrupt, though. :p
 

DeletedUser

Guest
We're by no means the first gang that's tried to get a handle on scouting costs.
Agreed, I'm searching through some other language forums that I can understand to see if I find anyone having attempted to get behind this there. So far not much luck though.

BTW: Just remembered a factor that will be messing with our scouting costs when comparing amongst another: the Advanced Scouting technology at the beginning of each new chapter. Unfortunately we don't know by what percentage it decreases the scouting costs. One post in the German forums suggests that the decrease is 30% consistently. I wouldn't set that in stone, but worth also taking a look at during your study Katwijk?
 
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DeletedUser

Guest
I'm not sure how to handle the timing issues, but I've added the Scouting Tech in my Costs table, in lieu of the NA entry for the next ring before you've acquired any of the sector in the current ring, and I'll make a point of only advancing my Scouting technology in between completed rings. So I'll be watching to see how much the scouting costs drop WHEN you get the new tech, which shouldn't be very tricky.

I also intend to build an absurd number of Workshops, and armories if I need them, rather than building ANY manufacturing. Manufacturing is expensive, so I'm going to try to use Supplies to buy UNboosted goods from the wholesaler, and then trade for my boosted goods. Just to keep it interesting.

Rhomboid480.png
I finally have an Excel spreadsheet
that I'm happy with, for collecting the data.

The city names are all listed, and the rings
are a good approximation of the map layout
so it should be fairly resistant to data entry errors
that are created by getting lost and confused.

It's certainly not as pretty as your presentation,
but the difficulty of just getting all of the city
names to line up nicely illustrates the need for
a data entry method that's fairly robust.

The cities at the horizontal corners of the
rhomboidal overlay can't possibly be included in
the allowed 200 Traders, so if they show up then
it's likely that a cubic transform is being used
to select trading partners. I'll be sending a note
to the following players, so we'll know for sure
before very long.

While we've clearly established that a pointy-topped global hexagon is being used to calculate scouting costs, I still haven't given up on my cubic transform for determining trading partners, by distance.
  • If you look at the fake cubic view from a few posts ago, we can use an orthogonal cut of 3-space constrained such that x+y+x= 19, and stack two equilateral triangles back to back for a diamond shaped area.
  • One convenient formula for the area of a rhomboid is A =(d1*d2)/2.
  • The height of an equilateral triangle is h=sqrt(3)*b/2
  • As we're dealing with two equilateral triangles, stacked back to back with our home city in the center of the space, our formula devolves into A=sqrt(3)/4*d squared
  • We want 200 cities plus 400 relic sectors, so we'll need to solve for 600 sectors, which yields d=37.22 sectors in the home row.
  • That's 18 sectors + our home sector + 18 sectors in our home row, or 18 rings.
  • Looping back, well have an "invisible" cubic array where each axis is sumsq(x,y,z)=37 squared, so x=y=z=26.2, which is also the vertical dimension (the +/- z axis) on either map. We'll bump it up to 14+14=28, so that the related hexagonal rings will contain at least 600 sectors.
  • For hexagonal rings, we're looking for 1+6+12+18+24+30+36+42+48+54+60+66+72+78+84=631 sectors in 14 rings.
  • The same home row is shared by both models
    • The cities in the corners of either array presentation would be unique to that presentation
    • We're viewing equilateral triangles that don't include the "extra" 31 sectors that were used to fill out the hex rings, and they slant away from us so they're a bit distorted
    • We're only talking about a half-dozen sectors, per corner, in either case, so it's not a very important distinction.
(revised on 1/21/2016)
 
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DeletedUser

Guest
Well, it's progress of a sort. One of the radio button traders was NOT on the hexagonal rings that I'm tracking.

Decimus.png


The problem is that DecimusAura not on my rhomboidal list either. So I did a body count and I have 13 cities in my home row plus 41 cites top and bottom, and that only accounts for 95 cities,rather than the 200 that I'm looking for. I can obviously add a few more rings, but I need to go back and analyze what's flawed about the theory.

(Update a few hours later. Duh! I thought I expanded the fake cubic array view into a square, but it was actually only a rectangle, so my geometrically convenient shortcut bit me. There's nothing fundamentally wrong with the model, it just needs to be bigger, and I've reworked the above derivations, and the model space, accordingly.)

