Square Hex

Has anyone ever played the Hex variant "Square Hex"? The rules and goal are the same, only the board is different. Here is an example of a so-called 8x8 board (there are 113 cells):
http://imageshack.us/a/img805/4651/squarehex8.png
The center cell is weaker than in Hex, as it only connects to four other cells. Also, the distances between sides is shorter along the edges of the board (8 cells long in this case) than through the center (15 cells long here), making the power of the cells more even than in Hex. The swap rule still works here, as there are losing moves for the first player on boards of size 3 and up.
What is everyone's opinion of this variant?

Hmm. Looks interesting. I'd play with someone, but it looks easier to do it in person.

It's interesting. It puts all four corners on an even footing.

The shape of the cells would make it harder for me to visualize
the connectivity than on a Hex board. For me, part of the appeal
of Hex is how straightforward it is, and this board is wrinkled
by comparison.

"The shape of the cells would make it harder for me to visualize
the connectivity than on a Hex board."
I agree, that is my main problem with it. Here is differently-styled board with the same adjacency graph that makes it a little easier to visualize, though it still isn't perfect:
http://imageshack.us/a/img844/1658/squhex.png

If anyone is interested, here is the adjacency graph of Square Hex (left) vs Hex (right):
http://imageshack.us/a/img28/86/sqvshex.png

"Looks interesting. I’d play with someone, but it looks easier to do it in person."

I read that as "Looks interesting. I’d play with someone, but it looks easier to do it in prison."

Just thought I'd share!

What isn't easier to do in Prison?

Walking on the beach :-)

Is there a proof that square hex is draw free like regular hex?

Is there a proof for which player has the advantage?

Well, the proof is the same as for regular hex, i.e if one player can't win, it means there is a "wall" preventing him to do so, which means the opponent has won.

And since it uses the swap rule, it should be a reasonably close game, same as Hex. Of course, one player still has the advantage, but we probably don't know who, same as in hex.

monospace test

Hi,

Square Hex looks nice and is a "restricted variant" of Hex. Maybe MJongo turn this ASCII graphics into a nice picture. (I hope that after hitting the Send message button, everything will be formatted in a monospaced font.)

Normal Hex 13
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Square Hex 7/13
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Normal Hex 13
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Square Hex 7/13
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@ Valette&MarleysGhost

The term 'advantage' is convenient as long as everyone is aware that it is misleading. There's is no 'advantage' in two-player perfect information zero-sum games, it's merely a good handle for human players to evaluate game positions.

A game as mentioned has a finite tree. That doesn't make the game finite (another recurring semantic mix up). The tree may well contain cycles. In the tree cycles appear as loops, see this example of a miniature game called MiniMancala. Finite tree, infinite game.

IF it is possible to draw (or otherwise establish) the complete tree of a game, THEN the truth of every position is:

\* a win for the moving side
\* a draw (if possible)
\* a loss of the moving side

So there's never an 'advantage'. The concept of 'advantage' is rooted in our inability to read the complete tree, not in the game. That's not to say it isn't a valid concept to discuss positions. It certainly is, or Chess commentator's would have a hard time ;-)

I like the fact that this new board is 2 old boards sliced in two down down the short diagonal, and then glued corner-to-corner. (see MJongo's adjacency graph in his most recent post.) So while there are regions that are identical to conventional play when it comes to connected-or-not (away from the new diagonals), things like ladders might end up being quite different due to the new diagonals.

I'd love to have a game!

Oh - we do know who has the advantage in both hex and sqhex - player 2

Given that without the swap rule player 1 has the advantage,
with the swap rule:
- if p1 plays a winning move, p2 swaps, and wins
- if p1 plays a losing move, p2 wins.

I think I disagree with Christian.

"""
IF it is possible to draw (or otherwise establish) the complete tree of a game, THEN the truth of every position is:

\* a win for the moving side
\* a draw (if possible)
\* a loss of the moving side

So there’s never an ‘advantage’.
"""

I would rewrite as:

"""
IF it is possible to draw (or otherwise establish) the complete tree of a game, THEN the truth of every position is:

\* a win for the moving side, in which case the moving side has the advantage
\* a draw (if possible), in which case neither side has an advantage
\* a loss of the moving side, in which case the other side has an advantage

So there’s never an ‘advantage’ except when there is, which in this game is all of the time.
"""

I fucking hate textile

@FatPhil

I can see you're human :)

Fatphil, you are correct of course, P2 can theoretically win, in both games :p

I hate textile as well.

