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Subject: New (?) connection game idea rss

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Gwylim Ashley
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This can be considered as a connection game with a territory aspect. The idea of this game seems quite natural, so I’d be interested to know if it’s been invented before.

Equipment

Any board made of hexagons (for example, a Havannah, Hex, or Y board) which has an odd number of hexagons (this is necessary to ensure no draws). Two different colors of pieces, one for each player.

Play

Players alternate placing a piece of their color on an empty hexagon. The swap rule should be used since the game has a first player advantage (i.e., on the second players first turn, they may choose to swap colors with the first player instead of playing a move).

Winning

A player wins by forming a group which partitions the rest of the board into areas, each of which contains less than half of the hexagons of the board.

Remarks

It is guaranteed that a player will win by the time the board is filled in. Further, the players’ goals are mutually exclusive: it is impossible to have two such groups on the board at once.

The swap rule is essential for boards with order 2 rotational symmetry and a center point; otherwise, there is a trivial winning strategy by playing at the center point and then mirroring the opponent’s moves.

Variants

Some other ideas I've thought about:

1. In determining if a group wins the game, instead of counting all the hexagons in each area, we only count the hexagons in that area which are on the edge of the board, and require that all are less than half of the total hexagons on the edge. In this case, the edge should have an odd number of hexagons to ensure there are no draws. In this variant, the shape of connections does not matter, only which edge points they connect.

2. Playing on a square board. In this case, it is necessary to add a capture rule: when a player surrounds an area less than half of the board size, all the pieces in that area are captured and removed from the board. Without a capture rule, a winner is not guaranteed, unlike in the hexagonal case (for example, consider filling the board with a checkerboard pattern).
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christian freeling
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gwylim wrote:
A player wins by forming a group which partitions the rest of the board into areas, each of which contains less than half of the hexagons of the board.

That's a smart condition! I haven't heard of this concept before, has anyone?
 
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Christian K
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Cool interesting idea. I do worry that a bit much time will be spent counting.
 
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David Bush
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What if a group itself occupied more than half the board, which I suppose could happen only on the last move, "partitioning" the board into a single area which is less than half the board? Would that win the game if nobody has won up to that point?
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Gwylim Ashley
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christianF wrote:
gwylim wrote:
A player wins by forming a group which partitions the rest of the board into areas, each of which contains less than half of the hexagons of the board.

That's a smart condition! I haven't heard of this concept before, has anyone?


Thanks If you haven't heard of it, I guess it's probably a new idea.

Muemmelmann wrote:
Cool interesting idea. I do worry that a bit kuch time will be spent counting.


Yeah, possibly. Though I think it will typically involve less counting than Go, for example (since areas clearly less than half the board don't need to be counted).

twixter wrote:
What if a group itself occupied more than half the board, which I suppose could happen only on the last move, "partitioning" the board into a single area which is less than half the board? Would that win the game if nobody has won up to that point?


Yes, that is the intention. I suppose the language of "partitioning" does not make so much sense in that case, but it seems like an unlikely case anyway.
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David Bush
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gwylim wrote:

twixter wrote:
What if a group itself occupied more than half the board, which I suppose could happen only on the last move, "partitioning" the board into a single area which is less than half the board? Would that win the game if nobody has won up to that point?


Yes, that is the intention. I suppose the language of "partitioning" does not make so much sense in that case, but it seems like an unlikely case anyway.

Okay, thanks. With regard to a square grid, are diagonally adjacent stones of the same color regarded as part of the same group? If so, a checkered pattern on an odd size grid would mean the larger group wins, because this would be the scenario I just asked about, right? And if orthogonal adjacency is required to connect same color stones, then a checkered pattern could not happen, because someone won the game many moves ago, yes? So I don't follow why capturing would be necessary, sorry.
 
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Gwylim Ashley
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twixter wrote:
With regard to a square grid, are diagonally adjacent stones of the same color regarded as part of the same group? If so, a checkered pattern on an odd size grid would mean the larger group wins, because this would be the scenario I just asked about, right? And if orthogonal adjacency is required to connect same color stones, then a checkered pattern could not happen, because someone won the game many moves ago, yes? So I don't follow why capturing would be necessary, sorry.