Meanwhile, the data collection for the scouting costs is going quite nicely.

en2Ring3.png


1 shows All of 2 Commentary
100 Scout I ~
200 230 30
300 330 30
410 430 20
510 540 30
630 660 30
done 780 ~
2 shows All of 3 Commentary
780 Scout I ~
920 1,800 880
1,100 2,000 900
1,200 2,100 900
1,400 2,300 900
1,600 2,500 900
done 2,800 ~
3 shows All of 4 Commentary
2,800 Scout 1 ~
3,000 9,700 6700
3,300 10,000 6700
3,700 10,000 Rounding??
~ ~ ~
~ ~ ~
~ ~ ~
~ ~ ~
 
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DeletedUser

Guest
reene is at the exact center of the en2 map. If you visit that city, and drag the map just a bit, you'll get a blue arrow that points to your own city, and you'll be able to quickly determine where you are on the world map.

Here are some other interesting landmarks on the en2: Winyandor map.

LandmarksCornersScore
reene Exact Center 55
rika 1 o'clock 21
Benfullar 3 o'clock 159
Katwijk Ring 23, 3:00 449
NicolaWright 5 o'cliock 114
acced 7 o'clock 164
paulineP 8:30 42 End of Spiral
cassaleigh 9 o'clock 22
Gazooka0645 l1 o'clock 0

If you visit the six cities on the odd numbered clock radials, you'll quickly notice that they are each on a corner of the current flat-topped global map pattern that is the result of the clockwise hexagonal spiral that's used to fill the map.

My city is near the center of the map, 23 columns to the right of dead center, so I'm in fat city, but as I was exploring the map I did notice that there's a area that has quite a few vacancies. In particular, if you visit reene's city, click on the map icon, drag the map just a bit, and follow the blue arrow to your own city, you'll find that the current vacancies are near ring 50. paulineP is at the very end of the spiral.

I've developed an Excel 2013 map, which is attached if you want to download it and take a look, to track Scouting Cost. Those costs are supposedly the same for everybody, if your notes are accurate, and therein lies the challenge. By identifying YOUR local cities you'll have a reliable way of keep notes regarding your map related activities, rather than getting lost all of the time.

I'm using a 14 ring pointy-topped hexagon, which will support 613 sectors, or 204 cities, to track my scouting costs as I carefully acquire one ring at a time, moving clockwise starting at 12 o'clock in each ring. Along with the scouting costs, we're also trying to determine whether the trading distances use the same hexagon as the scouts, of if there's something else going on. Enjoy!

Only if RhomboidalLocation Score
Lakandula Ring 18 left 3,412
JoyceD4 Ring 17 left 4,141
geoff54 Ring 17 left 36
phil j Ring 16 left 1,809
mashster Ring 15 left 13,483
Echoe Ring 15 left 6,939
Ninde Ring 15 right 1,363
Gogetic Ring 15 right 22
U die Today Ring 16 right 18
Canuck21 Ring 17 right 162
ajay1122 Ring 17 right 129
nigelselston Ring 18 right 15


KatwijkRing14 480.png
 

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DeletedUser

Guest
I'm fiddling with some Excel capabilities that are turning out to be far more useful than I anticipated.
  • We showed DecimusAura's UNdiscovered trades a few posts ago, and I'm using the Excel Find All function to get the related cell addresses from my map which allows me to easily enter an absolute cell reference, rather than the trader's name, in a sortable table.
  • That allows me to use the Excel Formula menu to Trace Precedents, and as a result I have a COMPREHENSIVE alphabetized list with an easy way to indicate, right on the map, regarding where I'm the most likely to discover active trading partners.
  • I've also rotated the names to emphasize that similar relic sectors, and therefore similar cities, lie on the 10 o'clock to 4 o'clock diagonal.
FindAll.png
Precedent.png
GoFind.png

(Updated on 1/24/2016) We're using the same Excel spreadsheet to track a band of vacancies as they sweep through Katwijk's neighborhood on the us2:Winyandor map. See https://us.forum.elvenar.com/index.php?threads/winyandor-vacancy-watch.1572/

us2Vacant 2016A24.png
 
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