2x2 board

A 2x2 Go Board:

2x2 board  

See also: Positions and Games on 2x2

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Example games

2x2 board  

 

 

White 4 captures two stones  

prisoners:

 

prisoners:

White 6 captures 1 stone  

prisoners:

Black 7 captures 3 stones  

prisoners:

There are some who would object to this move under superko rules.

Bill: Is there any rule set currently in use that has a superko rule that allows ?

score: White wins by komi value  

prisoners:

Tas: How about:

 

prisoners:

White 6 captures 1 stone  

prisoners:

Black 7 captures 3 stones  

prisoners:

No superko problems now.

back to start  

prisoners:

This can go on four times before stopped by superko, but neither player gains. Can a player cleverly use superko to his advantage?

game ends  

Assuming the superko rule it's possible for black to end the game here. The position is seki.

Tas: But no advantage...

impu1se: Presumably black wins with area scoring.

Bill Taylor proved that under area scoring the perfect play score is 1. The proof consists of two parts: 1) Black wins by at least 1 point. 2) Black wins by at most 1 point.

John Tromp's partial SGF file

Question

bugcat: In the first sequence, why does White play (6)? It seems clear to me that the move is bad for White. If White passes and Black captures then the score becomes even, at which point White can choose to repeat the sequence. Without superko, the two players could go on for ever, the sequence being:

1. Black places a stone
2. White places a stone diagonally opposite
3. Black extends
4. White captures
5. Black places a stone
6. White passes
7. Black captures
8. White places a stone
9. Black passes
10. Repeat from step 4.

To me it seems like there is an infinitely repeating sequence that oscillates in score between White +2 and jigo. I am talking about territory scoring with no pass stones, of course.