I am assuming orthogonal connections. In the case of a checkered pattern, there is no single group which partitions the board (each group contains only one stone, so it doesn't partition anything). The basic idea of this game was to create one group which somehow "dominates" the board, and this is the interpretation I came up with.
 
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Gwylim Ashley
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To put it another way, when we determine whether a group is winning, we only look at the pieces belonging to that group, not to all of the pieces of that player. Also, capturing is just a suggestion for resolving the issue; there may be other ways.
 
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Russ Williams
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gwylim wrote:
twixter wrote:
What if a group itself occupied more than half the board, which I suppose could happen only on the last move, "partitioning" the board into a single area which is less than half the board? Would that win the game if nobody has won up to that point?


Yes, that is the intention. I suppose the language of "partitioning" does not make so much sense in that case, but it seems like an unlikely case anyway.

FWIW it's legitimate sensible usage of the mathematical term "partition". A partition does not have to split a set into more than one subset.

For any nonempty set X, P = {X} is a partition of X, called the trivial partition.


(But indeed it could be worth confirming this for clarity in the rules.)
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Cameron Browne
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Hi Gwilym,

gwylim wrote:
A player wins by forming a group which partitions the rest of the board into areas, each of which contains less than half of the hexagons of the board.

I haven't heard of this winning condition before. Nice idea!

gwylim wrote:
1. In determining if a group wins the game, instead of counting all the hexagons in each area, we only count the hexagons in that area which are on the edge of the board, and require that all are less than half of the total hexagons on the edge. In this case, the edge should have an odd number of hexagons to ensure there are no draws. In this variant, the shape of connections does not matter, only which edge points they connect.

This sounds a bit similar to Star and *Star, although in those games group scoring is used to determine the winner.

Regards,
Cameron
 
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Michael Howe
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I like this idea. Have you played it? My only question is whether it adds anything strategically to a game like Hex, which is strategic all over the board and which you generally cannot win with just local tactics. On a Hex board, for example, is the play of your new game stereotyped along the short diagonal? Or does it branch out in strategically interesting ways that are different from Hex?
 
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Steven Meyers
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I'm having some trouble visualizing, but I think this game may have some resemblance to Mark Thompson's Gaia, which was described in Cameron Browne's book on connection games.

Steve
 
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Gwylim Ashley
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Thanks everyone, I appreciate all the feedback.

russ wrote:

For any nonempty set X, P = {X} is a partition of X, called the trivial partition.


(But indeed it could be worth confirming this for clarity in the rules.)


Yeah, actually this is how I would interpret "partition". But I think in normal English it has a different meaning.

camb wrote:

This sounds a bit similar to Star and *Star, although in those games group scoring is used to determine the winner.


Yes, I am familiar with those games, and you could consider them to be the main inspiration. Though this game is won by forming a single global connection, whereas Star and *Star are more local.

mhowe wrote:
I like this idea. Have you played it? My only question is whether it adds anything strategically to a game like Hex, which is strategic all over the board and which you generally cannot win with just local tactics. On a Hex board, for example, is the play of your new game stereotyped along the short diagonal? Or does it branch out in strategically interesting ways that are different from Hex?


I have only played a bit against myself and a computer player. The tactics are similar but not identical to Hex; local patterns which are equivalent in this game are equivalent in Hex, but not vice versa. For example, it's not possible to gain from threatening the bridge pattern in Hex when it is already surrounded by your stones (Example 8 on this page: https://www.hexwiki.net/index.php/Equivalent_patterns#Exampl...). But in this game, it's possible to reduce the size of the opponent's area 1 point by threatening it.

It seems very difficult to defend against a player occupying the center point, even if it is played as the second move. At least this is true on small Havannah-type boards. I haven't actually tried other shapes of boards.

swshogimeyers wrote:
I'm having some trouble visualizing, but I think this game may have some resemblance to Mark Thompson's Gaia, which was described in Cameron Browne's book on connection games.


