Finite Go variant: Loose

[luigi]

LOOSE

Introduction

Loose is a finite territory game for two players: Black and White. It's played on the intersections (points) of an odd-sized, initially empty square board. Both players must have access to a sufficient number of stones colored black on one side and white on the other.

The goal of the game is having the most stones on the board when both players have passed. Loose features surround capture, like Go, but surrounded stones are flipped instead of removed, and a natural, game-defining mechanism is used to favour (rather than ensure) eye creation upon captures. Since no stones are ever removed from the board, cycles are not possible.

Definitions

In this rules, adjacent always means orthogonally adjacent.

A group is a set of like-colored, adjacent stones.

A liberty is an empty point adjacent to a group. A false liberty is an empty point which is adjacent to at least one stone of each color and no empty points. Liberties which are not false are true.

$$B The a points are false liberties; \nthe b points are true liberties.
$$ --------------
$$ | . . . . . . .
$$ | . X X X . . .
$$ | X O O a X . .
$$ | X O b O O X .
$$ | X a O O a X .
$$ | . X b b X . .
$$ | . . X X . . .
$$ | . . . . . . .

Click Here To Show Diagram Code

[go]$$B The a points are false liberties; \nthe b points are true liberties.
$$ --------------
$$ | . . . . . . .
$$ | . X X X . . .
$$ | X O O a X . .
$$ | X O b O O X .
$$ | X a O O a X .
$$ | . X b b X . .
$$ | . . X X . . .
$$ | . . . . . . .[/go]

Play

Starting with Black, the players take turns placing stones with their color showing on empty points of the board, one stone per turn.

After a placement, all enemy groups with no true liberties are flipped, i.e. all the stones in them are turned round to show the player's color, after which the turn ends.

At the end of a turn, every group on the board must have at least one true liberty. Otherwise, the move is illegal and the player must choose another one.

Players can pass their turn at any moment. When both players pass in succession, the game ends, and the one with the highest score wins.

A player's score is the number of stones with his color showing that there are on the board, plus a komi (see below) in the case of White. In the event of a tie, whoever made the last move loses.

Komi

The komi is the even number of points which are added to White's score at the end of the game as a compensation for playing second. Before the game starts, the first player tells his opponent the even number which will be used as komi, and then the second player chooses which color to play.

Examples

• A capture:
  
  
  $$B After , all White's liberties are false...
  $$ ----------------
  $$ | O O . X . . . .
  $$ | O . X . . . . .
  $$ | O 1 . . . . . .
  $$ | O . X , . . . .
  $$ | . X . . . . . .
  $$ | X . . . . . . .

  Click Here To Show Diagram Code

  [go]$$B After , all White's liberties are false...
$$ ----------------
$$ | O O . X . . . .
$$ | O . X . . . . .
$$ | O 1 . . . . . .
$$ | O . X , . . . .
$$ | . X . . . . . .
$$ | X . . . . . . .[/go]

  
  
  
  $$W ... so White's group is flipped.
  $$ ----------------
  $$ | X X . X . . . .
  $$ | X . X . . . . .
  $$ | X X . . . . . .
  $$ | X . X , . . . .
  $$ | . X . . . . . .
  $$ | X . . . . . . .

  Click Here To Show Diagram Code

  [go]$$W ... so White's group is flipped.
$$ ----------------
$$ | X X . X . . . .
$$ | X . X . . . . .
$$ | X X . . . . . .
$$ | X . X , . . . .
$$ | . X . . . . . .
$$ | X . . . . . . .[/go]

  
  
• Not a capture:
  
  
  $$B After , White's group isn't flipped, \nsince the a points are true liberties.
  $$ ----------------
  $$ | a O X . . . . .
  $$ | O a X . . . . .
  $$ | O a X . . . . .
  $$ | O O X , . . . .
  $$ | . 1 . . . . . .
  $$ | X . . . . . . .

