Life In 19x19 :: trihexagonal go

Interesting. When are we going to see first trihexagonalevich?

making eyes in the center would be near impossible: you need at least 9 stones to enclose a single eye and be connected (vs 7 on the square lattice) and 12 stones to be alive in the center

How does that work Tryss? I can't see it.

I don't want to spoil the fun, but this idea has been implemented long ago in Medusa.
You can find the game at Sensei's and it is also featured in R. Wayne Schmittberger's 'New Rules for Classic Games' (John Wiley & Sons, Inc. New York; ISBN 0-471-53621-0).

Playing go on other graphs is such a obvious idea that I believe any claims of anteriority are pretty pointless.

I don't know how to render it, but a spherical trihexagoal board would be pretty cool.

a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids.

This is interesting; I wonder if there's an advantage in one or the other visualization. It does seem that Medusa has some additional rule variations that make it something different than "go on a different topology", which is what I was interested in

"His first idea was to simply apply the rules of Go and see how it worked out. As it turned out, regular concepts like 'ko' and 'seki' remained intact, but there was a big difference if a group was in 'atari', that is: if it had just one liberty left, like the white stone.
In Go a point has four liberties and extending from a group in atari may increase the number of its liberties by 2. In Rosette an extension increases that number at most by 1, and this one is consequently taken to keep the group in atari.
The attacker has the choice of direction and may lead the head of the 'escaping' group towards the edge or even around towards its own tail, to die.
Of course things were balanced by the fact that both players suffer or enjoy this to the same extent, but Mark concluded rightly that it gave rise to too much tactical involvement to leave much room for any long term strategy. So he invented a safety mechanism up and above the implicit safety mechanism of having two 'eyes', and called it a rosette.
A rosette is formed by six stones of one color, occupying a small hexagon. A group containing a rosette lives unconditionally."

Mark Berger, who's real name is Richard Kramberger, got the idea to play Go on the triple contacts of a hexgrid,

Author:	emeraldemon [ Mon Feb 06, 2012 2:01 pm ]
Post subject:	trihexagonal go
There was a thread a while back about alternative tilings for go (viewtopic.php?f=45&t=1163&hilit=hexagon&start=20). I was thinking about this again, and I like the trihexagonal tiling: Attachment: game2.png [ 49.43 KiB \| Viewed 16579 times ] Can you spot the snapback? This has the nice property that each point has 4 liberties, and it's uniform. Also it seems like 6 stones make life in the corner: Attachment: twoeyes.png [ 31.8 KiB \| Viewed 16579 times ]

Author:	cyclops [ Tue Feb 07, 2012 4:36 am ]
Post subject:	Re: trihexagonal go
I had to convince myself that your trihexagonal go board is not equivalent the our normal square go board. But of course it isn't. In normal go two neighbouring points don't share a common neighbour in trihexagonal go they do. I like your idea!

Author:	tj86430 [ Tue Feb 07, 2012 4:46 am ]
Post subject:	Re: trihexagonal go
Interesting. When are we going to see first trihexagonalevich?

Author:	perceval [ Tue Feb 07, 2012 7:19 am ]
Post subject:	Re: trihexagonal go
a bit off topic but i worked on this lattice (called the kagome lattice -from a japanese name for basket or something) during my physics day and the geometric properties are crazy ,and as a result the physics properties of the heisenberg model on it are crazy too (the ground state might have residual entropy at T=0 because it remains ennormously degenerated ). it would be very very different from a square lattice even if coordinance is 4 too: for example it is not bipartite ie you cannot divide it into 2 sublattices where no 2 summit on the same sublattice are niegihbors (this is trivial with a square lattice ) in some sense you always have bad shape: a 2 stone chain have only 5 lib instead of 6 in the square lattices. an empty triangle have 7 libs on the square, but a "full triangle" (3 stones of same color on same triangle) have 5 on the kagome. making eyes in the center would be near impossible: you need at least 9 stones to enclose a single eye and be connected (vs 7 on the square lattice) and 12 stones to be alive in the center on the other hand seki might be easier to get

Author:	emeraldemon [ Tue Feb 07, 2012 9:38 am ]
Post subject:	Re: trihexagonal go
tj86430 wrote: Interesting. When are we going to see first trihexagonalevich? I'd like to try it, but I'm not sure if there's an easy way to do the diagrams. For these I'm adding the stones manually in inkscape (svg editor). It's not too difficult, but it does require editing in another program. perceval wrote: making eyes in the center would be near impossible: you need at least 9 stones to enclose a single eye and be connected (vs 7 on the square lattice) and 12 stones to be alive in the center What about this shape? Attachment: centerlife.png [ 26.38 KiB \| Viewed 16482 times ]

Life In 19x19 http://www.lifein19x19.com/

trihexagonal go http://www.lifein19x19.com/viewtopic.php?f=45&t=5463	Page 1 of 2

Author:	Tryss [ Tue Feb 07, 2012 11:26 am ]
Post subject:	Re: trihexagonal go
And you only need 4 stone to be alive in the acute corner (the straight line is enough) : it's a cute corner

Author:	cyclops [ Tue Feb 07, 2012 6:24 pm ]
Post subject:	Re: trihexagonal go
In Esmeraldons first diagram can black connect his left group to his lower right group? I believe he can not.

Author:	hyperpape [ Wed Feb 08, 2012 6:23 am ]
Post subject:	Re: trihexagonal go
How does that work Tryss? I can't see it.

Author:	tj86430 [ Wed Feb 08, 2012 7:11 am ]
Post subject:	Re: trihexagonal go
hyperpape wrote: How does that work Tryss? I can't see it. The second points from the corner are miai.

