![[Diagram]](../../diagrams/41/8fc3a180310b503c7c8f3fe9434199ad.png)
Black to play and connect underneath
This move stands out to me because 'a' does not add any liberties to the white group.
![[Diagram]](../../diagrams/45/18c6bc8b0e62d922c8899b76e3580bce.png)
Black to play and connect underneath
The atari at 9 allows B to cut off 8. Playing 6 at 10 allows 7 at 6, cutting off the white stones as well.
![[Diagram]](../../diagrams/7/9ce11203c9f3c9d5837cf395663ee038.png)
Black to play and connect underneath
The atari at 'a' again forces white to connect at the marked stone, allowing black 'b' to kill off the white cutting stone.
![[Diagram]](../../diagrams/21/3026cd2a7fe30be186015c02f64f084b.png)
Black to play and connect underneath
3 @ the marked black stone.
Playing 1 on the other side still fails, as W cannot bridge under due to a connect-and-die.
Let's examine other responses.
![[Diagram]](../../diagrams/34/9905c048c8330690e6f21b4ae20d4f2a.png)
Black to play and connect underneath
This permutation reverts to above.
![[Diagram]](../../diagrams/19/63fe5debc7309a0e0d57ca5f3b2bd3f5.png)
Black to play and connect underneath
Easy variation for 6: a and b are miai to save 1 and sever the chain of W stones connected to 4. The continuations are given:
![[Diagram]](../../diagrams/17/7f77a652c09c5a814a0b6cb7be2ac2a9.png)
Black to play and connect underneath
4 at the marked spot; W's cutting stones are in a hopeless. situation.
![[Diagram]](../../diagrams/15/e3fc76bf36e9c6f2551116cf443883be.png)
Black to play and connect underneath
B has 7 liberties, W is trapped and has only 4.
![[Diagram]](../../diagrams/50/b2d2429f041f0325bd33a3b8ad0ea2ff.png)
Black to play and connect underneath
Little more complicated variation for 6. Pushing with 9 is key; if W plays a instead of blocking at 10, B connects underneath with 11 at 10.
![[Diagram]](../../diagrams/19/3a009de5412a6805ef93c136d375d5f5.png)
Black to play and connect underneath
If W insists on cutting B off by playing through 4, B returns the favor at 5, triggering a race. However, W only has 3 liberties to B's 5 or more. W cannot escape. 2 at 4 leads to 3 at 'a', postponing the inevitable.
![[Diagram]](../../diagrams/3/eb5bfe9787df6dc94aaa64a5404009dd.png)
Black to play and connect underneath
unkx80: I am not sure about your claim that Black has at least 5 liberties. It seems to me that
and
causes Black to have only 2 liberties.
![[Diagram]](../../diagrams/19/9fb6f19ac39ba2759fefee829cc43da3.png)
Black to play and connect underneath
After B at 'a', W at 'b', B at 'c', d and e are miai to trigger the capturing race, reverting to previous diagrams.
![[Diagram]](../../diagrams/52/c9b318a650f10b2f23a4fcce9bd77eba.png)
Black to play and connect underneath
This placement of 6 seems complicated. See continuation...
![[Diagram]](../../diagrams/7/5a0b9338d9ab93123406ce1401dd9868.png)
Black to play and connect underneath
B sacrifices the marked stones to prevent W connecting at 'a'. If W connects at a, B at b is atari and W's position collapses.
![[Diagram]](../../diagrams/42/9d43aa36fd658c242fda29026a246d9e.png)
Black to play and connect underneath
5 at the marked spot. Instead, W saves his stones, but allows B to bridge under.
![[Diagram]](../../diagrams/37/20e77b67a3bca1f8989b9e86980ef3de.png)
Black to play and connect underneath
On second thought, seems like B@1 fails?
Attempt number 2!
![[Diagram]](../../diagrams/9/f8847ee13afd387fc79c6ef9bca6718e.png)
Black to play and connect underneath
Perhaps the move at 'a' is too early. Let's try at 1.
![[Diagram]](../../diagrams/43/93c8bdaf45e792b5182c3fa4a77c2002.png)
Black to play and connect underneath
If W hanes to the right, a and b are miai to cut off at least 1 white stone, ensuring the connection
![[Diagram]](../../diagrams/2/13f83bc341e939aae8502b97bc92ebe8.png)
Black to play and connect underneath
If W hanes to the left, 3 and the response at 4 play out slightly differently; now a and b are miai for black to cut, and b and c are miai for black to save the cutting stones. W's only hope is to play b.
![[Diagram]](../../diagrams/32/380616d5c13d1414e9bcbb82396c5f45.png)
Black to play and connect underneath
Unfortunately, after 4, W's marked group is in atari and cannot escape.
![[Diagram]](../../diagrams/3/10c96e768b78cbe6799c50812f0744ea.png)
Black to play and connect underneath
If 4 here, this sequence follows.
@ a,
@ marked stone,
@ b, cutting off
. I believe the 7-8 exchange can be omitted, but I don't see why B would do that.
![[Diagram]](../../diagrams/51/5aba32ef4239d5da18dbfb0cf263b24f.png)
Black to play and connect underneath
4, 6 here reverts to the above
![[Diagram]](../../diagrams/39/2f51b1bfad06b321a8e789fb2790b5ea.png)
Black to play and connect underneath
@ a,
@ b,
@ c. White's stones have been cut off and are hopeless.