  Click Here To Show Diagram Code

  [go]$$B After , White's group isn't flipped, \nsince the a points are true liberties.
$$ ----------------
$$ | a O X . . . . .
$$ | O a X . . . . .
$$ | O a X . . . . .
$$ | O O X , . . . .
$$ | . 1 . . . . . .
$$ | X . . . . . . .[/go]

  
  
• Illegal move:
  
  
  $$B After , White's marked stone is \nflipped, but doesn't get any true liberties \nas a result, so Black's move is illegal.
  $$ . . . . . . . .
  $$ . . . X . . . .
  $$ . . O . O . . .
  $$ . 1 . W . X . .
  $$ . . O . O . . .
  $$ . . . X . . . .
  $$ . . . . . . . .

  Click Here To Show Diagram Code

  [go]$$B After , White's marked stone is \nflipped, but doesn't get any true liberties \nas a result, so Black's move is illegal.
$$ . . . . . . . .
$$ . . . X . . . .
$$ . . O . O . . .
$$ . 1 . W . X . .
$$ . . O . O . . .
$$ . . . X . . . .
$$ . . . . . . . .[/go]

Sample game

http://www.lifein19x19.com/forum/download/file.php?id=2066

[hyperpape]

$$B After B1, White's group isn't flipped, \nsince the a points are real liberties.
$$ ----------------
$$ | a O X . . . . .
$$ | O X X . . . . .
$$ | O X X . . . . .
$$ | O O X , . . . .
$$ | X X . . . . . .
$$ | X . . . . . . .

Click Here To Show Diagram Code

[go]$$B After B1, White's group isn't flipped, \nsince the a points are real liberties.
$$ ----------------
$$ | a O X . . . . .
$$ | O X X . . . . .
$$ | O X X . . . . .
$$ | O O X , . . . .
$$ | X X . . . . . .
$$ | X . . . . . . .[/go]

Isn't this group still alive, because the a stone doesn't count as a false liberty? It sounds like making life will be too easy.

[luigi]

$$B After B1, White's group isn't flipped, \nsince the a points are real liberties.
$$ ----------------
$$ | a O X . . . . .
$$ | O X X . . . . .
$$ | O X X . . . . .
$$ | O O X , . . . .
$$ | X X . . . . . .
$$ | X . . . . . . .

Click Here To Show Diagram Code

[go]$$B After B1, White's group isn't flipped, \nsince the a points are real liberties.
$$ ----------------
$$ | a O X . . . . .
$$ | O X X . . . . .
$$ | O X X . . . . .
$$ | O O X , . . . .
$$ | X X . . . . . .
$$ | X . . . . . . .[/go]

Isn't this group still alive, because the a stone doesn't count as a false liberty? It sounds like making life will be too easy.

In your example, Black can flip White's group by playing at a, which is the last true liberty of said group.

[badukJr]

Game is pointlessly changed too much

$$B
$$ ----------------
$$ | . a . O X . . .
$$ | O O O O X . . .
$$ | O . . O X . . .
$$ | X X X X X . . .
$$ | X X . . . . . .
$$ | X . . . . . . .

Click Here To Show Diagram Code

[go]$$B
$$ ----------------
$$ | . a . O X . . .
$$ | O O O O X . . .
$$ | O . . O X . . .
$$ | X X X X X . . .
$$ | X X . . . . . .
$$ | X . . . . . . .[/go]

a - Illegal move for black.

$$B
$$ ----------------
$$ | O O X . O X . .
$$ | O . a O O X X .
$$ | O O O O . . X .
$$ | X X X X X X . .
$$ | X X . . . . . .
$$ | X . . . . . . .

Click Here To Show Diagram Code

[go]$$B
$$ ----------------
$$ | O O X . O X . .
$$ | O . a O O X X .
$$ | O O O O . . X .
$$ | X X X X X X . .
$$ | X X . . . . . .
$$ | X . . . . . . .[/go]

a - Illegal move for black

$$B
$$ ----------------
$$ | O O X . O X . .
$$ | O . a O O X X .
$$ | O O O O . X X .
$$ | X X X X X X . .
$$ | X X . . . . . .
$$ | X . . . . . . .