Yes. It was quite difficult for me to find a description of Gaia on the internet (discussed in https://groups.google.com/d/msg/rec.games.abstract/IJLmQTNaA... for anyone curious), but it seems that Variant 1 (where only edge points are counted) is basically the same game. The only difference is in specifying an odd number of edge points, whereas Gaia has an even number, which requires either allowing draws, or making the game a race (i.e. the players' goals are not mutually exclusive), depending on the precise formulation (Gaia is a race).
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Gwylim Ashley
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gwylim wrote:

swshogimeyers wrote:
I'm having some trouble visualizing, but I think this game may have some resemblance to Mark Thompson's Gaia, which was described in Cameron Browne's book on connection games.


Yes. It was quite difficult for me to find a description of Gaia on the internet (discussed in https://groups.google.com/d/msg/rec.games.abstract/IJLmQTNaA... for anyone curious), but it seems that Variant 1 (where only edge points are counted) is basically the same game. The only difference is in specifying an odd number of edge points, whereas Gaia has an even number, which requires either allowing draws, or making the game a race (i.e. the players' goals are not mutually exclusive), depending on the precise formulation (Gaia is a race).


On further investigation, it seems that the first variant I described is identical to Bill Taylor's Free Y: https://groups.google.com/d/msg/rec.games.abstract/kzWw8FUbG....
 
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Gwylim Ashley
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Oh, so I believe the square version could also be played with Slither rules and still have no draws, if I'm reading the Slither paper correctly (http://www.lamsade.dauphine.fr/~bonnet/publi/slither.pdf).
 
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Luis Bolaños Mures
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I've thought of it before in the following, slightly more generalized form:

Quote:
Wynd is a drawless connection game for two players: Black and White. It's played on the cells of a finite, initially empty hexagonal tiling of any shape. An odd number of cells are marked in a special way and designated as star cells. On a hexhex board, a natural choice is to have seven star cells: the six corner cells and the single central cell.

Black plays first, then turns alternate. On their turn, a player must place a stone of their color on an empy cell. Star cells can be occupied like any other cell.

The game ends when there is a set of connected cells occupied by stones of the same color such that no set of connected cells outside of it includes a majority of star cells. The owner of the stones in the former set wins. Draws are not possible, and a board full of stones produces exactly one winner.

The pie rule is used to make the game fair.

Notes: Designating all perimeter cells plus the center cell as star points yields Gyre. On the Y or Gem-Y boards, designate all corners as star cells to replicate those games. On a slightly irregular hexhex board with sides alternating in length between n and n+1 cells, designate all perimeter cells as star points and you'll be playing Free-Y.

I've played it on the igGameCenter sandbox but never released it. I'm quoting from my notebook.

Center play seemed overly powerful to my taste, but it's probably not enough to break the game.

Also related:

Quote:
Caicus differs from Wynd in the following aspects:

Star points are replaced with movable red pieces. Their number and initial location are agreed upon by the players before the game.

On their turn, before placing a stone of their color on an empty cell, a player may choose to move a red piece in a straight line to an empty cell without going over any other pieces.

Red pieces start the game in an unclaimed state. After a placement, every unclaimed group of one or more connected red pieces without adjacencies to empty cells is claimed by the player with more stones of their color adjacent to it. Any such group with the same number of adjacencies to black and white stones is claimed by the player who didn't make the last placement. Claiming a group of red pieces is indicated by placing a stone of your color on top of each one of the pieces that conform it.

An idea for a variant: Stones are only shot from red pieces, as in Veletas. If all red pieces are claimed and no player has won, two new red pieces are placed on empty cells, one by each player, and the game continues.
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Gwylim Ashley
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luigi87 wrote:
I've thought of it before in the following, slightly more generalized form:

Quote:
Wynd is a drawless connection game for two players: Black and White. It's played on the cells of a finite, initially empty hexagonal tiling of any shape. An odd number of cells are marked in a special way and designated as star cells. On a hexhex board, a natural choice is to have seven star cells: the six corner cells and the single central cell.

Black plays first, then turns alternate. On their turn, a player must place a stone of their color on an empy cell. Star cells can be occupied like any other cell.

The game ends when there is a set of connected cells occupied by stones of the same color such that no set of connected cells outside of it includes a majority of star cells. The owner of the stones in the former set wins. Draws are not possible, and a board full of stones produces exactly one winner.

The pie rule is used to make the game fair.

