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Subject: Square grid connection game? rss

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Jared Hayter

Metuchen
New Jersey
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Is there an obvious reason why connection games like Hex don't work on a square grid? Is there in fact a square analog to Hex of which I am unaware? Thanks for the info.
 
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Nate Straight

Covington
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Twixt is a connection game with a square grid, though it's played a bit different. The differences in gameplay with a square grid connection game are pretty much required, though, as a game played on a square grid by Hex's rules would almost surely end in a draw every time. The charm, and tension, of Hex is that there is no possibility of a draw, but that depends on the topography of the hex-grid.
 
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David Bush
United States
Lexington
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The essential problem with a square grid, as opposed to a grid of hexagons, is that when four squares meet at a single point, there is some ambiguity about whether diagonally adjacent squares are adjacent for the purpose of the game or not. If your path and the opponent's path are allowed to cross each other at such a point and continue on their merry way, the blocking nature of the game is lost. Twixt is perhaps one solution to this dilemma, albeit a rather circuitous one. There are quite a few other connection games that work on a square grid or something close to one. Some are three dimensional, with the idea that the top piece determines who "wins the intersection." Akron and Druid are both implemented on the server at www.gamerz.net which has a GUI for both those games.

There is also "Square Hex," so called because the overall shape of the grid is square, although nowhere are more than three cells adjacent at the same point. You can see a picture of that and other Hex variants at http://www.geocities.com/twixtplayer/hexvar2.html
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Russ Williams
Poland
Wrocław
Dolny Śląsk
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What twixter said. Hex grids have connections only through sides, square grids have troublesome ambiguous corner connections. This is also part of why many wargames use a hex grid instead of square grid.

If you say that connections are only through sides, not corners, then Hex on a square grid can easily end in a draw. If you say that connections also work diagonally, then blocking becomes much harder.

There are various square grid connection games that have additional rules tacked on to deal with the corner connection problem. (E.g. a move can be claiming a corner to work only for you.) The book Connection Games is a good resource for such things.
 
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David Bush
United States
Lexington
Virginia
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I should mention that the book Connection Games, as well as the games Akron and Druid and a host of others, are all authored by the same person, Cameron Browne. He's a very prolific games programmer, and he adds another game to the list available on the Gamerz server (see the above link) about once or more every month it seems. Many of those games get implemented on the Gamerz GUI. Even if you don't like to play turn-based, you might enjoy looking at the graphic display for various games in progress. Here's a link for an Akron game which is just starting at the time I post this. Eventually the game will end and the link won't work anymore:

http://www.gamerz.net/pbmserv/Akron/Akron.php?379&html
 
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David Bush
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Lexington
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I just discovered, on the Gamerz server, a connection game on a square grid which might be what you are looking for: Crossway. The rules are at http://www.gamerz.net/pbmserv/crossway.html This one is by Mark Steere, another prolific inventor.
 
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Jared Hayter

Metuchen
New Jersey
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Interesting although the no checkerboard rule feels forced. I wonder how it would be different to just say that no line can cross another.
 
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David Bush
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Well how would what be different? It sounds like two different ways of saying the exact same thing, although your way sounds more confusing. Could you provide an example position where some move would be legal according to your variation and illegal in the standard game, or vice versa?

 
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Harald Korneliussen
Norway
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jaredhayter wrote:
Interesting although the no checkerboard rule feels forced. I wonder how it would be different to just say that no line can cross another.

If you think so, perhaps you'll prefer Bill Taylor's Quadrex. It's identical to Crossway, except when a checkerboard pattern threatens to form (three pieces are in place) the fourth is automatically filled with the color that prevents the checkerboard. Diagonal connections aren't necessary in this game.
 
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David Bush
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Lexington
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vintermann wrote:
jaredhayter wrote:
Interesting although the no checkerboard rule feels forced. I wonder how it would be different to just say that no line can cross another.

If you think so, perhaps you'll prefer Bill Taylor's Quadrex. It's identical to Crossway, except when a checkerboard pattern threatens to form (three pieces are in place) the fourth is automatically filled with the color that prevents the checkerboard. Diagonal connections aren't necessary in this game.

That raises some questions as well.



First of all, can cascade placements happen? If a black stone were placed at A in the above image, would that result in four more black stones automatically added beneath it?



Secondly, just to be clear, if a black stone were placed at A, would a white stone automatically be placed at B?