Author:	tromp [ Wed Feb 08, 2012 7:17 am ]
Post subject:	Re: trihexagonal go
hyperpape wrote: How does that work Tryss? I can't see it. The two "1-2" points are miai for separating the corner space into two eyes. So it's not Benson alive, but alive it is. -John

Author:	HermanHiddema [ Wed Feb 08, 2012 7:41 am ]
Post subject:	Re: trihexagonal go
Arguably, I would guess any single stone on an otherwise empty board is "alive" by that measure

Author:	christian freeling [ Tue Feb 28, 2012 10:07 am ]
Post subject:	Re: trihexagonal go
I don't want to spoil the fun, but this idea has been implemented long ago in Medusa. You can find the game at Sensei's and it is also featured in R. Wayne Schmittberger's 'New Rules for Classic Games' (John Wiley & Sons, Inc. New York; ISBN 0-471-53621-0).

Author:	daal [ Tue Feb 28, 2012 10:16 am ]
Post subject:	Re: trihexagonal go
I don't know how to render it, but a spherical trihexagoal board would be pretty cool.

Author:	HermanHiddema [ Tue Feb 28, 2012 1:12 pm ]
Post subject:	Re: trihexagonal go
christian freeling wrote: I don't want to spoil the fun, but this idea has been implemented long ago in Medusa. You can find the game at Sensei's and it is also featured in R. Wayne Schmittberger's 'New Rules for Classic Games' (John Wiley & Sons, Inc. New York; ISBN 0-471-53621-0). Playing go on other graphs is such a obvious idea that I believe any claims of anteriority are pretty pointless.

Page 1 of 2	All times are UTC - 8 hours [ DST ]
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group http://www.phpbb.com/

Author:	Bonobo [ Tue Feb 28, 2012 6:34 pm ]
Post subject:	Re: trihexagonal go
daal wrote: I don't know how to render it, but a spherical trihexagoal board would be pretty cool. Smallest (and easiest) way to do this would be an icosahedron, Wikipedia wrote: a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids. But I think I wouldn’t want to play this … no corners, no edges, this ain’t something for me lowly DDK D’oh. Trihexagonal, not triangular <hits forehead against table>

Author:	emeraldemon [ Tue Feb 28, 2012 8:23 pm ]
Post subject:	Re: trihexagonal go
christian freeling wrote: I don't want to spoil the fun, but this idea has been implemented long ago in Medusa. You can find the game at Sensei's and it is also featured in R. Wayne Schmittberger's 'New Rules for Classic Games' (John Wiley & Sons, Inc. New York; ISBN 0-471-53621-0). This is interesting; I wonder if there's an advantage in one or the other visualization. It does seem that Medusa has some additional rule variations that make it something different than "go on a different topology", which is what I was interested in Is anyone willing to try a trihexagonal malkovich?

Author:	christian freeling [ Wed Feb 29, 2012 3:20 am ]
Post subject:	Re: trihexagonal go
emeraldemon wrote: This is interesting; I wonder if there's an advantage in one or the other visualization. It does seem that Medusa has some additional rule variations that make it something different than "go on a different topology", which is what I was interested in Mark Berger, who's real name is Richard Kramberger, got the idea to play Go on the triple contacts of a hexgrid, like this: Why wasn't this translation possible? Quote: "His first idea was to simply apply the rules of Go and see how it worked out. As it turned out, regular concepts like 'ko' and 'seki' remained intact, but there was a big difference if a group was in 'atari', that is: if it had just one liberty left, like the white stone. In Go a point has four liberties and extending from a group in atari may increase the number of its liberties by 2. In Rosette an extension increases that number at most by 1, and this one is consequently taken to keep the group in atari. The attacker has the choice of direction and may lead the head of the 'escaping' group towards the edge or even around towards its own tail, to die. Of course things were balanced by the fact that both players suffer or enjoy this to the same extent, but Mark concluded rightly that it gave rise to too much tactical involvement to leave much room for any long term strategy. So he invented a safety mechanism up and above the implicit safety mechanism of having two 'eyes', and called it a rosette. A rosette is formed by six stones of one color, occupying a small hexagon. A group containing a rosette lives unconditionally." Mark called the game "Rosette" and published it in Games & Puzzles Magazine (issue 34). The point being: it's not always possible to translate Go to just any grid without encountering difficulties. The above 'atari' problem also plays a role on the trihexagonal tiling that is discussed here, That's why Medusa isn't a 'translation of Go' but a game fitting the grid as best as I thought possible. I never tried 'regular Go' on this grid, by the way: That's because it came in the wake of Medusa and presented itself as a simplified version. It may be worth a try though.

Author:	MarkSteere [ Wed Feb 29, 2012 7:31 am ]
Post subject:	Re: trihexagonal go
christian freeling wrote: Mark Berger, who's real name is Richard Kramberger, got the idea to play Go on the triple contacts of a hexgrid, You could have revealed that fact six posts back when you said "I don't want to spoil the fun, but this idea has been implemented long ago in Medusa," implying that Medusa was the first. Your claim of anteriority isn't just pointless in this circumstance. It's misleading and grossly misguided.

Author:	emeraldemon [ Wed Feb 29, 2012 8:03 am ]
Post subject:	Re: trihexagonal go
I intentionally chose a grid with 4 edges per vertex, to keep the tactics somewhat analogous. However, check out this "ladder": Attachment: ladder.png [ 32.64 KiB \| Viewed 16215 times ]