L+2 Group / Discussion

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First hane  

aLegendWai: How about if B2 plays at a? Will it live? If both can make Black live, which is better and why? Thanks for the answer.

unkx80: The following two diagrams should show the difference.

First hane  
First hane  

Second hane: failure  

[13] Answering this hane at 1-2 leads to disaster. Black can't play 8 at a because of shortage of liberties. If Black 6 at a, White 7 at 6 kills: see rectangular six in the corner.

I may be missing the bleeding obvious here - but doesn't Black 6 at 7 give life for black?

Improvement over dia (13)  

[14] tderz: Above right variation would be an improvement over dia [13] (= this left diagram).

W6 is a mistake here, if W8 does not lead to an escape or link-up.
Imagine a black attack at h or i.
Please note the usefulness of positional strength, i.e. black+square here.

Indeed, as Dieter suggested below, a black stone at g surely prevents a white escape and enables Black to proceed at B9 (kill).

I think it is this possible danger which makes W2 here so inferior.

best exchange for both?  

tderz: Hence White should play W6 now (the move in discussion).
Black could rest the case for now.
(a black+circle is present here)
If later black a and white b - black c are exchanged, white is left with 5 points.

Thin vs. strong life

RichardHunter: A Japanese book I have says this B2 also lives but is thin. The reason is at both b and c are sente, which is not the case if Black plays the 2-2 point as above.

Bill: I set up a difference game, but the advantage of the 2-2 is not so clear to me.

Difference game  

[11] For instance, B1 threatens to kill, but W2 protects the group. Now Black would have an advantage if he could play B3 with sente, but White plays W4, probably leading to mutual damage.

better display of difference?  

tderz: Black rather does something else (e.g. dia [14]) than descend to B1 in dia [11] above.

better display of difference???  

Bill: W2 returns to equity, no? Does Black have better than B3 - W4 ?

tderz: These are two separate questions:

  • With W2 on the right side White will get about 6 points in the corner at the price of gote.

This is not a likely sequence, because Black has no killing follow-up if White were tenuki-ing with W2.

Bill: In a difference game, all the second player has to do is stay even. Also, tenuki is not an option in a difference game. It's the only game in town.

tderz: I was not aware of the term/concept difference game when I used your 2-in-1-diagram,
I just liked the lay-out of it.
With regard to your It's the only game in town.,
I am too interested in the best variation,
which still might depend on factors not present in the diagram, see your [16].
What I am comparing here, is the right side with the right side of dia [11].
Sorry, if I gave the wrong impression of misusing difference game diagrams.

Bill: I did not notice until your comments that the link to the difference game page had been lost. I restored it. :-)

tderz:Still, I find B1 here better than sagari-B1 in dia [11] above. My reasoning is explained below in the ko variant which is life-threatening for White. The final answer to the question to which one would be better (sagari-B1 [11] or e.g. connection B1 here) lies in any actual game position where these positions would occur,

Bill: Except for questions of kos and threats, if one side is better in a difference game, the corresponding play is better. The difference game will tell you when whether one play is better or not depends on the whole game position. tderz: I took the freedom to emphasize your correct statement. I fully agree. Bill: I wrote that late at night, and didn't write exactly what I meant. I think you'll still agree, but let's talk on the difference game /discussion page.

i.e. which side is the bigger and/or more important one for black (top-left or below-right).

  • same reasoning for the question B3-W4 or Black h-White i (on the left).
better display of difference?  

tderz: The left corner has 6 points, the right corner will have most likely only obtain 5 points. (I just realized that Black had an extra move)

Bill: Yes. Two B3 s. ;-)

This is a definitive loss of 1 point.
The life-threatening exchange black a, white b is at black's deliberation.

If White now plays s.th. elses than W2, e.g. W2 at B3, then the extra weakness of the corner comes into play:

white tries too hard?  

tderz: The throw-in B3 has L&D implications.

white tries too hard?  

tderz: Black could play freely, White had to fear death by p- q-r

white tries too hard?  


white tries too hard?  

tderz: White eventually gives in,
Black plays B3 or s.

The evaluation of this outcome seems to depend much on the overall position:
Black has played an extra move black+circle,
White has got 5 points + a captured prisoner at s,
Black's position is reinforced.

Conclusion: no clear answer from me :-) ,
except that I find this variant better than dia [11] above.



Good question. If B1 here, White makes a bulky five inside Black's eyespace. Black can not play at a because of shortage of liberties. What I said is wrong !! --Dieter

Dieter -- black will not play at a, but capture -- white 4 is a snapback. I still see this as black lives. Dieter: Yes I noticed, but didn't have the time to re-edit my stuff. Hence the exclamation above.

Second hane: failure?  

Bill: How about B 6? Dieter: see above (though you were first). Maybe a white stone at b is appropriate to prevent escape. WRONG. Needs edit Dieter

Second hane: failure?  

L+2 Group / Discussion last edited by imabuddha on September 27, 2010 - 04:39
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