I'm stuck, and I'm wondering if someone would set me straight?

I have come to understand that in the 4-4 6-3 enclosure the best white can do without outside support is ko with the 3-3 invasion. I have interpreted this to mean that the only way white can live is by fighting a ko and if white avoids ko, white will die.

In my journal, I'm trying to work through the various 3-3 invasion scenarios for the 4-4 small knight enclosure: https://lifein19x19.com/viewtopic.php?p=219875#p219875

Schachus helpfully pointed out that in my first pass through these, I had ignored a clamp in one line which was easily fixed. Unfortunately, the same move (white clamp at B) raises a question about how black should respond to this sequence:

Click Here To Show Diagram Code

[go]$$Bc
$$ --------------------+
$$ . . . . . . . . . . |
$$ . . . . . a . . . . |
$$ . . . . X 3 2 O 6 . |
$$ , . . . . . X 1 4 c |
$$ . . . . . . . . 5 . |
$$ . . . . . . . . b . |
$$ . . . . . . . . . . |[/go]

As far as I can see on my own, A allows white to get out with the clamp at B. However, defending against the clamp seems to allow white to live unconditionally. The best I can come up with to defend the cut is to play C, but this seems to allow white to create the following living shape (or at least a shape I can't figure out how to turn into at least a ko for life):

Click Here To Show Diagram Code

[go]$$Wc
$$
$$ --------------------+
$$ . . . . . . 5 . . . |
$$ . . . . 4 3 . . . . |
$$ . . . . X X O O O 1 |
$$ , . . . . . X X O X |
$$ . . . . . . . . X 2 |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |[/go]

For reference, I found two prior discussions of this in L19, but at least to me, they don't seem to quite answer the question:

1. Shoryuu: https://lifein19x19.com/forum/viewtopic.php?p=141169#p141169. The posted SGF includes a sequence in which black plays A in the first diagram, but like my first attempt, does not consider the possibility of the clamp at B at all. And the discussion in that thread focuses on another line.

2. Uberdude: https://lifein19x19.com/viewtopic.php?p=209237#p209237. This again focuses on a different line, but one variation transposes into the first diagram. At this point, Uberdude agrees that A above is the right move and that the clamp at B is a feasible escape route. This is the same conclusion I came to above, but doesn't this then contradict the idea of ko being the best white can do in this situation? Uberdude does make the comment that the second line crawl necessary for escape is "worse than death". Is the answer just that the best white can do is ko is not meant to be taken as "if white tries to avoid a ko, white dies", but rather, "if white tries to avoid a ko, white dies or suffers a fate worse than death"?

You're correct in that protecting the 'b' clamp with a move like R14 does let White live, but the idea is that you can just play Q18 and let White play S14. You can respond to S14 with R14 or R15, and either let White desperately try to make a second eye on the second line while B gets thickness, or if you're stronger in the surrounding area, consider a sequence like S14, R14, T15, R15, S13, S11 to go for the kill. Both situations in general are optimistic for B.

Thanks for double checking this. Your argument definitely make sense, and it is the gist of Uberdude's post that I referenced. I guess the answer here is just that white can live unconditionally, but it's painful. So, my original interpretation of "the best white can do is ko" as "white can only live through ko" is incorrect. Rather, ko is best because the routes to unconditional life are inferior rather than nonexistent. That is an important distinction!

Click Here To Show Diagram Code

[go]$$Bc
$$ --------------------+
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . X 3 2 O 6 . |
$$ , . . . . . X 1 4 . |
$$ . . . . . . . . 5 . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |[/go]

This rarely occurs in pro games, but when it does, . . .

Click Here To Show Diagram Code

[go]$$Bc
$$ --------------------+
$$ . . . . . . . . . . |
$$ . . . . . . 8 . . . |
$$ . . . . X 3 2 O 6 . |
$$ , . . . . . X 1 4 . |
$$ . . . . . . . . 5 . |
$$ . . . . . . . 7 . . |
$$ . . . . . . . . . . |[/go]

This is the continuation, in the games at http://ps.waltheri.net/ .

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Everything with love. Stay safe.

Interesting. I eventually found the following sequence in a joseki dictionary (Takao Shinji, The 21st Century Dictionary of Joseki). But yours seems more flexible while still being unconditionally alive.

Click Here To Show Diagram Code

[go]$$Bc
$$ --------------------+
$$ . . . . . . . . . . |
$$ . . . . 9 8 0 . . . |
$$ . . . . X 3 2 O 6 . |
$$ , . . . . . X 1 4 . |
$$ . . . . . . . . 5 . |
$$ . . . . . . . 7 . . |
$$ . . . . . . . . . . |[/go]