A very good example of something that really falls on the border of being an empty triangle.jlt wrote:$$B
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X . . X . . , . . . . . , . . . |
$$ | . . X X . X . . . . O . . . . . O . . |
$$ | . . . . O O X X X O . . . . . X . . . |
$$ | . . . . . . . O O X O . . . . X O . . |
$$ | . . . . . . O . . X O . . . . X O . . |
$$ | . . . O . . . . X . O . . . . . O . . |
$$ | . . O , . O O X . , . . . . X , . . . |
$$ | . X . W B B O X . . O . X . . X . . . |
$$ | . . X . 1 . X . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . O X . . X . . , . . . . . , . . . |
$$ | . . X X . X . . . . O . . . . . O . . |
$$ | . . . . O O X X X O . . . . . X . . . |
$$ | . . . . . . . O O X O . . . . X O . . |
$$ | . . . . . . O . . X O . . . . X O . . |
$$ | . . . O . . . . X . O . . . . . O . . |
$$ | . . O , . O O X . , . . . . X , . . . |
$$ | . X . W B B O X . . O . X . . X . . . |
$$ | . . X . 1 . X . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Is this an empty triangle?
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Knotwilg
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Re: Is this an empty triangle?
A very good example of something that really falls on the border of being an empty triangle.jlt wrote:
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Knotwilg
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jlt
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dhu163
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Re: Is this an empty triangle?
Back to Uberdude's original example, my graph theory-ish explanation for why an empty triangle is good shape here is:
1) The eyespace is already "empty triangle like", being enclosed on all sides. Playing in the middle only makes a few more empty triangles, but the shape was already a bit overconcentrated.
2) The group is almost dead, and that is when one move can have a very large value.
___
From the perspective of nakade vital points, one move is worth so much when it is adjacent to all the eyespace. Then when either side plays there, it will shift control on all the eyespace. When white has no back-up eye, turning one eye into two is important.
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(Edit:20220213, building on hyperpape)
A healthy group with space around doesn't have to worry about making two eyes just yet and instead needs to ensure connection (to save dangling dragons) and successfully blocking off large territories.
Empty triangles are a valid criticism for both of these points :
1) empty triangles are over connected
2) empty triangles are slow to surround territory.
However here we have a life and death problem where a group is on the boundary of life and death. A different sort of rulebook (NP style) comes into play here, when a large group is surrounded and urgently needs to make eyes locally.
These situations are harder to recognise than others, can require seemingly unlimited reading, and yet can also be of critical importance. Hence why tsumego is valuable for building strength, even if it can feel like squeezing your brain into a fractured glass pane.
1) The eyespace is already "empty triangle like", being enclosed on all sides. Playing in the middle only makes a few more empty triangles, but the shape was already a bit overconcentrated.
2) The group is almost dead, and that is when one move can have a very large value.
___
From the perspective of nakade vital points, one move is worth so much when it is adjacent to all the eyespace. Then when either side plays there, it will shift control on all the eyespace. When white has no back-up eye, turning one eye into two is important.
---
(Edit:20220213, building on hyperpape)
A healthy group with space around doesn't have to worry about making two eyes just yet and instead needs to ensure connection (to save dangling dragons) and successfully blocking off large territories.
Empty triangles are a valid criticism for both of these points :
1) empty triangles are over connected
2) empty triangles are slow to surround territory.
However here we have a life and death problem where a group is on the boundary of life and death. A different sort of rulebook (NP style) comes into play here, when a large group is surrounded and urgently needs to make eyes locally.
These situations are harder to recognise than others, can require seemingly unlimited reading, and yet can also be of critical importance. Hence why tsumego is valuable for building strength, even if it can feel like squeezing your brain into a fractured glass pane.
Last edited by dhu163 on Sun Feb 13, 2022 3:48 pm, edited 2 times in total.
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hyperpape
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Re: Is this an empty triangle?
One conciliatory option is to say "it is an empty triangle, but it would be unhelpful to mention it." In such cases, competent speakers may disagree, as there's very little practical difference between "it's true but not worth mentioning" and "it's false." For more background on why one might say that, here's a great introduction to a bit of philosophy: https://aeon.co/ideas/what-we-say-vs-wh ... mplicature.