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Subject: Connection games with capture? rss

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Michael Howe
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Yet another longwinded debate about semantics. You guys are good at this.
 
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Rex Moore
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mhowe wrote:
Yet another longwinded debate about semantics. You guys are good at this.

Define "longwinded."
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Nathan James
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Heisenberg is connection with capture ... plus redeployment of the captured pieces.

Maybe that's even more semantic trouble?
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David Bush
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russ wrote:
VirginiaMilne wrote:
In Conhex you can capture a region by gaining more than half the corners for that region :)

At least it feels like capture to me :D
And similarly in Hex you can "capture" a hex by placing a stone in it, and in Tic-Tac-Toe you "capture" a square by drawing your symbol in it...

These examples do not really meet any plausible definition of "capture" for me. :)

(It seems to turn pretty much every game with locations which can be occupied into a "capture game".)
In ConHex, claiming a region is a cascade effect, which differs from directly claiming a single cell in Hex.
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Russ Williams
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twixter wrote:
russ wrote:
VirginiaMilne wrote:
In Conhex you can capture a region by gaining more than half the corners for that region

At least it feels like capture to me
And similarly in Hex you can "capture" a hex by placing a stone in it, and in Tic-Tac-Toe you "capture" a square by drawing your symbol in it...

These examples do not really meet any plausible definition of "capture" for me.

(It seems to turn pretty much every game with locations which can be occupied into a "capture game".)
In ConHex, claiming a region is a cascade effect, which differs from directly claiming a single cell in Hex.
Yes... and? Since when is being a cascade effect rather than a direct single action part of what "capturing" is about?

Are you saying that it being a cascade effect somehow makes it more of a "capture"?

And so "capturing" a space on the board in ConHex is more of a "capture" than removing a group in Go or a piece in Chess, because there's not cascade effect when you remove pieces in Go and Chess, but single immediate actions?

I feel like I've entered the Twilight Zone in this thread.
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David Bush
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russ wrote:
twixter wrote:
russ wrote:
VirginiaMilne wrote:
In Conhex you can capture a region by gaining more than half the corners for that region

At least it feels like capture to me
And similarly in Hex you can "capture" a hex by placing a stone in it, and in Tic-Tac-Toe you "capture" a square by drawing your symbol in it...

These examples do not really meet any plausible definition of "capture" for me.

(It seems to turn pretty much every game with locations which can be occupied into a "capture game".)
In ConHex, claiming a region is a cascade effect, which differs from directly claiming a single cell in Hex.
Yes... and? Since when is being a cascade effect rather than a direct single action part of what "capturing" is about?

Are you saying that it being a cascade effect somehow makes it more of a "capture"?

And so "capturing" a space on the board in ConHex is more of a "capture" than removing a group in Go or a piece in Chess, because there's not cascade effect when you remove pieces in Go and Chess, but single immediate actions?

I feel like I've entered the Twilight Zone in this thread.
More of a capture? Who is saying this? Seems to me you are entering this Twilight Zone all by yourself. Remember how this particular discussion started. Stephen Tavener said:
"Depends on your definition of capture, but ConHex may qualify."
So. my remark pertains to this statement. It depends on your definition of capture. Maybe the indirect nature of claiming a region makes it seem like a capture. Maybe it doesn't. It's entirely your call.
 
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Russ Williams
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twixter wrote:
More of a capture? Who is saying this?
You seemed to be suggesting it as justification why ConHex is a game with capture; otherwise I'm utterly confused why you mentioned it. I honestly have no idea what you were getting at now, if you don't think it's relevant to whether ConHex is a game with capture.

Quote:
So. my remark pertains to this statement. It depends on your definition of capture. Maybe the indirect nature of claiming a region makes it seem like a capture. Maybe it doesn't. It's entirely your call.

OK... Color me confused. It seems about as relevant as noting that ConHex is a 2-syllable title and Hex is a 1-syllable title... Evidently I'm missing something.

