New game: Orcoon

[Luis Bolaños Mures]

ORCOON

Orcoon is a drawless connection game for two players: Black and White. It's played on the intersections (points) of a square board, which is initially empty. The top and bottom edges of the board are colored black; the left and right edges are colored white.

Black plays first, then turns alternate. On his turn, a player must either pass or place one stone of his color on an empty point.

It's illegal to form this pattern, its rotations or its mirror images on the board:

x . o
o . x

After a placement, any two like-colored, diagonally adjacent stones must share at least one orthogonally adjacent, like-colored neighbor.

When a player passes his turn, his opponent can place as many stones of his color as he wants on empty points of the board, one after another, subject to the above restrictions. If by doing so he connects the two opposite board edges of his color with a chain of orthogonally adjacent stones of his color, he wins the game; otherwise, he loses.

The pie rule is used in order to make the game fair. This means that White will have the option, on his first turn only, to change sides instead of making a regular move.

_________

Orcoon was born as a typical connection game where a player had to connect his two opposite sides of the board in order to win. I knew things couldn't be so easy on a square board, though, and I soon found a couple of deadlock patterns:

x x o
x . .
o . x

o x
x . . .
o . x . o
. . . x
x o

I could have simply banned them, but that would have been awkward, not to mention that there might be an unlimited number of them, each one more convoluted than the others.

One possible solution would be considering that two like-colored stones are also connected if they are a knight's jump away from each other and the two intervening points orthogonally or diagonally adjacent to both stones are empty, like this:

x .
. x

The game would be already drawless this way, and my impressions during playtesting were pretty good, but connections would no longer be permanent, something I considered essential to the game's spirit.

I was tempted to release that version anyway, but, after giving it a second thought, I finally came up with the current end game rule, and I liked it from the start. I think it's a nice way to naturally incorporate deadlocks into the game while preventing them to ever become a problem. Two main implications must be noted here:

a) More often than not, deadlocks won't occur, in which case the game will proceed as a normal connection game. When one player connects his two opposite sides of the board, he can simply pass to win the game.

b) When a deadlock pattern occurs, the character of the game changes in a dramatic way. Implicitly, you can now win either by connecting your two opposite sides while dodging the deadlock or by being the first player to connect your two sides to the deadlock itself, thus introducing a race component into the game.

[Steven W. Meyers]

Post by Luis Bolaños Mures
x . o
o . x
After a placement, any two like-colored, diagonally adjacent stones must share at least one orthogonally adjacent, like-colored neighbor.

The above restrictions seem very similar to those of your other game
Konobi. Could you please explain the difference?

Steve

[Luis Bolaños Mures]

Post by Steven W. Meyers

Post by Luis Bolaños Mures
x . o
o . x
After a placement, any two like-colored, diagonally adjacent stones must share at least one orthogonally adjacent, like-colored neighbor.

The above restrictions seem very similar to those of your other game
Konobi. Could you please explain the difference?
Steve

Thanks for asking, Steve. In Konobi, diagonal connections are only allowed on certain conditions, and this pattern is always forbidden:

x o
o x

In Orcoon, diagonal connections are always forbidden, as is the following pattern:

x . o
o . x

In Orcoon, you needn't check anything to find out if a diagonal placement is allowed or not, so this game has greater clarity than Konobi. Also, the occasional race component increases the strategical interest, IMHO. In exchange, Konobi is a pure connection game, and some people may find its trickier tactics more interesting to analyze.

I hope this answers your question. I personally like the more flowing gameplay of Orcoon best, but I guess it's a matter of taste.

Those who don't like to come accross a race every now and then might want to try the variant with the knight's jump connections instead, either with the featured game ending protocol (which I recommend, as I consider it better suited to this particular game) or as a typical connection game. Anyway, you'll notice that the game is fundamentally the same in all cases.

[Steven W. Meyers]

Post by Luis Bolaños Mures

Post by Steven W. Meyers

Post by Luis Bolaños Mures
x . o
o . x
After a placement, any two like-colored, diagonally adjacent stones must share at least one orthogonally adjacent, like-colored neighbor.

The above restrictions seem very similar to those of your other game
Konobi.  Could you please explain the difference?
Steve

x o
o x
x . o
o . x
In Orcoon, you needn't check anything to find out if a diagonal placement is allowed or not, so this game has greater clarity than Konobi. Also, the occasional race component increases the strategical interest, IMHO. In exchange, Konobi is a pure connection game, and some people may find its trickier tactics more interesting to analyze.
I hope this answers your question. I personally like the more flowing gameplay of Orcoon best, but I guess it's a matter of taste.
Those who don't like to come accross a race every now and then might want to try the variant with the knight's jump connections instead, either with the featured game ending protocol (which I recommend, as I consider it better suited to this particular game) or as a typical connection game. Anyway, you'll notice that the game is fundamentally the same in all cases.

