Nerf corners

[gwf_hegel]

The problem of giving each position the right number of liberties would be a challenge though. This is how it could be done on the entire sphere

[Samraku]

I think any board projected on the entire interior of the surface of a solid, would likely lack the least change properties we’re likely to want. Like the traditional board is not projected into the entire 2d plane, but only a subset thereof, I am thinking of projecting onto a small finite region of a possibly infinite geometry

It should still have 4 corners, and it should still have connections mostly similar to a square lattice on the euclidean plane, but those corners should be analogous to those concave angles in the cross board

[gwf_hegel]

But how would that be different from the normal goban?

[gwf_hegel]

Another approach could be to play on an unbounded goban with a separate win condition, such as surrounding any of an infinite grid of regularly spaced star points. Or the first player to achieve 60 points.

[Samraku]

Because the normal goban has 4 convex corners

[Samraku]

Yeah, I don’t want to eliminate corners, though, just nerf them

[yebellz]

I think it comes down to how we define “corners” and what it means to “nerf” them.

I interpret the original proposal to “nerf corners” as a tongue-in-cheek suggestion that modern post-AI fuseki has become too much of a corner-focused game. Relatively speaking, I think that fuseki immediately prior to the advent of superhuman Go AI had relatively less emphasis on the corners, and while the philosophy of “corners then sides then center” still placed priority on the corners, there was more strategic balance between wanting to secure territory in the corners vs wanting to have potential to expand into the sides and center.

Thus, I think the spirit of the original post is meant to suggest that the game could be changed in order to reintroduce strategic balance between securing corners vs contesting other parts of the board. However, this notion is not about some specific, fixed sets of points on the board (especially, if we are allowing the board itself to modified), but rather the general idea of restoring balance between different strategic options, such as the balance in priority between territory vs influence.

Hence, when we start modifying the board, I don’t think it’s enough to simply point to the fact that some corners points have been removed and claim that we’ve done enough to address this. Rather, when some parts of the board are removed/modified, it may completely change what we even think of as a “corner”.

For example, consider this rhetorical proposal of chopping off all four “corners” and “sides” by removing the first three lines:

This is ultimately reducing the 19x19 board to a 13x13, by keeping only the central part (and this is often done in over-the-board play with pieces of paper, if one wants to play 13x13, but only has a 19x19 board available).

I think it would be incorrect to claim that the above change has managed to “nerf corners” (and sides). Rather, from a strategic perspective, I would say that the above shift to playing on 13x13 has “buffed corners” (or “nerfed center”), based on my understanding of 13x13 strategy being an even more territorial and corner-focused game than 19x19.

[Samraku]

I don’t think anyone is proposing such a degenerate case of “removing corners”. Indeed, most proposals have attempted some degree of least change

[yebellz]

I’m taking the modification to an extreme to make a rhetorical point, but it is meant to refer to several proposals seen across these posts:

1. Nerf corners - #59 by Rascataplan
2. Nerf corners - #68 by stone.defender
3. Nerf corners - #69 by PRHG
4. Nerf corners - #74 by Samraku

I think that one needs to clarify what one is ultimately trying to achieve with various proposals, which comes back to what we mean by “corners” and what mean to “nerf” them.

For example, I think that in @stone.defender’s proposal, by removing the original corner regions, we now instead have a goban with 8 corners. This may result in a game (note: unsure strategic speculation of a new variant) that is more strategically focused on securing these eight corners and with even less emphasis on developing into the center.

I think @PRHG hits upon some of the lack of clarity in the original proposal and how various people have interpreted it:

@PRHG

I guess it depends how the corners should be nerfed. Does the original poster dislike how efficient it is to get territory in the corner region, or do they dislike the tactical effect that the 2-liberty intersections have on fights? If it’s the latter, what about removing the corners?

[Samraku]

@yebellz

For example, I think that in @stone.defender’s proposal, by removing the original corner regions, we now instead have a goban with 8 corners. This may result in a game (note: unsure strategic speculation of a new variant) that is more strategically focused on securing these eight corners and with even less emphasis on developing into the center.