That people are considering merely placing pieces onto empty spaces, without removing anything at all, to be an attribute of capturing games still feels like the Twilight Zone to me. Is Tic-Tac-Toe a capturing game? Is the point here that "capture" means whatever an individual wants it to mean?
 
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christian freeling
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Did Russia 'capture' Crimea or 'occupy' it. In real live you can capture territory, but in say Go 'capture' means capturing stones, not occupying territory (or every placement would be a capture). So different definitions seem possible without crossing into the Twilight Zone.

For me it's easier to see a spectrum of interpretations than to choose one. As I've mentioned her recently somewhere, vagueness is what keeps threads going.
Hail Vagueness!
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Keeping the semantic debate going:

Do you ‘capture’ enemy marbles in Abalone Classic when you push them away from you and out of the board?
(Missing a “tongue in cheek” emoticon here)
 
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christianF wrote:

Did Russia 'capture' Crimea or 'occupy' it. In real live you can capture territory, but in say Go 'capture' means capturing stones, not occupying territory (or every placement would be a capture). So different definitions seem possible without crossing into the Twilight Zone.

For me it's easier to see a spectrum of interpretations than to choose one. As I've mentioned her recently somewhere, vagueness is what keeps threads going.
Hail Vagueness!
OK, I give up. In Tic-Tac-Toe, players are evidently capturing squares on the board, and so it's a game with capture, like pretty much all games. E.g. in Bridge we capture tricks, in Poker we capture money. Every game is a capture game.

So the correct answer to Craig's original question is "Duh, Craig -- of course there are connection games with capture! Every game has capture!"
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Craig Duncan
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russ wrote:

So yeah, I guess Craig needs to clarify what he meant by "capture".
An interesting discussion. At the time of my original posting, I did have in mind capture in the sense of removing-an-opponent-piece.

But, I've no linguistic objection to referring to several other types of disadvantaging one's opponent as "capture."

I suppose that on reflection I'd say there are numerous cases in which the word "capture" is not an abuse of English. Perhaps we could offer a vector analysis:

<[removal, immobilization, conversion], [permanent, impermanent], [playing piece, territory]>

I'm sure that's got problems but it's my seat-of-the-pants attempt to characterize several possible types of capture. I don't claim it's exhaustive of all types.

So...

Chess capture = <removal, permanent, playing piece>

Othello capture = <conversion, impermanent, playing piece> (impermanent, because captured Othello pieces can sometimes be converted back)

Bashni (stacking checkers) capture = <immobilization, impermanent, playing piece> (yes, it a captured piece can be moved by the capturer, as part of the stack; maybe "deactivated" or "neutralized" is better than "immobilized," I don't know)

ConHex capture = <conversion, permanent, territory> (well, you convert the territory color from neutral to your color, so "conversion" kinda sorta works here.

Shogi capture = <conversion, impermanent, playing piece> (impermanent because a re-entered piece can be captured and converted back to its original side)


 
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christian freeling
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russ wrote:
christianF wrote:

Did Russia 'capture' Crimea or 'occupy' it. In real live you can capture territory, but in say Go 'capture' means capturing stones, not occupying territory (or every placement would be a capture). So different definitions seem possible without crossing into the Twilight Zone.

For me it's easier to see a spectrum of interpretations than to choose one. As I've mentioned her recently somewhere, vagueness is what keeps threads going.
Hail Vagueness!
OK, I give up. In Tic-Tac-Toe, players are evidently capturing squares on the board, and so it's a game with capture, like pretty much all games. E.g. in Bridge we capture tricks, in Poker we capture money. Every game is a capture game.

