Joseki-related life-and-death example 1

Joseki.  

This is a common 4-4 point enclosure joseki.

Joseki.  

can also be played at a. In fact, it is the most common reply in professional games.

can also be played at b.

ends the joseki.

Discussion I

White is alive.  

The group in the corner is alive, as discussed in L+2 group.

However, a Black descent at a is a threat to the White group.

Ko.  

If White tenukis, Black can start a two-stage ko with the sequence from to .

Dead.  

The atari at is a mistake. After , white is caught in a shortage of liberties and is unable to play at a.

Discussion II

Diagram 1: White is alive.  

Diagram 1: In this diagram, White is alive too. (See J+1 group.)

However, the descent at a threatens to kill unconditionally. ^[1]

Diagram 2: Dead.  

The throw-in at followed by the placement at is the tesuji. After which, a and b are miai, while c and d are also miai. White dies in a bent four in the corner dead shape.

dia 3: Black starts with a  

tderz: White will have about 5-6 points. (depending on the timing of the n-m-p exchange).

Black ends in sente.

dia 4: Black starts with b  

tderz: White will have about 4-1=3 points or less (depending on the timing of the n-m-p exchange).

Black ends in gote.

Conclusion: starting with b in dia.^[1] seems to be about 2 points better for Black, and it seems to me that Black is relatively free to chose when to play, because White has no sente variation herself for improvement.

I hope that no errors crept in.