This is from the problems within the WBaduk client. Specifically this is question 190 from the 19k-15k set.

The problem asks for black life but I am confused how this isn't a dual life problem?

The answer is black S4 then white goes to R1 and black makes life by playing S2. I don't understand why white doesn't play S2 instead.

You are correct that white S2 does lead to seki. In life and death problems, seki is usually seen as "good enough" for life. There are some problems that ask you to avoid seki, but in this case it seems fine. Black can't do better.

I don't see why white doesn't play that way. Either way white gets sente and this way black has the possibility of a half point ko for later.

Perhaps white fears that black will use the threat of ending the seki at R3 as a ko threat in some larger fight? But that would be a strange ko threat - you basically never want to do that.

Or maybe white wants the extra liberty at the 1-1 point for his outside wall?

It could also just be the variation the problem writers wanted to include. Maybe they thought seki wouldn't be a good answer for 19-15k players?

_________________
"You have to walk before you can run. Black 1 was a walking move.
I blushed inwardly to recall the ignorant thoughts that had gone through
my mind before, when I had not realized the true worth of Black 1."
-Kageyama Toshiro on proper moves

at S4 is fine for me but I don't understand how at S2 would lead to seki ?
I would then play and that all over for white isn'it ...

Click Here To Show Diagram Code

[go]$$Bc
$$ . . . . . . . |
$$ . . . . O O O |
$$ . . . . O X X |
$$ . . . O X 1 . |
$$ . . . O X . X |
$$ . . . O X 2 O |
$$ . . . O 3 O . |
$$ --------------[/go]

_________________
Converting the book Shape UP! by Charles Matthews/Seong-June Kim
to the gobook format. last updated april 2015 - Index of shapes, p.211 / 216

Can black put white in atari to capture him?

_________________
"You have to walk before you can run. Black 1 was a walking move.
I blushed inwardly to recall the ignorant thoughts that had gone through
my mind before, when I had not realized the true worth of Black 1."
-Kageyama Toshiro on proper moves

of course he can't ... seky... or maybe...

_________________
Converting the book Shape UP! by Charles Matthews/Seong-June Kim
to the gobook format. last updated april 2015 - Index of shapes, p.211 / 216

This problem is also featured in Lee Changho's Life and Death series, vol.1, problem 37 on pp.75-76. The solution given there is the same as the one proposed by the WBaduk client. If anyone can read Chinese, you might find more on this in the book.

The variation leading to seki is one point better for white, and white retains sente in both variations, so I don't understand why the authors would choose this variation.