So the correct answer to Craig's original question is "Duh, Craig -- of course there are connection games with capture! Every game has capture!"
Ok Ok, I'm just pointing out that people in the world of games and in the real world may not interpret 'capture' the same way. And not in the first in itself either. I think agreements should be made a priori, because indeed, does Abalone feature capture, or Emergo (goal: capture all opponent's pieces!) or Shogi or Momentum? A general definition covering them all (and probably many more) would seem impossible.
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Richard Moxham
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I think a mainstream definition of capture would be that something (and it might be either material or territory) which belonged to your opponent at the start of your move doesn't belong to him any longer at the end of it.

Outside of that ... well, you can if it pleases you call a chair a table without breaking the law of the land, but most people are under the impression that discouraging that approach to language is the reason we have dictionaries.
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Brian Svoboda
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Near the end of Cameron Browne's book "Connection Games" there's game idea called "Hamilton" I think that has a connection winning condition but a Chess-style capture. A player places a piece, then can in turn move to capture adjacent pieces, tracing out a Hamiltonian Path[1]. He notes that the idea is interesting, but that it was rather broken and that he couldn't work it into a functioning game. There may be other examples from Connection Games that have connection as their goal but also include Chess-style capture mechanics. I haven't read the book in full myself.

[1] https://en.wikipedia.org/wiki/Hamiltonian_path
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Back to the list of games, Onyx should qualify (without too much of a stretch in the definition of a capture meeple).
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eobllor wrote:
Back to the list of games, Onyx should qualify (without too much of a stretch in the definition of a capture meeple).
Uh-oh, its description says "It is unique from other connection games by having a capture rule." So in fact Onyx is the only connection game with capture, and there are no others. The situation is becoming ever more complicated and confusing.
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christian freeling
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russ wrote:
eobllor wrote:
Back to the list of games, Onyx should qualify (without too much of a stretch in the definition of a capture meeple).
Uh-oh, its description says "It is unique from other connection games by having a capture rule." So in fact Onyx is the only connection game with capture, and there are no others. The situation is becoming ever more complicated and confusing.
I guess this was meant in jest, at least if we agree that LOA and Inertia are connection games. They both feature pure, undiluted and undisputed capture.
 
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Craig Duncan
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Thanks to everyone who named a game with capture, or a game with at least kinda sorta capture!

I believe I've peeked at the rules to all the suggested games, and unless I have missed it, I don't see a game with a capturing mechanism involving movement, e.g. where the capturing piece moves and thereby captures an opponent piece via displacement (with the captured piece being removed).

Below is a possible rule set for one such game -- though as of now it is almost completely untested. I'll have to playtest it adequately when I find some spare time.

-------------------------------------------------------

TRACTOR

Played on the intersections of a square grid with two opposite sides labeled white and two opposite sides labeled black. The board starts empty.

On his turn, a player has two actions, as below (and in the order below). Exception: on turn 1, Player 1 gets no second action.

1. Placement

A player places a stone a stone on an empty point, subject to the following rule: a stone cannot be placed on a point if that point belongs to a square whose three other corners are already occupied (by stones of any color).

2. Placement or movement

For a player's second action, he may PLACE a second stone according to the same rule above, or MOVE a stone that was placed in a previous turn (i.e. he may NOT move the stone that was placed in action 1 of the current turn). Movement occurs according to the movement rule below.

Tractor beam movement: a stone may slide along an empty line of points provided it comes to rest adjacent to a friendly stone that lies in the line of movement. (The friendly stone "pulls" the moving stone toward it until the stones are adjacent.) An exception = "squish capture": if the line between the pulling stone and the moving stone contains (i) an enemy stone adjacent to the pulling stone, and (ii) at least one empty point, then the moving stone displaces the enemy stone, which is then removed from the board. (The empty point is needed to give the moving stone space to initiate its motion.)

Passing is not allowed, i.e. a player must perform as many of his allotted two actions as is legally allowed. By contrast, if no legal placements or movements are possible at the time of an action, then that action is forfeited.

Victory:
A player wins by creating a group of orthogonally-adjacent stones that connect his two sides.

