Isn’t “group” polysemous and thus impossible to rigorously define? I think strings are easier to work with when you want to strictly define something
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Yes, my mistake. I should have said “string”. Thank you.
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You mean like using geometry or something more complicated?
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We had enough trouble with what a hane was, I’m not sure if we can handle trying to define a tiger’s mouth 
you might want to look at benson’s work at senseis libtary.
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I totally don’t understand the concept of “blind” eyes on that SL page:
Or better: either I don’t understand it, or it is not explained well, or it is nonsense 
“bb” here has the same value as “r”, inasmuch as the whole thing is unconditionally alive, i.e. never mind which “b” spot W may play, B can capture it and stay alive.
Whereas here:
W can play either left or right directly adjacent to the B stones marked with “x” and kill via Snapback.
Or what am I missing?
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There’s a ko threat for white at the right b, so r and b are not the same. But I don’t know how important that difference is for those eye concepts.
They’re different in Benson’s Algorithm because b is a vital region of one string but not the other, which will lead to the string it’s not a vital region of being eliminated for only having 1 vital region
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Oh, I see, yes, you’re right.
Yes, that also 
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I had to look up the concept in Sensei’s library before I could understand your sentence.
To my German speaking brain it’s missing commas.
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My sentence could have more commas, but I skimped on them in the first part to keep the first/second part demarcation clear, as I thought it would be more confusing if extra commas obscured where the correct break between the sections was
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Ultimately, Benson’s algorithm is not meant to classify life/death or the presence of eyes in a broader, general sense, but rather a more narrow definition of “pass-alive” or “unconditionally alive” groups, which refers to which stones cannot be captured even if the other player only passes.
When we usually speak about the general strategic notion of life, death, and eyes, we typically talk about a broader set of situations.
For example, in the below position, we would typically say that Black is settled and alive, since White cannot prevent Black from making two eyes, even if White plays first:
However, this position is not “unconditionally alive” (or “pass alive”), in the specific technical sense dealt with by Benson’s algorithm.
Note that in common discussion, Go players may often call the above position “unconditionally alive”, but they are using this phrase in a different sense (that Black is alive, regardless of who plays first).
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yes, I think Benson’s algorithm was relevant to the differences between b and r, though
And for example, here’s a group that is alive, and there is not even a ko threat against it, but it isn’t Benson-algorithm pass-alive.
(In addition to there being no ko threat, there is no move that threatens a subsequent ko threat. But white can move to threaten a subsequent move that threatens a subsequent ko threat - in theory this kind of thing could be relevant in some special higher-step ko situation).
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Good example; without Benson’s Algorithm I could see myself mistakenly thinking that was pass-alive, at least without looking closer
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I don’t get it. Does this apply to a ruleset where suicide is allowed?
No suicide required! If white gets 4 moves in a row, white can capture black.
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4 moves in a row? Which Go rules allow that?
Is this still about Go?
How it would come up in regular go is as Hexahedron described above: white makes a move that threatens to make a move that threatens to make a ko threat.
A situation where that is useful could look something like this:
Black can start a multi-step approach move ko in the lower left:
When it’s white’s turn to find a ko threat, she doesn’t have any direct threats but can start the slow process of creating a threat in the upper right:
Several moves later (see the full line here) black has made it into a direct ko, and now white needs to make use of the prepared ko threat at G9:
So that’s how one side can get multiple moves in a row in a regular game of go! The same idea can be extended to any number of moves in a row, if you make an approach-ko with enough steps. Here is a problem I made where black gets 24 moves in a row in the optimal line:
24 moves in a row
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The discussion is in the context of “pass-alive”, which is a much narrower definition of life checked for by Benson’s algorithm. See my post above that attempts to clarify: Mathematical definition of an eye - #32 by yebellz
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