Hex played on a square grid...?

Would the idea of hex played on a square grid work? Does it already exist as a known game?

There are several closely related games which could be regarded as Hex on a square grid, for example Crossway.  It's on Boardgamegeek and iggamecenter.com. I think there's another called Quax.

You can play slither at this site, it is a connection game on a square grid

I played Crossway at superdupergames, but I think there is a learning curve quite separate from Hex. The rule that only the first diagonal connection works leads to a sense of shifting board geometry.

Or check out this geeklist:

https://boardgamegeek.com/geeklist/57850/

If you just want to use squares to make the board, you could play Hex on a tessellation of squares by offsetting them 50%, which is then functionally identical to a hex board. Personally I'd prefer representing the cells as circles or triangles.

http://www-cs-students.stanford.edu/~amitp/game-programming/grids/#derivation

Yes, any game with just one significant rules difference is unlikely to have the same learning curve as the original, as far as i know. Crossway is much faster and more brutal than Hex. It feels more like Twixt in that respect. The basic problem of adapting Hex to a square grid is the ambiguity of diagonally adjacent tokens of the same color. Are they connected or not? Until this question is answered, it's not clear what "Hex on a square grid" even means. piqo, if you mean to keep the rules of Hex but play on a square grid, you could say for example that NW to SE adjacent diagonals are connections, while SW to NE diagonals never are. Some early boards by Piet Hein did this, when Hex was called Con~Tac~Tix. Hein switched to hexagons, I believe, because the position is much easier to read this way. But if you want to change the rules so that both NE~ SW and SE ~ NW might connect, this must change the nature of the game fundamentally. If both ways are allowed to be connections across the same intersection, that would be more like a race than a blocking game, which does not seem particularly interesting. The Crossway solution is to forbid anywhere on the board a 2x2 group of four stones where two white stones are diagonally adjacent one way, and two black stones are diagonally adjacent the other way. This means some vacant cells may be forbidden to white, and some may be forbidden to black. The Quax solution, as I understand it, is to allow any pattern, but if you wish to claim a particular diagonal, you must spend a move to do so. It's as if there were an additional grid of cells superimposed on the square grid, for all the adjacent diagonals, and you may play on a diagonal cell only if you have two diagonally adjacent tokens of your color in the main grid which correspond to this diagonal cell. I have never played Quax. Doubtless there are other ways to resolve diagonal adjacency.

Tom Stoppard's play After Magritte opens with an entertaining sequence set in a room with two items suspended from the ceiling, one of which is the standard bulb and lampshade, and the other a basket of fruit.  It is not initially apparent to the audience, but soon becomes so, that the two are in fact counterweights to each other via an unseen system of pulleys.  As the curtain rises, a man is preparing to change the lightbulb, which has blown.  Naturally enough, his removal of the bulb causes the basket of fruit to begin descending.  Noticing this, he removes an apple from the basket, but now the lampshade starts coming down instead.  He therefore takes a bite out of the apple and calmly replaces it, whereupon equilibrium is restored.

From a standpoint of more or less total ignorance, I had always assumed that the thought process which led Corey Clark to the invention of Slither was more or less analogous to this.  A transfer of Hex to the square grid would yield insufficient connectivity unless diagonal connections were permitted - but that would yield too much.  So a mechanism had to be found which reduced the diagonal connectivity without removing it altogether.  Et voilà.

Thank you all for replying! I will try all of these games.

Do you think the solution to the problem of both players potentially winning and making the game a race could be resolved by making both players have to only be able to connect orthogonally?

I hope that sentence made sense.

Thanks,

Piqo

Gonnect by João Pedro Neto is a very interesting connection game on a square grid — Go rules with the objective to be the first to connect any two opposite sides.

If only orthogonal connections are allowed, then any cell has at most four direct connections to other cells. Either player could force a draw. Imagine any two adjacent rows across the board left to right are regarded as a row of dominoes which are aligned vertically. The player connecting left to right can block the opponent with the simple strategy that whenever the opponent plays in one cell of a domino, respond by playing in the other cell of that domino. The player trying to connect top to bottom can never break this simple blockade, and he can do the same trick as well, so best play will always result in a draw.

True, I didn't think of that...

The question that pops into my head is - WHY?

Hex played on hexagons is just so... perfect! Why try to substitute beautiful hexagons with inferior squares?

Precisely Marius.

Their eyes have been distorted by many years of playing Chess or Go, that's why.

It's not that square grid connection games are attempting to improve upon or replace Hex; rather, they offer strategy and tactics which are interesting in their own right. I personally love the massive variety of square connection games which has emerged from various attempts to "orthogonalize" hex.

Seven neighbors is better than only six provided by hex grids, any connection game on an hyperbolic plane where each cell have seven neighbors?

I don't know about a hyperbolic plane, but my variant Pex is based on one of the 14 known tilings of the Euclidean plane by congruent convex pentagons. Half the interior cells are adjacent to five neighbors, and half are adjacent to seven. It's on iggamecenter and Boardgamegeek.

No ypercube, my eyes haven't been distorted by chess or go. I HIGHLY prefer hexagons over squares. On the contrary, I've been trying to hexagonalize chess, not orthogonalize hex. Also, I'm only 14, so I haven't really been around long enough to have had my eyes 'distorted' by chess.

I was just curious. :p

I was just curious. :p

Why did that write twice?

