Linear boards

Even a linear or one-dimensional 1xN board permits playing Go, unfortunately with only limited strategical variations. The most obvous change from a regular 2-dimensional board is that the number of liberties that a stone may posess is one at the end of the line, and two anywhere else. (Alternatively, one may introduce a circular board, where all stones have two liberties.)

1xN diagram ^[1]  

One can define a 'living group' as in the diagram. Black has two points,

1xN diagram  

and any attack by white ...

1xN diagram  

will result in an expansion of blacks territory.

Now, my quesiton is: Has this type of board been analyzed?

Bill: Yes. See Small Board Go.

ScheWek?: Are there any tables of solution (e. g. how big black wins on each of the different Sizes?

I assume it should be possible to completely solve this type of board, maybe along the lines of Nim??

Bill: See Nimgo.

1x3 board  

For example, the 1x3 game is finished when black places the stone in the center.

1x4 board  

On the 1x4 board, after black plays, there is no place for white.

1x5 board  

Similarly on the 1x5 board.

1x6 board  

On the 1x6 board, white can make one move, reducing blacks points to 1.

GoranSiska Although I find this silly I have to disagree with your analysis.

1x4 board  

White may play here. If black takes.

1x4 board  

Now black stone in the corner has only 1 liberty left so it's a ko. The continuation again depends on the rule sistem :). So I guess Go is still hard - even on linear boards.

macho I don't find this silly, and I have to disagree with both your analyses. On the previous 1x4 board Black still wins, assuming you're using the standard superko rule. However, on the 1x5 board, an opening play at tengen actually loses for Black.

GoranSiska I still find it silly. Which part of my analysis are you disagreeing with? That the position turns into a ko or that the continuation depends on the rule sistem? And what makes you think the superko rule is standard?

white throws in twice  

white re-takes the right ko  

black has no threats and must pass  

White wins by four points here, almost as many points as there are spaces on the board. Imagine winning a 19x19 game by 360 points!

unkx80: Black plays at . See Nimgo. thanatos13: that's not allowed, at makes 0 liberties which is illegal.

193.132.150.21 :

However, it's different if passes are allowed, so the Nimgo analysis doesn't completely apply.

Tengen(?)  

Black makes a strategic sacrifice, as with Nimgo

Pass  

Now both players pass. Result depends on the scoring system.

Same ending  

If prisoner count matters, this is a better opening for black.

Bill: I am glad that people are exploring this. It can be a lot of fun. :-)

However, with small boards and with linear go in particular, you must agree on the rules. Different rules can produce radically different results.

May I suggest area scoring? All you have to do is look at the board to tell the score. You do not have to keep up with captures. :-)

May I also suggest my rules? It is too easy with linear go to get anomalies. While some people embrace them if the follow from rules they like, others, myself included, do not.

Example: 1x4 go

1x4 board  

= pass

By some rule the game would end in this position, but it is anomalous, with an unresolved ko. By my rules the game continues.

Diagram 2  

Diagram 3  

= pass

After the game ends with three consecutive passes, and Black wins by 4 points.

To me, this is a more satisfactory ending than the one with an unresolved ko. :-)

Linear go? Isn't there already a go variant played in 1 dimension called alak? Meh, the rules are different than the ones mentioned here though. There's my 2 cents. ~srn347

Phelan: There is. Sensei's has a page about it: Alak

[1] The usual order is width×height and not small×large.