-------------------------------------------------------


Examples

In the diagram below, no stone can be placed at the point marked with "," since this would be the fourth occupied corner of a square.

O
.__.__.__.__.
| | | | |
.__.__x__o__.
X | | | | | X
.__.__,__x__.
| | | | |
.__.__.__.__.

O


Note that each point is typically a corner in more than one square. E.g. the "," point above is a corner in four different squares (to the NE, NW, SE, and SW). If any of the squares for which a point is a corner has three corners occupied, then placement on that fourth corner is illegal.

Note too that this placement rule prevents the dreaded square grid deadlock from arising via the "cross-cut" pattern. E.g. this can't happen by placement:

O
.__.__o__.__.
| | | | |
.__.__o__x__x
X | | | | | X
x__x__x__o__.
| | | | |
.__.__.__o__.

O


Note that the "can't place a fourth corner" rule doesn't just prevent the cross-cut pattern from arising, but other types too:

For instance, if there is...

x__O
| |
,__x


...then neither the o player nor the x player can place a stone at the cell marked ",".

Also, not even the x player can play at the "," cell below:

x__x
| |
,__x


Thus, the only way the fourth corner of a square can be occupied is via moving into that position. And note that the tractor-beam movement rule prevents the cross-cut position from being created by movement.

Below is an example of movement. The x stone on the far left can slide to the "," spot, being pulled by the x stone in that line.

O O
.__.__.__.__. .__.__.__.__.
| | | | | | | | | |
.__.__o__o__. .__.__o__o__.
X | | | | | X --> X | | | | | X
x__.__,__x__x .__.__x__x__x
| | | | | | | | | |
.__.__o__.__. .__.__o__.__.

O O


If there is an o stone where the comma is, then the leftmost x stone can slide and capture the o stone, as below:

O O
.__.__.__.__. .__.__.__.__.
| | | | | | | | | |
.__.__o__o__. .__.__o__o__.
X | | | | | X --> X | | | | | X
x__.__o__x__x .__.__x__x__x
| | | | | | | | | |
.__.__o__.__. .__.__o__.__.

O O


Note, though, that in the alternative board below the leftmost x below CANNOT capture the sandwiched o stone, since there is no empty space for the "run up" to a "squish."

O
.__.__.__.__.
| | | | |
.__.__o__o__.
X | | | | | X
.__x__o__x__x
| | | | |
.__.__o__.__.

O


OK, that is the idea of the game.

Barely playtested, as noted above. And there is likely some flaw, but it seems to me a potentially interesting base from which to explore. I'm not sure deadlocks are impossible. They probably are possible, but my hope is that they'd be rare enough to produce a tolerable draw rate.

E.g. perhaps new deadlock positions are created by the rules above. Or perhaps the rules will lead to seki situations where neither player wants to place or move, and the game goes "cold" as players tediously fill the remaining squares until one player is forced to play into the seki.

That said, tweaks are still possible, so maybe emerging problems will prove to be fixable. E.g. one can imagine a more permissive capture rule which does not require a run-up. (Such a rule would permit x to capture in the final board above, for instance.) Or one can imagine a more permissive capture rule that does require a run-up but that allows a moving stone to scoot a single enemy stone along with it and squish it against a pulling stone (i.e. the captured stone needn't start out adjacent to the pulling stone).

Food for thought...
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Craig Duncan
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Rats. Here's a possible deadlocked board in the game of Tractor, the rules to which are explained in the previous post:

O
.__.__.__o__o__.__.
| | | | | | |
.__x__x__o__o__.__.
| | | | | | |
x__x__x__o__o__.__.
X | | | | | | | X
x__x__,__o__o__.__.
| | | | | | |
.__o__o__x__x__x__x
| | | | | | |
.__o__o__x__x__x__x
| | | | | | |
.__o__o__.__.__.__.

O


There's no way to get a stone in the "," space, consistent with the rules above. The double walls prevent captures of the pieces already on the board.