Click Here To Show Diagram Code

[go]$$B
$$ ----------------
$$ | O O X . O X . .
$$ | O . a O O X X .
$$ | O O O O . X X .
$$ | X X X X X X . .
$$ | X X . . . . . .
$$ | X . . . . . . .[/go]

a - Legal move, because addition of stone that does not even contact group? Really obtuse.

[luigi]

Game is pointlessly changed too much

Yes, the game is quite different from Go, but this is not meant to be Go anyway. It's just a interesting variant designed with the purpose of avoiding cycles. In that sense, I don't think it's pointless.

[hyperpape]

At this moment, all the moving player's groups must have at least one true liberty. Otherwise, the move is illegal and the player must choose another one.

What does this mean then?

[luigi]

At this moment, all the moving player's groups must have at least one true liberty. Otherwise, the move is illegal and the player must choose another one.

What does this mean then?

"At this moment" means "after all enemy groups without true liberties have been flipped".

$$B After , White's group is flipped, \nsince it has no real liberties.
$$ ----------------
$$ | 1 O X . . . . .
$$ | O X X . . . . .
$$ | O X X . . . . .
$$ | O O X , . . . .
$$ | X X . . . . . .
$$ | X . . . . . . .
$$ | . . . . . . . .

Click Here To Show Diagram Code

[go]$$B After , White's group is flipped, \nsince it has no real liberties.
$$ ----------------
$$ | 1 O X . . . . .
$$ | O X X . . . . .
$$ | O X X . . . . .
$$ | O O X , . . . .
$$ | X X . . . . . .
$$ | X . . . . . . .
$$ | . . . . . . . .[/go]

$$B The position after the capture.
$$ ----------------
$$ | X X X a . . . .
$$ | X X X a . . . .
$$ | X X X a . . . .
$$ | X X X a . . . .
$$ | X X a . . . . .
$$ | X a . . . . . .
$$ | a . . . . . . .

Click Here To Show Diagram Code

[go]$$B The position after the capture.
$$ ----------------
$$ | X X X a . . . .
$$ | X X X a . . . .
$$ | X X X a . . . .
$$ | X X X a . . . .
$$ | X X a . . . . .
$$ | X a . . . . . .
$$ | a . . . . . . .[/go]

Note that, after the capture, the resulting Black group has plenty of true liberties (the a points).

I have added a sample game to my OP. I hope it helps. I have also added the pie rule to balance the game.

[hyperpape]

I'd say the pie rule is extremely ugly for go, as it encourages bizarre play that (unlike what I'd assume would be true in hex) doesn't converge to natural play. I suspect that any move above the second line fails as a balancing play, and I wouldn't even count on a corner move on the second line working.

Edit: silly me. That's the pie rule in Go. I have no idea what it would be like in this game.

[luigi]

I'd say the pie rule is extremely ugly for go, as it encourages bizarre play that (unlike what I'd assume would be true in hex) doesn't converge to natural play. I suspect that any move above the second line fails as a balancing play, and I wouldn't even count on a corner move on the second line working.

Edit: silly me. That's the pie rule in Go. I have no idea what it would be like in this game.

I've just chosen the pie rule because I find it a bit more elegant that komi, but I know many people won't agree. Could you elaborate on why it should feel more bizarre in Go than it does in Hex?

[hyperpape]

I've just chosen the pie rule because I find it a bit more elegant that komi, but I know many people won't agree. Could you elaborate on why it should feel more bizarre in Go than it does in Hex?

Well, take it with a grain of salt: I'm not good at Hex. In fact, I've not played much at all. But in go, it is quite hard to make real use of a random second line stone. We have joseki and whatnot that will be played elsewhere, and we just have this stupid idiotic stone left lying around.

In Hex, it seems like the initial stone may not be placed that well, but I don't perceive the same lack of fit. Play a couple of moves and it will be part of the game, I think, unlike the 2-7 point in Go.

[hyperpape]

Oh, another point: the pie rule would probably lead to trick plays being abused in go. That's no fun!

[luigi]

in go, it is quite hard to make real use of a random second line stone.

Well, it should be, or else it wouldn't balance the game at all. I think it's the same in any game.

We have joseki and whatnot that will be played elsewhere, and we just have this stupid idiotic stone left lying around.