Notes: Designating all perimeter cells plus the center cell as star points yields Gyre. On the Y or Gem-Y boards, designate all corners as star cells to replicate those games. On a slightly irregular hexhex board with sides alternating in length between n and n+1 cells, designate all perimeter cells as star points and you'll be playing Free-Y.

I've played it on the igGameCenter sandbox but never released it. I'm quoting from my notebook.

Center play seemed overly powerful to my taste, but it's probably not enough to break the game.


I see, thanks. I like how you generalize Y and Gyre as well, it's really quite a neat idea.
 
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Luis Bolaños Mures
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I just remembered: a few months ago, I briefly wrote about this idea in a public forum.
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HU MAN BIN
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christianF wrote:
gwylim wrote:
A player wins by forming a group which partitions the rest of the board into areas, each of which contains less than half of the hexagons of the board.

That's a smart condition! I haven't heard of this concept before, has anyone?


Please can you explain why is it smart condition?
Is it the only condition to be smart? or are there smarter conditions?
Thank you for any useful comment.

 
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christian freeling
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hu man bin wrote:
christianF wrote:
gwylim wrote:
A player wins by forming a group which partitions the rest of the board into areas, each of which contains less than half of the hexagons of the board.

That's a smart condition! I haven't heard of this concept before, has anyone?


Please can you explain why is it smart condition?
Is it the only condition to be smart? or are there smarter conditions?
Thank you for any useful comment.


You can easily make a partition into a small and a large area. The winning condition requires you to do something considerably more difficult, especially against equal opposition. I consider that smart. It is not the only smart condition and the increasing stage does so far as my comment is concerned not apply.
 
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Gwylim Ashley
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hu man bin wrote:

Please can you explain why is it smart condition?


The basic idea is "build a group which partitions the board somehow". But there may ways of making this precise, and in general, there may be many groups on the board which partition it somehow. The "trick" in this case, is requiring that all other areas of the board have less that half the total hexagons (or the "star cells", in Luis's generalization): this ensures that only one group can satisfy the condition. In a way, it seems like the "most natural" choice of rule for this type of game, which we see in the fact that it's already been thought of independently.

hu man bin wrote:

Is it the only condition to be smart? or are there smarter conditions?


Of course it's not the only such condition. What is a smart condition is anyway subjective, and is not sufficient for a fun game. So far I haven't seen any reason to want to play this game rather than Hex.
 
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HU MAN BIN
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christianF wrote:
hu man bin wrote:
christianF wrote:
gwylim wrote:
A player wins by forming a group which partitions the rest of the board into areas, each of which contains less than half of the hexagons of the board.

That's a smart condition! I haven't heard of this concept before, has anyone?


Please can you explain why is it smart condition?
Is it the only condition to be smart? or are there smarter conditions?
Thank you for any useful comment.


You can easily make a partition into a small and a large area. The winning condition requires you to do something considerably more difficult, especially against equal opposition. I consider that smart. It is not the only smart condition and the increasing stage does so far as my comment is concerned not apply.


Making the game difficult for the players does NOT mean that is smart condition. I do not understand why are you calling it smart. Making things easier is smart only if making them easier is very hard. Otherwise you are just making things complex and that`s it.
Is the condition of connecting sides to win a hex game smart or not?
For sure it is very smart.
The big problem of hex variants is not how to play it in a squared grid. When I see the number of tries to play it on a squared grid I laugh loudly.
I hope that you understood my comments.
The most difficult for a game designer is to make rules simple and to focus on the game play.
A funnier game play does not mean dumb game.
Look at Luis he posted dozens of connection games not one is funny!!!
Slither is not funny! Many games Christian Freeling produces not one is funny.

 
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HU MAN BIN
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I will add this.
If you create any variant of any game be sure that the variant will lead to a really new game.
A strong Go player as long as he can be strong playing a variant of Go then this variant is nothing more than a Go game.
But if the variant of Go is really a new game then all what this expert know will worth zero.
Take an expert player of Hex game for example. If he plays a variant of Hex game on squared grid will be need to change his way of playing? no.
So creating a variant on squared grid will worth zero. Waste of time.
When I create "one for you one for me " a hex variant, I create a new game. Why?
Because all what an expert player knows about Hex will not give him an advantage.
You add new rule and you change drastically the game play.


 
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