That said, I think it would take some deliberate conspiring between both players to produce this configuration in a real game. So I'd be surprised if this were to arise in practice.

Still, if the sine qua non of connection games is that they be drawless even in theory, this ain't that.
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Craig Duncan
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Here's a simple idea for capture in a square grid connection game -- sort of a simplified version of Luis's Brique. (I wouldn't be surprised if Luis has already tried out this idea and found it wanting for some reason!)

------------------------------

PINCH

Played on the intersections (points) of a square grid with two opposite sides labeled white and the other two opposite sides labeled black. The board starts empty. On a turn, a player places a single stone of his/her color on ANY empty point.

Pinch capture:
If after placement a player has two of his/her stones orthogonally adjacent at a right angle to an enemy stone, then that enemy stone is removed and replaced by a stone of the player's color.

Victory: A player wins by creating a group of orthogonally-adjacent stones that connect his two sides.

------------------------------


Examples:
Player X to place

x__o x__o x__x A "pinch
| | --> | | --> | | "capture"
.__. .__x .__x takes place



Note that "playing into a pinch" doesn't result in self-capture:

o__. o__x The x stone
| | --> | | is NOT
.__o .__o captured



This in turn means that double captures are possible, if an opponent plays poorly:

o__. o__x Player O o__x x__x
| | --> | | --> plays --> | | --> | |
.__o .__o elsewhere x__o x__x



I'll give this game idea a whirl when I get home from work this evening. One appealing feature is that its rules, in a rather organic fashion, prevent cross-cut patterns from ever arising.

One key question, if the game is at all viable, will be whether or not to allow "chain captures":

With chain captures:

Player X’s turn. The sequence below shows the automatic effects of Player X placing at “,” below:

.__x__o__.__.
| | | | |
.__.__o__x__.
| | | | |
.__x__o__.__.
| | | | |
.__.__,__.__.

|
|
\|/
V

.__x__o__.__.
| | | | |
.__.__o__x__.
| | | | |
.__x__o__.__.
| | | | |
.__.__x__.__.

|
|
\|/
V

.__x__o__.__.
| | | | |
.__.__o__x__.
| | | | |
.__x__x__.__.
| | | | |
.__.__x__.__.

|
|
\|/
V

.__x__o__.__.
| | | | |
.__.__x__x__.
| | | | |
.__x__x__.__.
| | | | |
.__.__x__.__.

|
|
\|/
V

.__x__x__.__.
| | | | |
.__.__x__x__.
| | | | |
.__x__x__.__.
| | | | |
.__.__x__.__.


All o stones are captured!


With no chain captures:

The sequence below shows what happens when Player X plays to “,” followed by Player O playing at the new point labeled “,”

.__x__o__.__.
| | | | |
.__.__o__x__.
| | | | |
.__x__o__.__.
| | | | |
.__.__,__.__.

|
|
\|/
V

.__x__o__.__.
| | | | |
.__.__o__x__.
| | | | |
.__x__o__.__.
| | | | |
.__.__x__.__.

|
|
\|/
V

.__x__o__.__.
| | | | |
.__.__o__x__.
| | | | |
.__x__x__.__.
| | | | |
.__.__x__.__.

|
|
\|/
V

.__x__o__.__.
| | | | |
.__.__o__x__.
| | | | |
.__x__x__,__.
| | | | |
.__.__x__.__.

|
|
\|/
V

.__x__o__.__.
| | | | |
.__.__o__x__.
| | | | |
.__x__x__o__.
| | | | |
.__.__x__.__.

|
|
\|/
V

.__x__o__.__.
| | | | |
.__.__o__o__.
| | | | |
.__x__o__o__.
| | | | |
.__.__x__.__.


Thus, the original play by X to “,” was a bad move.

One strong fear = that the game will end up typically going cold, with players trading turns playing at useless points, until one of them is forced to play at a disadvantageous point, thereby enabling their opponent to make a winning capture.