Thanks for clarifying, I think I understand now.

In my opinion a race element in a connection game is not necessarily a
bad thing, depending on how it is done. Gonnect, for instance, is a
very good connection game with a race element.

Steve

[Luis Bolaños Mures]

Post by Steven W. Meyers
In my opinion a race element in a connection game is not necessarily a
bad thing, depending on how it is done. Gonnect, for instance, is a
very good connection game with a race element.

I agree. I'd say that a race element is not a bad thing provided that there are enough blocking options, and there are plenty of them, both in Gonnect and Orcoon, thanks to the limited connectivity of the square board.

FWIW, I've now played Orcoon ten times against human players without any deadlock arising, but they may be more common between expert players. I've also played a few games against the Zillions machine, and the 3x3 deadlock pattern appeared once.

Here's one of the games I've played on the igGC sandbox:

http://gc1.iggamecenter.com/gm.php?sid=268610&lang=en

[Luis Bolaños Mures]

Post by Steven W. Meyers
Thanks for clarifying, I think I understand now.
In my opinion a race element in a connection game is not necessarily a
bad thing, depending on how it is done. Gonnect, for instance, is a
very good connection game with a race element.
Steve
In my opinion a race element in a connection game is not necessarily a
bad thing, depending on how it is done. Gonnect, for instance, is a
very good connection game with a race element.

I agree. I'd say that a race element is not a bad thing provided that there are enough blocking options, and there are plenty of them, both in Gonnect and Orcoon, thanks to the limited connectivity of the square board.

FWIW, I've now played Orcoon ten times against human players without any deadlock arising, but they may be more common between expert players. I've also played a few games against the Zillions machine, and the 3x3 deadlock pattern (and therefore a race) appeared once.

[Luis Bolaños Mures]

Post by Steven W. Meyers
Thanks for clarifying, I think I understand now.
In my opinion a race element in a connection game is not necessarily a
bad thing, depending on how it is done. Gonnect, for instance, is a
very good connection game with a race element.
Steve

I agree. I'd say that a race element is not a bad thing provided that there are enough blocking options, and there are plenty of them, both in Gonnect and Orcoon, thanks to the limited connectivity of the square board.

FWIW, I've now played Orcoon ten times against human players without any deadlock arising, but they may be more common between expert players. I've also played a few games against the Zillions machine, and the 3x3 deadlock pattern (and therefore a race) appeared once.

[christian freeling]

Post by Luis Bolaños Mures

Post by Steven W. Meyers
Thanks for clarifying, I think I understand now.
In my opinion a race element in a connection game is not necessarily a
bad thing, depending on how it is done. Gonnect, for instance, is a
very good connection game with a race element.
Steve

I agree. I'd say that a race element is not a bad thing provided that there are enough blocking options, and there are plenty of them, both in Gonnect and Orcoon, thanks to the limited connectivity of the square board.

Havannah is essentially a race game too so the hexboard does nicely :)

On another note, it says here that two messages 'have been removed'. That's a novelty at rga (as far as I know). Anyone knows by whom and why?

[Luis Bolaños Mures]

Here's one of the Orcoon games I've played on the igGC sandbox:

http://gc1.iggamecenter.com/gm.php?sid=268610&lang=en

[Luis Bolaños Mures]

Post by christian freeling

Post by Luis Bolaños Mures
I agree. I'd say that a race element is not a bad thing provided that there are enough blocking options, and there are plenty of them, both in Gonnect and Orcoon, thanks to the limited connectivity of the square board.

Havannah is essentially a race game too so the hexboard does nicely :)

Yes, I'm sure it does. Of course, there are less blocking options on a hex board, but I guess ring threats play a similar role in Havannah. Since you have to lose time answering them, they slow your connection down just like a blocker would. I have almost no playing experience with Havannah, though, so I'm just not sure about their real incidence. In any case, I suspect they're the most interesting aspect of the game :)

Post by christian freeling
On another note, it says here that two messages 'have been removed'. That's a novelty at rga (as far as I know). Anyone knows by whom and why?

That was me, sorry. :) I re-posted a message because of typos, but I hadn't removed the original one yet and the re-posted one was marked as a quote of the former, so I removed both. I didn't expect the removal to be reported, though. That's new indeed.

