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DifferentSizedBoards

 

Linear boards
    Keywords: Question

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.)

[Diagram]
1xN diagram

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


[Diagram]
1xN diagram

and any attack by white ...


[Diagram]
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.


[Diagram]
1x3 board

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


[Diagram]
1x4 board

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


[Diagram]
1x5 board

Similarly on the 1x5 board.


[Diagram]
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.


[Diagram]
1x4 board

White may play here. If black takes.


[Diagram]
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?

[Diagram]
white throws in twice

[Diagram]
white re-takes the right ko

[Diagram]
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 B2 at B3. See Nimgo.



This is a copy of the living page "Linear boards" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.