 
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Craig Duncan
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Quote:
One key question, if the game is at all viable, will be whether or not to allow "chain captures"
Hmmm... It seems I will have to allow chain captures, otherwise the following sequence is possible, yielding a cross-cut:

With no chain captures:

The sequence below shows what happens when Player X plays to “,”:

.__.__o__x__.
| | | | |
.__.__o__x__o
| | | | |
.__x__o__o__o
| | | | |
.__.__,__o__o

|
|
\|/
V

.__.__o__x__.
| | | | |
.__.__o__x__o
| | | | |
.__x__o__o__o
| | | | |
.__.__x__o__o

|
|
\|/
V

.__.__o__x__.
| | | | |
.__.__o__x__o
| | | | | No further captures
.__x__x__o__o take place
| | | | |
.__.__x__o__o

The board above has a cross-cut. I've labeled it below; it's the cell marked with the comma:

.__.__o__x__.
| | | | |
.__.__o__x__o
| | | ,| |
.__x__x__o__o
| | | | |
.__.__x__o__o

So Pinch requires chain-captures, apparently.
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cdunc123 wrote:
Here's a simple idea for capture in a square grid connection game -- sort of a simplified version of Luis's Brique. (I wouldn't be surprised if Luis has already tried out this idea and found it wanting for some reason!)
I came up with a different simplified version of Brique a few years ago. I don't remember if I found a flaw in it or if I was just too lazy to release it. Maybe we can find out together; here it is:

Omnibrique

After a placement by X, all A points in any instances of the following patterns are colored X.

X B B X
A X X A


The status of A and B points before X's placement (empty or occupied by either color) is irrelevant.

Connect your allocated sides, etc.
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luigi87 wrote:
cdunc123 wrote:
Here's a simple idea for capture in a square grid connection game -- sort of a simplified version of Luis's Brique. (I wouldn't be surprised if Luis has already tried out this idea and found it wanting for some reason!)
I came up with a different simplified version of Brique a few years ago. I don't remember if I found a flaw in it or if I was just too lazy to release it. Maybe we can find out together; here it is:

Omnibrique

After a placement by X, all A points in any instances of the following patterns are colored X.

X B B X
A X X A


The status of A and B points before X's placement (empty or occupied by either color) is irrelevant.

Connect your allocated sides, etc.

Interesting! Thanks, Luis.

One question. I assume that there's a converse rule for O, right?

After a placement by O, all B points in any instances of the following patterns are colored O.

O B B O
A O O A


I wonder if defense will be too hard in both Pinch and Omnibrique...
 
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Luis Bolaños Mures
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cdunc123 wrote:
luigi87 wrote:
cdunc123 wrote:
Here's a simple idea for capture in a square grid connection game -- sort of a simplified version of Luis's Brique. (I wouldn't be surprised if Luis has already tried out this idea and found it wanting for some reason!)
I came up with a different simplified version of Brique a few years ago. I don't remember if I found a flaw in it or if I was just too lazy to release it. Maybe we can find out together; here it is:

Omnibrique

After a placement by X, all A points in any instances of the following patterns are colored X.

X B B X
A X X A


The status of A and B points before X's placement (empty or occupied by either color) is irrelevant.

Connect your allocated sides, etc.

Interesting! Thanks, Luis.

One question. I assume that there's a converse rule for O, right?

After a placement by O, all B points in any instances of the following patterns are colored O.

O B B O
A O O A
Yes, I forgot to mention that. X was meant to represent any player.

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I wonder if defense will be too hard in both Pinch and Omnibrique...
Quite possibly. Maybe I didn't release Omnibrique because I realized it was merely a somewhat faster (looser, more aggressive) version of Crossway. Pinch should be a bit faster still because of the chain reactions.
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Luis Bolaños Mures
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Your Tractor idea reminds me of the connection-game-with-capture Apex. Available for Zillions of Games.
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