Many connections or few is not the relevant bit but rather that the places the corner region are connected to are all, of themselves, not distant from each other. After all, the relevant bit is the number of adjacent nations and nations are pretty much always contiguous. Except sometimes temporarily when dissected during war, but that is very rarely relevant at the grand strategy level.
You're falling into the trap of thinking map graphics are significant here. "Distance" is not relevant, because a province cannot be connected to a distant province; it's literally contradictory.
Distance is relevant. There's a big difference between having to cross two provinces and having to cross seven. This has nothing to do with the appearance of the map.
And that's not semantics, it's the fundamental point.
The fact that being on the corner of the map image is irrelevant is a semantic point, since it should be obvious that the use of the word "corner" when talking about gameplay is referring to the pattern of nodal connections that normally occurs there. Going "yeah, but it's not really a square because nodes!" is true but disingenuous.
Interconnectedness is what makes "corners";
Interconnectedness on the scale of regions though; not on the scale of individual provinces. The number of individual connections isn't really relevant to this, it's just a matter of chokepoint numbers. Furthermore, it's not merely a quantitative interconnectedness (that is, how many connections) that makes the difference, but their qualitative location.
if there is an area where there are few paths in and out (because the nodes in the area have few connections), it's a corner.
No, this is fundamentally untrue. The nature of a corner is about the relationships of the paths, not their number. Let's consider it in terms of corner empire. If the empire's borders all tend toward a certain group of provinces which are close* to each other, then it's a corner nation. In a non-corner nation, this is not the case; there are border provinces whose distance to a given other border province represents the full breadth* of the nation. In a corner nation, however, the border itself can represent a region of the country; all border provinces are somewhat close to each other, and there are non-border provinces which are more distant from any border province than the distance typical between any pair of border provinces. If we were modeling this for an intensive definition of a corner, the way to do it, then, would be to create a ratio of distance* between the most central (that is, distant from a border province) and the nearest border, and the two border provinces which are most distant from each other. This isn't perfect since square-cube law** means it's not independent of realm size, and it disregards that there is such a thing as directionality in the sense that in a central region, you could cross a realm from one border to another along such a path that you start at a border province, go to the most central non-border province, and thereafter go towards the border province most distant from the originating border province, and in a central nation you would always be getting more distant* from the originating border province whereas in a corner province, you would "turn around" after reaching the middle province and thereafter draw somewhat closer to the originating province before reaching your destination. That is probably meaningful if we want to distinguish a corner from an edge, but they kinda go together anyway so considering this is already generating very long posts, perhaps we shouldn't do that.
If there is a balanced number of connections in all provinces, there are no corners, as corners in a gameplay sense are areas that are significantly (for some subjective measure of significance) less accessible than others (otherwise there's no real meaning to it).
If you define something with such vague terms as "less accessible", it can have no meaning which is not therefore at least as vague.
You're getting stuck on map image. The image isn't relevant except as an abstraction and something pretty to look at. Again, look at Ragnarok Comes. It's a half-wrapped map that is very densely connected that behaves like a full-wrap map because of that density.
If anyone is stuck on the map image, isn't it you? I haven't been talking about it the whole time, except to mention that it goes together with the generation of the node web.
The map as a data structure has no edges or corners (in the cartographic sense, anyway). It's a connected series of nodes. The issue is not how the nodes are shown on a map (which can be wrapped or not, as the map-maker pleases; I yet again point to Ragnarok Comes), it's how densely connected the nodes are, and whether they're uniformly dense in their connections. If they are not uniformly dense, you'll have "corners" in the underlying nodes even if you wrap the map image.
Yes, this is correct. As an example, the Marverni game on my blog has me starting in a corner on a wrapped map, for example, which gave me a substantial advantage. However, this brings us back to the respect in which the map image actually does matter: The node web is built based on the map image, and therefore it tends to generate corners where the map image also has corners. Because of this, wrapped maps have the specific balance advantage that they rarely have corners, whereas non-wrapped maps generally have four corners and four or more edges of non-trivial length.
Players are placed randomly in any case, and actual distances vary according to gameplay and happenstance; distances of capitals take secondary importance.
This is false, and tremendously relevant. Players are placed procedurally, not randomly. The more players (and thrones) there are, and the more densely connected a map is, the harder it becomes to place all players at a "reasonable" distance without increasing map size.
It's true, the placement is procedural. I'm not seeing the relevant distinction, though. It's possible that I don't fully understand this aspect of your position. How is it that distance between capitals remains of greater importance than proximity of borders and of a preponderance of provinces in general? And, for that matter, what relation to the larger argument are you intending to highlight here?
Again, the relevant points are not the "shape" of the map, or whether it conceptually "wraps"; it's just node-to-edge density (province to connections in Dom terms) and shortest paths. If you want densely connected maps, then we need to move away from Dom3 conventions on what "good" map sizes are, because a map with high connectivity sets itself up very differently, in ways that very directly impact gameplay and often outcome, than a map with low connectivity and the same ratio of provinces per player.
I think the core disagreement here is that I don't see province to connections as an appropriate approximator of relative edge density. Except, I guess, in very small maps (say, three or five provinces per player) where the connections of a single individual province are relevant as a significant part of the overall realm rather than just for purposes of chokepoints.
I'll also note that although you're saying it plays out very differently, you're not really saying how. I'm not seeing meaningful ways that are independent of general distance. And regarding the relevance of general distance, I don't agree that number of connections per province and number of connections one must travel to get to a given province are inherently correlated except over very small distances or at (and near) the ends of the spectrum provided in your extreme examples of a ring and total connectivity. Without having done the math, it seems intuitively obvious to me that this effect decreases exponentially as we draw nearer to he middle of the range, and at any number of connections between about 3.5 per province and (provinces - (1/1.5)*provinces) this effect should be very small, and the amount of difference has much more to do with which connections are in place than how many. In Dominions where each connection is vastly more likely to connect a province to one that it's also close to along a different connection than one that it is otherwise distant from, I don't see how this relates to anything at a scale of movement greater than one or two provinces.
*Distance being a number of provinces, there's no need to falsely assert once more that distance only exists on the map image. We could also count the total movement costs as distance, but though that would be functionally accurate, it would increase complication beyond what's necessary for the purpose of this discussion.
**This term being used for brevity and familiarity; I'm aware that the web is not two-dimensional and therefore the exponents in question are not 2 and 3, and that they in fact are mutable depending on details. I'm not going to construct a general model because that would be a hassle and it's not actually useful since there's no way I'll be coding an alternate map generator or anything else which might use it.
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Topic: Dom5 Round502 - Get back to work! (Read 36394 times)