This is my last try to post the Square Hex 7/13 board inside a regular Hex 13 board. The acute corners are filled with two triangles and there are long "sticks" parallel to the main diagonal, glueing together two parts of the Hex board.

FatPhil is wrong when saying that the board is sliced along the short diagonal. The corner pieces old Square Hex have three neighbours, just like the obtuse corners of the board. (The acute corners have only two neighbours.) This means that these boards is sliced in a more complicated manner, keeping the obtuse corners on the board and making the acute corners similar to the obtuse ones.

,_
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/,,,,, _/, _/,\_/,\_/,\_
\,,, _/, _/, _/,\_/,\_/,\_
/, _/, _/, _/,\_/,\_/,\_/,
\_/, _/, _/, _/,\_/,\_/,\_/
/,\_/, _/, _/,\_/,\_/,\_/,
\_/,\_/, _/, _/,\_/,\_/,\_/
/,\_/,\_/, _/,\_/,\_/,\_/,
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/,\_/,\_/,\_/,\_/,\_/,\_/,
\_/,\_/,\_/,\_/,\_/,\_/,\_/
/,\_/,\_/,\_/, _/,\_/,\_/,
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/,\_/,\_/,\_/, _/, _/,\_/,
\_/,\_/,\_/,\_/, _/, _/,\_/
/,\_/,\_/,\_/, _/, _/, _/,
\_/,\_/,\_/,\_/, _/, _/,,,/
,,\_/,\_/,\_/, _/, _/,,,,,
,,,,\_/,\_/,\_/, _/,,,,,,,/
,,,,,,\_/,\_/, _/,,,,,,,,,
,,,,,,,,\_/,\_/,,,,,,,,,,,/
,,,,,,,,,,\_/,,,,,,,,,,,,,
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,,,,,,,,,,,,,,,,,,\_,,,,,,
,,,,,,,,,,,,,,,,,,,,\_,,,,/
,,,,,,,,,,,,,,,,,,,,,,\_,,
,,,,,,,,,,,,,,,,,,,,,,,,\_/

Sorry for spamming, but textile is messing this up.

I'll admit to being a primate, and nothing else!

The fact that humans, and primates, do not play perfectly means that the concept of a winning position is almost always diluted. One can throw away a winning position. Initially one might think that game theory has to wash its hands of such situations, but it doesn't have to, as long as you can model the likelyhood of errors being made, so that you can use mixed strategies. With this lack of knowledge (which is behind the imperfect play) I would argue it makes sense to refer to "advantages" most of the time.

But why not all of the time?

If all I have to do to get checkmate is to queen my pawn, do I not have an advantage?
If all I have to do to get a checkmate is to perform 33 moves of bishop-knight check, do I not have an advantage?
If all I have to do to get a checkmate is have Anand at a Houdini console giving me advice with a big grin on his face, do I not have an advantage?

Those are all, in some way "should, as far as we can tell, win from here" positions. Isn't that what "advantage" is?

(Of course, some might also say that once you've got the full game tree (or directed graph), you've no longer got a *game*.)

@Thomas Werner - Take a normal hex board (in particular an LG one) in a paint package, and blank out the lines you want to remove. If you can't find a free hosting site (looks like imageshack works for others), then I can host the image on my website.

And I wouldn't say I was wrong - the gluing operation clearly changes something (namely the connectivity of pieces along the join), otherwise it wouldn't be an operation that needs to be done!

_Those are all, in some way 'should, as far as we can tell, win from here' positions. Isn't that what 'advantage' is?

(Of course, some might also say that once you've got the full game tree (or directed graph), you've no longer got a game.)_

Yes, and they would be right. I don't think we disagree. Maybe the last sentence of my post - "The concept of 'advantage' is rooted in our inability to read the complete tree, not in the game. That's not to say it isn't a valid concept to discuss positions. It certainly is, or Chess commentators would have a hard time" - was somewhat underexposed.

Indeed, I don't think we disagree deep down at all!

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@FatPhil: A text file says more than a thousand images. ;-)

nicely done!

Wow, that's really neat!

Also notice how a Square Hex board is like four Y boards connected together, while a Hex board is two:
http://imageshack.us/a/img11/7101/squarey.png

Also, as a corollary to that, if you cut a Square Hex board along a diagonal, and make what was originally the center square to be a corner, you now have a regular Hex board.

Looks like fun. Reminds me a little of Conhex, which I really like these days.