I also wonder which of these games was invented first.
 
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Harald Korneliussen
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Yes, cascades must be allowed, otherwise deadlocks can occur, as far as I can see. Crossway was invented in June 2007. Looks like Quadrex was a month earlier at least, since it was on Rognlie's play-by-email server from May.

I wonder what a Go variant with the Quadrex completion rule would feel like.
 
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Nick Bentley
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Madison
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Another square grid connection game, which solves the problem in a completely different way, is Gonnect. Perhaps more impure than you're looking for since it involves a capture rule, but since some consider it one of the best modern abstract games, I thought it worth mentioning.

It's a straight up combination of Hex and Go, and it preserves tactics and strategies from both, which is rather amazing in my opinion.

Although people are prone to calling Go a perfect game, I get annoyed at its kludgy endgame and scoring rules (don't shoot me!). Gonnect fixes it. Because it's a deep abstract it might never catch on, but it really deserves to.
 
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Virginia Milne
New Zealand
Auckland
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Talking about a Go variant of a square grid connection game. There is one. It is called Gonnect. The rules are very similar to Go, but you win by connecting any pair of opposite sides with your pieces of your colour. One big difference from Go is that you cannot pass. Eventually if you run out of moves you have to fill in your eyes and you lose your group. If you cannot move you also lose. These mechanisms overcome the square grid impass problem.

As people experiment they are finding more and more ways of playing connecting games on a square grid. But none of them quite equal hex for simplicity of rules.
 
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Mark Steere
United States
Palo Alto
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twixter wrote:
I just discovered, on the Gamerz server, a connection game on a square grid which might be what you are looking for: Crossway. The rules are at http://www.gamerz.net/pbmserv/crossway.html This one is by Mark Steere, another prolific inventor.

Good to see that David Bush, Twixt player extraordinaire, has discovered Crossway.

Jared, what you call forced I call technically specific. The goal is to preclude any possibility of misinterpretation. Just saying lines can't cross doesn't cut it, not by a long shot.

When I designed/invented/discovered Crossway I went to announce it on rec.games.abstract as an adaptation of Hex to a Go board and what did I see? An announcement of Hex adapted to a Go board from Bill Taylor from, if I recall, a day or two earlier. That sucked. Fortunately I discovered that Bill missed the mark (IMO - sorry Bill) with Quadrex and his other two attempts to adapt Hex to a Go board. The automatic chain reaction mechanism isn't real Hex-like. Crossway is and will remain the only true adaptation of Hex to a Go board. It's not as simple as Hex but it's as close as you're ever going to get on a square grid. No game design is as elegant as Hex, but Crossway arguably has a richer gameplay. There are 8 directions of connectivity instead of just 6 which facilitates more tactical possibilities.

Nick, Go is a total kludge. It's based on a simple, fundamental mechanism so it has to exist and it has to be ancient, but it's a kludge. They call Go a "minute to learn" game... lol. Of course there's the Tromp-Taylor rule set for finishing Go, but according to the authors, using only the core rule set will lead to inconvenience and impatience when played on a real board. The recommended, extended rule set is incomprehensible, at least to me. There's no easy way out here, except perhaps single capture Go. I'd rather play Go as it is though, with all of its faults, than a neat and tidy Go variant.

Go is not the perfect game. Tanbo is the perfect game.

-Mark
 
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Nick Bentley
United States
Madison
Wisconsin
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Agreed that crossway is as close as any game will ever come to square-grid Hex.
 
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Gregorio Morales
Spain
Alicante
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Gonnect,http://homepages.di.fc.ul.pt/~jpn/gv/gonnect.htm, by João Pedro Neto, is a very interesting connecion game in a square grid. Basically, it's like Hex, but allowing Go captures. I like Hex very much, and I still think Hex is better than gonnect, but Gonnect is quite funny and challenging too.

have fun!

P.S. I think Gonnect is in PbeM Server too...
 
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Benedikt Rosenau
Germany
Göttingen
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Quax is a connection game on a square grid. Maybe Quax is Quadrex, but it is not Quadrex as described.

The problem with straightforward implementations of Hex-like games on a square grid comes from crosscuts (Go term). Crossway just forbids these, whereas Quax does not see crosscuts as a connection, instead it demands creating a special connection that by definition prevents the other player from connecting the crosscut. These connections cost a move.
 
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