All you need to know about Carpenter's Square - 11

Diagram 11.1: White to play

How does the extra bend at Black square affect the outcome?

Diagram 11.2: Solution 1

Black 2 is normally not a good move in standard Carpenter's square shapes covered earlier but it is good now. Black 6 is important to help form a seki. If White 7 plays Black 8 instead, black simply plays 'a' and white is one liberty too short in the capturing race.

Diagram 11.3: Solution 2

If white plays White 3 black needs to be careful. Black 4 is a calm move. In the end 'a' and 'b' are miai so black is unconditionally alive.

Diagram 11.4: Black fails (8=3)

If black is tricked into playing Black 4 , following White 5 and White 7 , both forcing moves, White 9 is good. Black can win the capturing race by playing 'a' but that is a T-four dead shape. So black corner is completely dead.

Diagram 11.5: Black fails too

Black 2 from the other side is normally incorrect. White 5 is the best point. Apart from Black 6 , playing anywhere else would result in a big-eye killing shape (please verify). So there is a messy ko fight now. In practice, if black isn't happy with Solution 1 (where all his points are gone), and he has plenty of ko threats, it may be worthwhile to try this diagram. This corner is a two-stage ko, and for black to win an approach move is needed. So winning this ko won't be easy for either side, a good way for black to complicate situations on the board.

Conclusion: Black's corner should be unconditionally alive, unless he chooses other options.