If there is anything better than board made of hexagones, I'm sure Nashcertainlywould havediscovered it :) Maybe I'm old-fashioned, but I agree with Florian. Why we looking for variants ifthere is stillso muchto discover in hex :) Nevertheless, it isnice toread visionarythoughts here ;)

A useful rule (though apt to vex) is"Movement, squares; and placement, hexes".

We'll try that again, since it's kind of important in a poem....

A useful rule (though apt to vex) is

"Movement, squares; and placement, hexes".

The "why explore other games in [genre X]? The game [prototypical genre X game] is good already" statement has always puzzled me. After all, isn't having more interesting games to choose from strictly better than having less such games? If one assumes every territory game is a worse Go, every checkmate game is a worse Chess, every race game is a worse Breakthrough, and every connection game is a worse Hex, then one misses out on thousands of fascinating modern abstracts.

I'm surprised no one has mentioned a well-established connection game based on a square grid: Twixt.

There is a variation of Twixt (I call it X; see below for the reason) which I think answers the original question.  In Twixt, each point/hole/cell is connected to eight others according to (2,1) (1,2) (-1,2) (-2,1) (-2,-1) (-1,-2) (1,-2) (2,-1); in other words, all cells which are a knight's move away.  In X, we replace this connection pattern with the simpler (1,0) (1,1) (0,1) (-1,1) (-1,0) (-1,-1) (0,-1) (1,-1); in other words, all cells which are adjacent either horizontally, vertically or diagonally.  As in Twixt, connections in X don't happen if your opponent already has a connection link blocking your potential link.  (Perhaps others have thought of this game independently; it's kind of an obvious idea once you know Twixt.)

Another way to think of X is that it is Hex on a square grid, but diagonal connections between squares happen only if your opponent has not already claimed the orthogonal diagonal.  For example, if the order of play is

1243

on this very small board, the 1 and 3 are connected for the first player, but 2 and 4 are not connection for the second player, because they are blocked by the earlier 1-3 connection.

It is easy to play X with graph paper and pens of two different colors.  I prefer to play it "Twixt style" (moves go on grid points (like Go), color in all possible links after making a move) rather than "Hex style" (color in the squares, plus a little bit of a diagonal connection if you got there first).  If you play it "Twixt PP style" and allow links to cross if they are the same color, then the board is sometimes covered with "X"s -- hence the name "X".  (By the way, the PP and non-PP variants are identical, except for the appearance of the board.)

I played X in the mid 1980's, and it seemed like an interesting, viable game.  (I was actually playing a torus version, but of course the local tactics are the same as in the connect-opposite-sides version.)

In case it's not obvious: ties are not possible in X, and moves cannot hurt you, so the first player has a winning strategy.

Oops, my board got mangled and I don'e see a way to delete or edit.  It should be

12

43

Isn't that the same as Crossway?

And yep, I think every connection game enthusiast has "invented" this game independently before already (I did as well).

@DavidStoner: I think the reasoning is as follows. Let's say we have a really great game of genre X. If we slightly modify the rules, inventing variants and the like, we might get a new game that is still very good because it is based on the original great game. But at some point, for games that are too similar to each other, we might want to play the worthier variant.

Of course if the modifications change the strategy in a fundamental way, we could as well stop considering the variant as a variant, rather as an independent game.

There is a reason for Hex being considered as the greatest, purest connection game.

If we compare Crossway and TwixT for example, they are essentially the same game, only a different connection pattern. However, in my opinion TwixT's strategy offers far more than Crossway, that's why I prefer TwixT

Crossway differs from X. X never forbids playing in certain cells. X is like Quax and Twixt in that it uses an additional grid, the grid of diagonal connections, which is superimposed on the main grid. So it could be argued that none of these three games are really played on a square grid. But Crossway is.

Are there actually positions where this mechanics makes a difference in respect to win/loss?

Absolutely. If you are forbidden from playing in a cell, you cannot use that cell to connect in a different direction. Here's a contrived example on a 3x3 grid. V's goal is to connect top to bottom.

• HVH
  
• ##V
  
• V#H
  

# means vacant. In X, H to move could win playing in the center cell. In Crossway, H is forbidden to play there, and cannot stop V from playing there and winning on the next move.

That's true, thanks. :)

It's just that positions like that never occured when I played either of the games..

I think overall the games are still pretty similar, especially on larger grids and optimal play.

(wrong account, sorry)

Richard: amusing poem!

(But arguably only applicable to abtract strategy games, as hexes have proven more suitable than squares for wargames.) :)

Piqo: besides Slither (playable here at littlegolem), some other good square connection games worth checking out are by Luis Bolaños Mures:

https://www.boardgamegeek.com/boardgame/123213/konobi

https://www.boardgamegeek.com/boardgame/144342/kopano

https://www.boardgamegeek.com/boardgame/124095/quentin

https://www.boardgamegeek.com/boardgame/130222/vimbre

All such games indeed need to somehow address the issue of diagonal connection which arises on a square grid but not a hex grid.

*And* (just a personal vendetta)

"Placement, fair; but movement, better".

X appears to me to be functionally identical to Quax. Two cells orthogonally adjacent are just as good as connected; no need to waste a move to connect them, meaning the only "important" connection moves would be to connect diagonally, which is equivalent to playing on a square in Quax. And while in Quax, you can play a square before playing any adjacent octagons, which at first glance appears to make that game distinct, it is always a suboptimal move to do so instead of one of the bordering octagons.