(Assume white cannot connect to the outside or threaten the life of the black strings.)
1. What's the miai value of versus black playing there?
2. What's black's best continuation if he answers locally?
Bill: Is it OK to alter the diagram like so? That's a much easier question to answer.
Calvin: (11k). Yes, you can change it. However, now that I look at it more, there's a special sequence in the first example, so maybe it's not so good. To be specific, I'm just trying to gauge approximate value of ignoring a second-line block move in general. (If that makes any sense.) You can assume the right hand side of the board is infinite if that helps. Is this an easier one? Feel free to simplify it more, and maybe add it to the miai values list pages. If this situation is equivalent to one of the examples there and I've just missed it, let me know. It's most similar I guess to Corner12ConnectionValue, but with an open edge, and not just in the immediate corner, so intuitively I'd expect it to be larger than the 2.67 given for the corner.
emeraldemon: Before we can count the value, we have to know the best play for both sides. Is above sente? If so, maybe a play like:
reconnects. Does this seem like a reasonable play?
Chris Schack: I think it depends on how likely the ko ( at ) is to be fought. Avoiding that ko costs a couple of points.
Ok, here goes. I can't really imagine how to deal with infinite territory, so I decided I'd rather take an easier problem, and we can maybe extrapolate from there. So first, the following position, where black avoids the ko at all costs:
By my calculations, the local count is +0.03125, and the temperature is 7.96875.
Here are the relevant plays. It's kindof a lot, so bear with me:
So if I've done everything correctly, when white is komaster, the position above has a temperature slightly less than 8 points. If nobody sees serious flaws in this, I'll try to work out the sequence when black is komaster, but if I'm doing something wrong, someone please stop me before I invest too much more time in this!