True, the first stone doesn't fit with the joseki, but that's just because no joseki have been developed for it yet. If the pie rule had been used systematically in Go, there would be plenty of suitable opening theory built on it.

[hyperpape]

A trick play is a prepared trap that is understood to be inferior, but has a very subtle refutation that will probably not be apparent to the opponent. Such moves reward careful preparation over knowledge of the game. They're bad for the same reasons that chess's extensively developed opening theory is considered a bug of the game.

As for joseki, there's a difference. The go board has four corners, each of which may see joseki played*. The one corner will end up being an odd man out.

To be a balancing move, the move has to have some effect on the result of the game. Granted. But I think there's a difference between a stone that influences the result and a stone that is in the right place. The relation between the balancing stone and the "natural" stones on the board will be awkward and forced. With komi, each player plays each stone in a natural place, and the game has a flow. With the pie rule, there will be an odd man out.

I'm no chess player, but I think there might be an analogy to the way that material handicaps are felt to be an ugly method of balancing the game between uneven players.

* As has been pointed out in other discussions on the boards, high level play features a lot less joseki than you might think, and a lot more improvised patterns. So really the point is about the natural development and flow of the stones.

[luigi]

I think I have discovered a very interesting property of Loose, but I need your help to either prove or disprove it.

In Go, barring cycles and passing prematurely at an equal score, a game can only end in a tie if there is an odd number of points in seki. In Loose, I'd say this is impossible, but I can't be completely sure.

If that's the case, however, then Loose will be effectively drawless without the need for any tie-break rule.

For example:

$$B
$$ -----------------
$$ | . O . X . X O .
$$ | O O O X X X O .
$$ | X X X O O O O .
$$ | . . . . . . . .

Click Here To Show Diagram Code

[go]$$B
$$ -----------------
$$ | . O . X . X O .
$$ | O O O X X X O .
$$ | X X X O O O O .
$$ | . . . . . . . .[/go]

In Go, this is the simplest situation with an odd number of points in seki, whereas in Loose, whoever plays first will kill by simply filling the opponent's eye.

Can you find any Loose positions with an odd number of points in seki? Do you think they're possible or not? I'm really curious about it.

EDIT:

As for the komi/pie rule discussion, maybe I will opt for komi after all. I've been following your interesting discussion on the pie rule in the other thread and I understand the reasons why you don't like it, namely that it's not actually an even trade and that it disrupts the natural flow of the game. I also understand that it's kind of a waste to use the pie rule if the game already has a scoring system which can be easily adjusted to balance the game with great precission.

My only issue with komi is the fact that it should be different for players with different skills. For example, in 5x5 Go, good players should set komi at 25 points (the whole board), but for absolute beginners that would be too much. For this reason, I wouldn't use a fixed komi even if I knew the value which made the game balanced at the highest levels of play. I think it's better to let the players negotiate it before the game in this way: first Black suggests a komi, then White may choose to swap sides.

[luigi]

As for the komi/pie rule discussion, maybe I will opt for komi after all. I've been following your interesting discussion on the pie rule in the other thread and I understand the reasons why you don't like it, namely that it's not actually an even trade and that it disrupts the natural flow of the game. I also understand that it's kind of a waste to use the pie rule if the game already has a scoring system which can be easily adjusted to balance the game with great precission.

My only issue with komi is the fact that it should be different for players with different skills. For example, in 5x5 Go, good players should set komi at 25 points (the whole board), but for absolute beginners that would be too much. For this reason, I wouldn't use a fixed komi even if I knew the value which made the game balanced at the highest levels of play. I think it's better to let the players negotiate it before the game in this way: first Black suggests a komi, then White may choose to swap sides.

Update: I've finally settled for komi instead of the pie rule. I've also removed most of my boring introduction.

I'm starting a game on an 11x11 board:

$$Bcm1
$$ ------------------------
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . 1 . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ ------------------------

Click Here To Show Diagram Code

[go]$$Bcm1
$$ ------------------------
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . 1 . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ ------------------------[/go]

Does anyone want to give it a try? I'll play with anyone.