[Luis Bolaños Mures]

Post by Luis Bolaños Mures
x x o
x . .
o . x
o x
x . . .
o . x . o
. . . x
x o
I could have simply banned them, but that would have been awkward, not to mention that there might be an unlimited number of them, each one more convoluted than the others.

Over the past few days, I've been trying to find more such deadlock patterns by trial and error and have found none yet. This is getting intriguing.

I still think there must be more of them, but if I managed to prove the opposite I might be tempted to ban those two and make Orcoon a pure connection game.

Could anyone help me with this issue? I know I should use some kind of logical procedure, but I have no idea where to start. All I know is every new pattern must consist of a partial combination of the previous ones, and so bigger than them, but that doesn't seem to be helping much.

I'd appreciate any methodological advice - or conclusive proof, for that matter :)

[Luis Bolaños Mures]

Post by Luis Bolaños Mures
Over the past few days, I've been trying to find more such deadlock patterns by trial and error and have found none yet. This is getting intriguing.
I still think there must be more of them, but if I managed to prove the opposite I might be tempted to ban those two and make Orcoon a pure connection game.

Good news!

After a little more research, I've finally come to the conclusion that there aren't any other deadlock patterns in Orcoon than the four ones (including diagonal connections) that I mentioned in my original post, so I'll probably change the rules to make it a pure, drawless connection game, without races. To be honest, all I have for the moment is a partial proof, but it might be enough to my purposes. Here it goes:

It's an obvious fact that every new deadlock pattern, except for the initial one regarding diagonal connections, is based on the previous ones, i.e. it's a deadlock because trying to connect the stones in it by adding a single stone necessarily results in the formation of a different (and simpler) deadlock. For instance:

3 x x o
2 x . .
1 o . x

a b c

Here, if White plays b2 or Black plays b1, b2 or c2, an illegal diagonal connection will be made. If White plays b1 or c2, instead, the following deadlock is formed:

x . o
o . x

What I have found out is that there can be no deadlock patterns based on the 5x5 one:

5 o x
4 x . . .
3 o . x . o
2 . . . x
1 x o

a b c d e

This pattern has a unique property: all the empty points in it form a closed circuit, and all the relevant points around are occupied by stones belonging to the pattern itself. As a result, it's immune to the influence of any other blocking patterns on the outside. The crucial implication is that, if we remove one stone from this deadlock pattern to try and construct a different one based on it, at least one placement in the inner circuit will be enabled in all cases, thus preventing any blockade:

- Removing the central Black stone enables White c2 and Black b2.
- Removing the white stone on c1 enables White b3.
- Removing the black stone on b1 enables White b3.
- [Rotated points omitted.]

The only thing still to be proved is the impossibility of other deadlock patterns based on the 2x3 and 3x3 ones, but the more I think of it the more confident I am that they are indeed impossible. It seems like the combination of all the patterns up to a certain point always produces at most one new pattern, which suggests that, if there were just one more of them, it would have to contain the 5x5 one, a possibility I have just disproved.

I'm excited about this game now. I loved its gameplay from the beginning, maybe even more so than that of Quentin, but I did have some little reservations about race positions. Now that it's about to turn into a pure connection game, I think it could the best one from this streak of square board static connection games that I have released in the last weeks. I'm aware that the prohibition of several specific formations is still an aesthetic issue, but they are really easy to spot from the first play, and the 5x5 one is extremely rare anyway.

I'd like to read other people's opinions of all this.

[Luis Bolaños Mures]

Post by Luis Bolaños Mures
- Removing the black stone on b1 enables White b3.

... and Black c2.

[Luis Bolaños Mures]

Post by Luis Bolaños Mures
The only thing still to be proved is the impossibility of other deadlock patterns based on the 2x3 and 3x3 ones, but the more I think of it the more confident I am that they are indeed impossible.

Er...

x o
o . . x
x . . o
o x

This is another closed circuit pattern (like the 5x5 one), but it's only based on diagonal connections (like the 2x3 one).

My, the square board is more treacherous than I thought!

It's a pity, because the game showed promise.

Back to the drawing board...

[Luis Bolaños Mures]

Post by Luis Bolaños Mures
x o
o . . x
x . . o
o x

This is still a deadlock if one or more of the black stones are moved to the adjacent corner points of the 4x4 area, so there are six variants of this pattern in total (!). For instance:

x . o
o . . x
. . o
x o x

Here, the b4 and a2 stones have been moved to a4 and a1, respectively.

