# Bughouse Go

__Keywords__: Variant

For a while now, I have had, in my KGS user info, a line saying "Ask me about bughouse go. I want to spread this game." Then, a few nights ago, when conversation died, I revived it be starting a conversation about my ideas for bughouse go. JasonD encouraged me to put something on SL about this, and that it what I am starting now. - HandOfPaper

The Basic Idea

Just as in bughouse chess, you have 2 boards with 2 players each, for a total of 4 players. The players are on 2 teams of 2 players each, with each team having one member being white on one board and black on the other. In bughouse chess, a move by a player consists of a normal move on his/her own board or the placement, on any unoccupied point of the board, of a piece captured by the teammate. In bughouse go, a move likewise consists of a normal move or the placement of a whole group captured by your teammate. Now I want to get into some further details.

Timing

Since there are two games on two different boards, questions can arise about how the moves on two different boards are related timewise. While I imagine there are at least a few other interesting ways to have timing arranged, here are two that immediately come to mind:

Synchronized. The black players move on both boards, and then the white players move on both boards.

Independent. Timing of moves on one board does not affect timing of moves on the other board.

ISSUES: There are ways time can become a strategic element in a bughouse game and lead to degenerate modes of play in the endgame. I need to make sure these don't happen. Thanks to federles of KGS for pointing this out to me.

A More Detailed Description of the Rules

The basic rules of go are still the same, whatever you take them to be.

As for the bughouse rules, here is how a few things go:

1. Before the game starts, a coordinate system must be agreed upon and applied to both boards.

2. Once that is done, using that coordinate system, all four players must agree on a subgroup G of the dihedral group D_4 of order 8. The relevance of G to gameplay is described next.

3. When a chain is captured on one board and gets placed on the other one, it must be placed in such a way that its new position can be obtained from its old position, read now as a position on the other board(this is why the same coordinate system must be used for both boards), by a translation and a member of G.

4. Only one chain may be placed at a time on a chain-placing move, even if other chains were captured when it was. This rule ensures that two eyes still live.

5. A group may be placed on a set of points if and only if:

The group's orientation is in keeping with rule 3, all the points on which it is being placed are unoccupied, and the usual rules of go are not violated (it will not result in suicide for itself or any group to which it is being joined, and the ko rule is obeyed--- but a stronger rule is needed).

A Ko Rule Covering Both Boards

It is necessary to extend the ko rule to cover repetitive positions whose repetitive nature extends across both boards. One example I have thought of is this:

Now suppose we are using synchronized timing and suppose it is black's turn. Suppose each black player has, at their disposal, a 2-stone horizontally oriented group. Then suppose each takes the two white stones on the inside of this formation. Then, if each white player likewise has a 2-stone horizontally oriented group at their disposal, then they may both capture back and the 2-stone horizontally oriented groups will all stay in circulation forever if there is nothing bigger elsewhere.

Therefore the ko rule needs to be extended. One possible extension is that it now applies whenever a group captures another group whose position is obtainable from its position by a translation and an element of G and places itself in atari by doing so.

Another way to do this is to extend the superko rule. A total position consists of the ordered quadruple (T1,P1,T2,P2), where T1 is the player whose turn it currently is on board 1, P1 is the position on board 1, and T2 and P2 are defined analogously. Then you may say that moves which allow the total position to return to a state it had before are forbidden and get an extended superko rule.

Subgroups of the Dihedral Group D_4

There are 10 subgroups, which come in 8 D_4-conjugacy classes. This yields 8 different variants as far as gameplay is concerned, but players must choose a subgroup (and not just a conjugacy class) in order to be completely clear on how they'll play before they start.

Order 8: 1. The entire group! This consists of the reflections through vertical lines, horizontal lines, and diagonal lines of slope +/-1, as well as rotations through multiples of a right angle.

Order 4:

2. The rotations! These are just the rotations through multiples of a right angle.

3. The symmetry group of a nonsquare rectangle: This consists of rotations through multiples of 180 degrees, and horizontal and vertical reflections.

4. The symmetry group of a nonsquare rectangle that has been rotated 45 degrees: This consists of rotations through multiples of 180 degrees and reflections through diagonal lines of slope +/-1.

Order 2:

5. The symmetry group of the N: This consists of rotations through all multiples of 180 degrees.

Reflections

6. This consists of a vertical reflection and the motion which does nothing.

7. This consists of a horizontal reflection and the motion which does nothing. This is conjugate to #6.

8. This consists of a reflection through the line going from A1 to T19 and the motion which does nothing.

9. This consists of a reflection through the line going from A19 to T1 and the motion which does nothing. This is conjugate to #8.

Order 1:

10. The trivial subgroup! This consists of the oft-mentioned motion which does nothing, also known as a 360-degree rotation.

Scoring

For now, at least, all players should agree on a scoring system (AGA, Japanese, Chinese, etc.) and a natural way to assign a score to a team is to add the individual scores of the players on that team. The extension of the scoring method used in bughouse chess, which is declaring a team to win if it is the first to have a member win on that member's own board, likely leads to degeneracies like those encountered in bughouse chess. Therefore using this is not advisable. The scoring method and the timing rules chosen should be considered together to ensure that no unwanted degenerate modes of play appear in the game. More work needs to be done on this. If the extended ko rule becomes involved also, then the situation becomes really dire...