BQM 253

    Keywords: EndGame, Question
[Diagram]
value?  

(Assume white cannot connect to the outside or threaten the life of the black strings.)

1. What's the miai value of W1 versus black playing there?

2. What's black's best continuation if he answers locally?


[Diagram]
value?  

Bill: Is it OK to alter the diagram like so? That's a much easier question to answer.


[Diagram]

value?

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.

Bill: Thanks, Calvin. I'm glad you are interested in an approximate value. These things are not so easy. (Comparable to the monkey jump in difficulty.)



emeraldemon: Before we can count the value, we have to know the best play for both sides. Is W1 above sente? If so, maybe a play like:

[Diagram]

A possible continuation

W5 reconnects. Does this seem like a reasonable play?

Chris Schack: I think it depends on how likely the ko (W5 at B6) is to be fought. Avoiding that ko costs a couple of points.


[Diagram]

W komaster


emeraldemon: Good point. It seems like if white is komaster this sequence is bad for black.
So maybe B4 has to be somewhere else?

[Diagram]

W komaster

W7 connects



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:

[Diagram]
Initial Position  

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:

[Diagram]
Black plays  

Local Count +8


[Diagram]
White plays  

W1 here is sente. Now the temperature is 1.96875, and the count is 0.03125


[Diagram]
Continuation: black followup  

W2 Tennuki, B3 sente, Count=+2


[Diagram]
Continuation: black followup  

B3 sente, Count = +1


[Diagram]
Continuation: black followup  

B3 tennuki, B5 sente, count = 0


[Diagram]
Continuation: black followup  

B3, B5 tennuki, B7 sente, count = -1


[Diagram]
Continuation: black followup  

B3, B5, B7 tennuki, B9 sente count = -2


[Diagram]
Continuation: black followup  

B3, B5, B7, B9 tennuki, W10 & B11 sente, count = -3


[Diagram]
Continuation: white followup  

W3 tennuki, B4 sente, count = -1

[Diagram]
Continuation: white followup  

W3 & B4 sente, count = -1.5

[Diagram]
Continuation: white followup  

B2 tennuki, B4 sente, count = -2.875


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!

emeraldemon


BQM 253 last edited by Dieter on July 5, 2008 - 12:48
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