[Luis Bolaños Mures]

Another one, just for the sake of completeness:

x x o o
x . . o
o . . x
o o x x

[Luis Bolaños Mures]

Major revision, possibly turning this into a decent game:

After a placement, any two like-colored, diagonally adjacent stones must share at least one orthogonally adjacent, like-colored neighbor. No other placement restrictions are used.

On their turn, a player must place a stone or pass.

The game ends when both players pass in succession.

A player's score is the number of placements on empty stones, without the above restriction, that they would have to make in the final position in order to form a winning chain. The player with the lowest score wins. In the event of a tie, whoever passed first wins. Passing first can be indicated by taking possession of a special token called "button".

Komi can be used instead of the pie rule to balance the game. Note that if a player forms a winning chain before the end, their score is 0 and their opponent's score is arguably infinite, although it can be given a finite value to improve the effectivenes of komi if the need arises. Reasonable values in this case might be the number of empty points and the number of moves to form a winning chain before the opponent's last move, perhaps with a fixed penalty added to it.

This idea might work as a general pattern-building game system as well. Like here, placements that prevent the opponent from building the winning pattern (for some convenient definition of "prevent": on the whole board, with any group...) would be banned.

The resulting hybrid connection-territory games are to connection games what territory games are to annihilation games: they provide a scoring method to determine a winner on points when no sweeping victory has been claimed.

[Moh Bel]

You wrote I quote :
I've designed Paper and Pencil Go, Quaxtep, Yodd, Xodd, Ayu, Hyper, Loose, Konobi, Quentin, Brique, Vimbre, Kopano, Trisq, Sligo, Stoical Go, Alpha, Veletas, Whirlwind, Squer, Rhode, Cation, Morpheus, Lear, Flicker, Carteso, Rumbo and Linage.

Which one is not crappy game?
All are not only crappy games but above all plagiarized games.
And you dare because I was banished from bgg forum abstract to tell that vertical vs horizontal was not invented by me. By referring to Hex game.
Either you are dumb either you are of bad faith.
I invented the concept of capturing differently : one player can capture only vertically and his opponent vertically. Why is it interesting to break the capture in two? I let you answer to this question. We can use other dimensions (up-down, orthogonal-diagonal or any other binary dimension.
In Hex game there is no capture at all.
In many games one player can move in one direction and the other on the opposite etc...
You are just trying to hide the fact that you plagiarized my idea.
It is not surprising that you waited so long to say that Hex game is similar to my idea.
I know all the tricks of the thieves and the "atajo de ladrones".

You have both you and Corey only one neuron.
History will show you are fake game designers.
History will that Hazen is the best game designer of this century.

Corey is so dumb that he can not get the flaw I pointed out to.
He has no idea that his game Meanderthal (I called it like this and he never mentioned that I was the inventor of the name) is EASILY SOLVABLE. Almost like tic tac toe.

[Luis Bolaños Mures]

Post by Moh Bel
I invented the concept of capturing differently : one player can capture only vertically and his opponent vertically. Why is it interesting to break the capture in two? I let you answer to this question. We can use other dimensions (up-down, orthogonal-diagonal or any other binary dimension.
In Hex game there is no capture at all.

Carteso doesn't use that capturing method because there is no capture in Carteso.

[Moh Bel]

Post by Luis Bolaños Mures

Post by Moh Bel
I invented the concept of capturing differently : one player can capture only vertically and his opponent vertically. Why is it interesting to break the capture in two? I let you answer to this question. We can use other dimensions (up-down, orthogonal-diagonal or any other binary dimension.
In Hex game there is no capture at all.

Carteso doesn't use that capturing method because there is no capture in Carteso.

Trick of the thieves.
Read this :A group, regardless of color, is owned by Vertical if it spans more rows than columns, and by Horizontal if it spans more columns than rows. If a group spans exactly as many rows as columns, it's owned by neither player.

What is owning versus capturing?
When you flip a token in Othello is similar to capturing it.
When you control a territory is similar to capturing land.
In any case you will finish by vomiting your theft.
You know why?
Because my concept does not fit with such crappy game Cartezero. Even i you revised it as you wish it will remain botched game.

[Corey L. Clark]

Hazen I told you to only speak when spoken to. How soon we forget

[Luis Bolaños Mures]

I think the following mechanism is finite and guarantees a final position without crosscuts:

On your turn, do one of the following:

a) choose a 2x2 area with at least one empty point and place a stone of your color on each empty point in that area, or

b) flip two enemy stones which are part of the same crosscut.