Yes, but it’s still a valuable suggestion as it gets us thinking about other creative solutions which might accomplish a similar thing with fewer attendant side effects, for example my brainstorming about a board with 4 concave corners

@yebellz

I think @PRHG hits upon some of the lack of clarity in the original proposal and how various people have interpreted it:

Also a valuable contribution

@yebellz

I think that one needs to clarify what one is ultimately trying to achieve with various proposals, which comes back to what we mean by “corners” and what mean to “nerf” them.

I don’t think that’s self-evident. Instead of getting distracted with semantics, actual proposals, however imperfect, allow us to solidify how corners might be nerfed, and thereby get at the specifics of how corners are OP without getting bogged down in defining exactly what each proposal is trying to accomplish, as that may not be clear even to the proposer

More details can come out of the discussion organically

[Samraku]

@yebellz

I’m taking the modification to an extreme to make a rhetorical point, but it is meant to refer to several proposals seen across these posts:

And yet none of those are the degenerate case you’re talking about: they differ in kind not just quality, so I think you’re strawmanning the proposals put forth thus far

[yebellz]

It seems that you are taking an overly hostile view towards my posts. I don’t mean to suggest that any of the proposal should not have been put forward, but rather just want to encourage more discussion about the strategic implications of these proposed variants.

It feels like you are discouraging my posts. However, I hope that my discussions are contributing to the conversation. In general, I think that even outright criticism of other proposals should not be discouraged.

[benjito]

I’m not sure I understand this objection. Toriodal Go (as described at Senseis Library and Wikipedia) is finite. It may feel infinite in the sense that all intersections have 4 liberties, but the game cannot continue infinitely and will end in a similar timeframe as standard go.

[Vsotvep]

@Samraku

Is there a geometry where a polygon can have only concave angles?

It depends a bit on how one defines “interior”, but spherical geometry allows this: any polygon on a sphere with n edges, which are geodesics (i.e. two points are connected by straight lines that are the shortest distance “as the crow flies”), divides the surface of the sphere in two polygons, where one of them must have a sum of angles ≤ n * 180 degrees and the other ≥ n * 180 degrees.

But I guess if you define the interior of a polygon to be that part such that the sum of the interior angles (those angles that lie on the interior part) is less than or equal to the sum of the exterior angles, then by definition it’s impossible.

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@gwf_hegel

Another approach could be to play on an unbounded goban with a separate win condition, such as surrounding any of an infinite grid of regularly spaced star points. Or the first player to achieve 60 points.

Interesting proposal… My intuition says there will be no winning strategy for either player, where any optimally played game will continue ad infinitum without either of the players surrounding any points.

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@yebellz

I think it would be incorrect to claim that the above change has managed to “nerf corners” (and sides). Rather, from a strategic perspective, I would say that the above shift to playing on 13x13 has “buffed corners” (or “nerfed center”), based on my understanding of 13x13 strategy being an even more territorial and corner-focused game than 19x19.

This was my proposal to nerf corners:

a 21x21 board.

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Another proposal closer to toroidal Go but quite different: add an extra intersection (next to the board perhaps) that is connected to each of the four corners of the 19x19 board. Each corner then has 3 liberties, the extra point has 4 liberties, all points with 3 liberties are connected to exactly 2 other points with 3 liberties.

Or visualise it like this:

Instead of adding a single point, you could add a second goban, where each corner points of the first goban is connected to the corresponding corner point of the other goban:

Now it’s only a single step to cube-go.

[trohde]

@Vsotvep

cube-go

OK, now that I have made some first small steps with 9x9 Toroidal Go, I want to play a little 9x9 Cube Go … is there a Web site where I can do that?

[yebellz]

I’ve played a few games of Cube Go (note the graph is slightly different than that depicted above) via OGS with @Kosh:

Playing Cube Go (Vorlon Go) on OGS

Yes you can… [Screenshot%20(49)cropped] To play on OGS the board has to be represented flat. This can be done by playing on a 14x18 grid and using that part of the board that would be cut out to fold into a cube: [2] The unused lines around the outside, rows 1&18, columns A&O are there to prevent stones registering as captured when they are not but that still leaves the issue of stones that have been captured in a way that doesn’t register: [3] The marked white stone captures the two bla…

In that thread, it’s discussed how we managed to use OGS to help relay and record the games, but it was kind of a rough hack, and we both used a cardboard model to help make sense of the game. I don’t know of any website that properly implements Cube Go, but maybe the Go Variants server could consider tackling this project, after implementing Sierpińsky Go.