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Subject: Has anyone examined the topological underpinnings of Power Grid? rss

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David desJardins
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aaxiom wrote:
Topology (graph theory) is clearly abundantly present in Power Grid. Has anyone examined the boards in any sustained manner to determine whether there is a proven balance in the board design from an "edge / vertex" perspective? (If no proven balance, than an imbalance would exist).


I've taken several graduate and undergraduate classes in topology but I don't have any idea what this question means.
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J Weintraub
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Only thing I can think of is that he means to ask if the costs are balanced relative to the number of connections each city has.

Of course, I don't think this is even something that needs to be balanced for the game to be balanced, since anyone can start anywhere, and there's few enough cities that eventually everyone's gonna have to power the more expensive ones.
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Nick Short
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It always seemed to me that the boards were intentionally unbalanced, but that the strong player interaction of the game will create competitive forces that work to smooth out any previously existing imbalances.

I'd expect that you could make fairly random maps and they would play in a reasonably balanced fashion due to the player interaction.

(This is of course coming from someone who only knows the base definition of topology, but no real insight into the subject. But I have played a considerable amount of Power Grid.)
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Yours Truly,
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There must have been a moment at the beginning, where we could have said no. Somehow we missed it. Well, we'll know better next time.
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In an interview I heard with the designer, for the costs he mentioned looking at a topographical map, and taking into account things like rivers, as well as mountains. That's all the details I can remember him mentioning. It's the boardgames with scott PG ep, if you want to catch the snippet (http://www.boardgamegeek.com/thread/112597). Might be something as simple as counting the lines on the topo map, for some of the costs.

I personally think it's really cool that he built that kind of realism into the maps.
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Richard Sampson
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I must admit, I sort of question whether a great deal of thought went into those numbers. I could understand coming up with a number based on geographical difficulties as previously mentioned, but I don't think it was very mathematically deep since there are those spots where the direct connection is more expensive than passing through a neighboring city (eg. 24 connection to Boise is worse than the 9+12). These essentially create a direct connection that might was well not be there and doesn't really serve a purpose to the game (except to confuse?). That is not to say I have a problem with the game. I just don't think the connection costs (at least in the base game) were done with any sort of mathematical rigor as it seems to me the OP is suggesting.
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David desJardins
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aaxiom wrote:
The layout of the board has certainly been carefully planned, and I'm confident (but certainly cannot definitively state this without Mr. Friese's comments) that the underlying mathematics was a primary consideration (why a connection between two cities was 19, as opposed to 15, as an example).


I always thought it was pretty random. There's no particular reason that one set of values rather than another will play better, since the players adapt to wherever the cheap connections happen to be. There's a variant posted on BGG that uses tiles to build random maps with random connections, and I suspect that version of the game plays just fine.
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Werner Bär
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ras2124 wrote:
I could understand coming up with a number based on geographical difficulties as previously mentioned, but I don't think it was very mathematically deep since there are those spots where the direct connection is more expensive than passing through a neighboring city (eg. 24 connection to Boise is worse than the 9+12). These essentially create a direct connection that might was well not be there and doesn't really serve a purpose to the game (except to confuse?).

Friedemann defined the connection costs based on real geography (with more connections between cities drawn than there are now on the board). Then he went through the map and deleted the connections where an indirect route was less expansive on as the direct connection in question. But he missed a few instances.
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David desJardins
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aaxiom wrote:
Ah, THAT topology! Now it all makes sense. I may have clearly read something into this that wasn't there to begin with. Too much Knizia, I suppose.


Geographical map features are topography, not topology.
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Nick Short
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DaviddesJ wrote:
aaxiom wrote:
Ah, THAT topology! Now it all makes sense. I may have clearly read something into this that wasn't there to begin with. Too much Knizia, I suppose.


Geographical map features are topography, not topology.
Yes, two very, very different subjects. I fully believe that the maps are strongly rooted in real life topography. However, I have no clue about the topological factors that may have went into the maps.
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Iain Cameron
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the short answer to the original question...NO!
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unkle
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Still, one of the very few rules that seems almost always true is that connection from A->B is always cheaper than connection A->C->B. At least on the maps I've played.

Which makes sense, given the way FF designed them. And would make a random map very different (to me at least).
 
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Michael Gibbs
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topology and graph theory are different things.
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Chris Martin
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unkle wrote:
connection from A->B is always cheaper than connection A->C->B
Wrong.

USA map:
Boise → Cheyenne: 24
Boise → Billings → Cheyenne: 12 + 9 = 21

That took me two minutes of quick inspection of the most basic map to find.

And you specifically said "always cheaper", which excludes equalities, so:

German map:
Saarbrucken → Stuttgart: 17
Saarbrucken → Mannheim → Stuttgart: 11 + 6 = 17

Erfurt → Dresden: 19
Erfurt → Halle → Leipzig → Dresden: 6 + 0 + 13 = 19
 
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Philip Eve
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unkle wrote:
Still, one of the very few rules that seems almost always true is that connection from A->B is always cheaper than connection A->C->B. At least on the maps I've played.

This property (at least, a version in which the A->B connection is permitted to be the same price as the connection A->C->B) is called "the triangle inequality".
 
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unkle
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chrisjwmartin wrote:
unkle wrote:
connection from A->B is always cheaper than connection A->C->B
Wrong.

USA map:
Boise → Cheyenne: 24
Boise → Billings → Cheyenne: 12 + 9 = 21

That took me two minutes of quick inspection of the most basic map to find.

And you specifically said "always cheaper", which excludes equalities, so:

German map:
Saarbrucken → Stuttgart: 17
Saarbrucken → Mannheim → Stuttgart: 11 + 6 = 17

Erfurt → Dresden: 19
Erfurt → Halle → Leipzig → Dresden: 6 + 0 + 13 = 19


Well good catch ! And thanks for spending the 2 minutes that I did not spend and making sure I knew how badly I screwed up !

Of course, I knew about equalities, since Paris is a triple city and I mostly play Megawatts (France/Quebec, and NOT Germany/USA), which probably 2 seconds of inspection of where I come from could have tell you

(And nitpicking on people who do not speak their mothertongue here is a little easy, but anyway)

I must say I did not expect it that way, since it does not help blocking in phase 1-2. But it does not change the game radically. Still an awsome, terrific and nearly broken game, whcih is among my favorites.
 
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Chris Martin
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Heh sorry - was a little abrupt I suppose. Ma francais c'est pas bon, donc je ne dis pas choses mal a tu!

But it was when you said "given the way FF designed them". He designed them by placing a grid down and counting the squares, adding modifiers for difficult terrain. So if A -> B -> C is through easy terrain, and A -> C is across high mountains and wide rivers, then the triangle inequality will not hold.
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unkle
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Clearly no hard feelings here :-) Especially knowing your musical likings, we should have stuff to discuss after some trash-talking on boardgames

It is true that to my surprise, France is a map where the triangle inequality holds, and since it is the map I play most (and prefer, with probably Italy being a close second), I generalized my observations here a little too quickly. So there is no real rules for a PG map. Doesn't change the fact I'd play PG on any map, at any time.
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Chris Martin
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unkle wrote:
Clearly no hard feelings here :-) Especially knowing your musical likings, we should have stuff to discuss after some trash-talking on boardgames

It is true that to my surprise, France is a map where the triangle inequality holds, and since it is the map I play most (and prefer, with probably Italy being a close second), I generalized my observations here a little too quickly. So there is no real rules for a PG map. Doesn't change the fact I'd play PG on any map, at any time.

Well, there are rules for PG maps: the rules are that reality is king. And I like it that way!

(Joy Division fan eh?)
 
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