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.)
will result in an expansion of blacks territory.
Now, my quesiton is: Has this type of board been analyzed?
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??
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.
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 wins by four points here, almost as many points as there are spaces on the board. Imagine winning a 19x19 game by 360 points!
However, it's different if passes are allowed, so the Nimgo analysis doesn't completely apply.
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
By some rule the game would end in this position, but it is anomalous, with an unresolved ko. By my rules the game continues.
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
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