To flip a stone means to replace it with a stone of the opposite color.

[Luis Bolaños Mures]

Post by Luis Bolaños Mures
a) choose a 2x2 area with at least one empty point and place a stone of your color on each empty point in that area, or

This is only to preserve material balance; it's not necessary for decisiveness.

[Luis Bolaños Mures]

Same for this one:

On your turn, do one of the following:

a) Place a regular stone of your color on an empty point.

b) Replace a regular enemy stone in a crosscut with a permanent friendly stone and a regular friendly stone in the same crosscut with a regular enemy stone.

If, at the start of your turn, you have no moves available, replace all permanent stones of both colors with regular stones of the same colors and then make a regular move.

[Luis Bolaños Mures]

Same for this one:

On your turn, you will face one of these situations:

a) There are no crosscuts on the board. In this case, place a stone of your color on an empty point.

b) There are one or more crosscuts on the board. In this case, perform one or two swaps such that, after the last of them, no crosscuts remain on the board. A swap consists in replacing a friendly stone in a crosscut with an enemy stone and an orthogonally or diagonally adjacent enemy stone with a friendly stone.

[Luis Bolaños Mures]

Post by Luis Bolaños Mures
a) There are no crosscuts on the board. In this case, place a stone of your color on an empty point.
b) There are one or more crosscuts on the board. In this case, perform one or two swaps such that, after the last of them, no crosscuts remain on the board. A swap consists in replacing a friendly stone in a crosscut with an enemy stone and an orthogonally or diagonally adjacent enemy stone with a friendly stone.

Very similar idea:

On your turn, place a stone of your color on an empty point. If this placement creates one or more crosscuts, perform one or two swaps such that, after the last swap, no crosscuts remain on the board. A swap consists in replacing a friendly stone in a crosscut with an enemy stone and an orthogonally or diagonally adjacent enemy stone with a friendly stone.

[Luis Bolaños Mures]

Mark Steere has pointed out that this works with only one swap if your turn is skipped when you have no legal moves available.

[Luis Bolaños Mures]

Refinement:

On your turn, if possible, swap two orthogonally or diagonally adjacent stones so that the number of crosscuts on the board is reduced from greater than zero to zero.

If this is not possible, swap two orthogonally or diagonally adjacent stones, at least one of which is part of a crosscut, without increasing the number of crosscuts on the board.

If this is not possible (because there are no crosscuts), place a stone of your color on an empty point.

[Luis Bolaños Mures]

Also interesting: https://marksteeregames.com/Swaptimum_rules.pdf

[Luis Bolaños Mures]

Post by Luis Bolaños Mures
On your turn, if possible, swap two orthogonally or diagonally adjacent stones so that the number of crosscuts on the board is reduced from greater than zero to zero.
If this is not possible, swap two orthogonally or diagonally adjacent stones, at least one of which is part of a crosscut, without increasing the number of crosscuts on the board.
If this is not possible (because there are no crosscuts), place a stone of your color on an empty point.

Refinement:

On your turn, perform exactly one of these actions:

• Place a stone of your color on an empty point.
• Swap two orthogonally or diagonally adjacent stones so that the number of crosscuts on the board is reduced. If this is not possible, swap two orthogonally or diagonally adjacent stones of different colors, at least one of which is part of a crosscut, without increasing the number of crosscuts on the board. (A stone can be part of more than one crosscut.)

You win if there is a chain of orthogonally connected stones of your color touching the two board edges of your color.

[Luis Bolaños Mures]

Refinement:

A crosscut is a 2x2 area containing two diagonally adjacent black stones and two diagonally adjacent white stones.

A supercut is a crosscut along with eight additional stones orthogonally adjacent to like-colored stones in the crosscut.

On your turn, perform exactly one of these actions:

* Place a stone of your color on an empty point.
* Swap two orthogonally or diagonally adjacent stones. This action must decrease either the number of crosscuts or the number of supercuts on the board, and it must not increase the number of crosscuts.

You win if there is a chain of orthogonally connected stones of your color touching the two opposite board edges of your color. Draws are not possible.

[Luis Bolaños Mures]

Deadlock patterns are multiplying. Here's another one:

o x x
. . x
x . .
x x o

This one is not even a closed circuit, so there might be yet another one based on it.

It's curious that there are deadlocks of almost any size up to 5x5: 2x2, 2x3, 3x3, 3x4, 4x4 and 5x5 so far. Only 4x5 is missing...