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April 4th, 2005

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Odd board situation

Jaco Swanepoel (8k) and I (5k) had an interesting 3-handicap game last Thursday, in which I was given quite a beating. However, we did take a picture of the board position in the middle of the game, simply due to the large number of complicated, unresolved positions on the board, particularly interesting corner positions. If I remember correctly, it’s White’s move next:

My understanding is that the bottom left is a 2-stage ko for the life of Black’s group, the bottom right might be a thousand-year ko, or a seki, depending on Black, and if Black plays first, he can get a seki in the top left, or with poor defence by White, we may get a bent four in the corner. As a result of the odd position in the bottom left, one of the issues for me was whether under non-Japanese rules, the bent-four in the upper left corner would practically really be dead.

Any comments on my analysis?

Posted by Steve in Game records

3 Comments »

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3 Responses to “Odd board situation”

  1. konrad says:

    Your assessments are correct, except regarding the possible bent four in the corner. If white misdefends the top left will become ko, not bent four – with a stone at 1-3 a dead bent four cannot arise. This is an important point to understand – it is easy to confuse the dead bent four in the corner shapes (as defined in the Japanese rule set – they are dead because the implied ko has not yet been initiated, and only the attacking side can initiate the ko) with related ko situations which are not dead as they stand since the ko is already in progress or can be initiated by either side.

    If a bent four did arise (perhaps via the good old sleeve tesuji), the positions at the bottom would not be relevant to the interpretation of the rule, since the question that matters is whether white has an unremovable ko threat at the end of the game. The kos at the bottom will be resolved at the end of the game, and no unremovable ko threat will remain. In theory, a seki provides an unremovable ko threat that refutes the argument behind the Japanese rule, but if the bottom right becomes seki the cost of white making a ko threat there would be bigger than the ko being fought (black would allow the top left to live and kill the bottom right instead) so in this case the rule makes sense even if the justification is convoluted.

  2. Steve says:

    I don’t see why a bent-four can’t arise with incorrect defence by White. If black extends to the 2-1 point, and White responds at the empty 3-1 point, hoping for a ko when Black throws in at the 2-1 point, Black can simply extend to the 1-1 point instead, and the result is a bent-four in the corner. See the first diagram on Sensei’s Library bent-four page to see what I mean.

    So, assuming that a bent-four did arise as above, and a seki formed in the bottom right. Then, by Japanese rules, the top left is dead, giving black 20 points there, and the bottom right is a seki, so no points for either. Net: Black is 20 points ahead in those 2 corners.

    Under other rules, everything gets finished off, except the bottom right seki and the bent four. Black creates a bent-four shape in the top left, White captures, Black plays on the 2-1 point, White throws in at the 1-1, and Black captures. Now, if White passes, black captures, and the position is the same as above. Now what happens depends on what shape was formed in the bottom right, correct? If Black has made a bulky five shape by taking and connecting the ko, approaching it is not a ko-threat – Black will connect the ko at the top, and when White captures the bulky five, Black will play on the vital point, and both of White’s groups die.

    But what if the ko in the bottom right is still lying there (would it be?)? Then the approach is a ko threat. Then Black would respond by capturing the ko in the bottom right, White would capture the ko in the top left, Black would create a bulky five in the bottom right, and White would capture in the top left. Then White has 6(?) points in the top left (3 points+captures), and black has 20 in the bottom right, so net +14 for Black. So the position in the bottom right could be used by White to gain 6 points if it weren’t for the Japanese rules?

    Unfortunately, my counting isn’t so good, and this stuff is really tricky for me. Now I’m confused again…

  3. konrad says:

    Sorry, I screwed up twice – what I said about no bent four if there is a stone at 3-1 is rubbish – for white to play at the other 3-1 didn’t occur to me – as you point out, black would play at 1-1 and the group is dead. But if black throws in at 2-1 instead there is no ko, since white has 2 outside liberties and can live by squeezing at 3-2. Instead, I only looked at white throwing in at 1-1 immediately, which does become ko because black has time to take away an outside liberty, preventing the squeeze. So white should just play 4-1 for seki.

    Regarding the bottom right, yes, the seki shape is bulky five so white’s approach can never be a ko threat anyway.

    You’ve succeeded in confusing me re the thousand year ko – my understanding was that the game isn’t over until it is resolved (i.e. it cannot still be lying there at the end of the game), but there is a possible complication if white has no ko threats and black has an unremovable ko threat at the end of the game, then black could potentially claim that white is dead as it stands and refuse to spend another move there. I don’t know how Japanese rules would resolve this – my guess is that they would reject the claim since they don’t seem to entertain the idea of unremovable ko threats, and that black would have to play the three moves required to take the group off the board.

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