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 Post subject: To capture or not to capture?
Post #1 Posted: Fri Feb 21, 2020 2:50 am 
Lives in sente
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I recently watched videos about this joseki

Click Here To Show Diagram Code
[go]$$Bc
$$ | . . . . . . . . . . . . .
$$ | . . 2 . . . . . . . . . .
$$ | . . . . . . . . . . . . .
$$ | . . . O 8 . . . . , . . .
$$ | . 0 4 3 6 1 . . . . . . .
$$ | . . 5 7 9 . . . . . . . .
$$ | . . . . . . . . . . . . .
$$ ---------------------------[/go]


Click Here To Show Diagram Code
[go]$$Bcm11
$$ | . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . .
$$ | . . . 9 0 . . . . . . . .
$$ | . 6 5 O O 1 . . . , . . .
$$ | . O O X O X 8 3 . 7 . . .
$$ | . . X X X . 2 4 . . . . .
$$ | . . . . . . . . . . . . .
$$ --------------------------[/go]


Click Here To Show Diagram Code
[go]$$Bcm21
$$ | . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . .
$$ | . . . X O . . . . . . . .
$$ | . O X O O X 5 1 . , . . .
$$ | . O O X O X O X . X . . .
$$ | . 4 X X X 2 O O 3 . . . .
$$ | . . 6 . . . . . . . . . .
$$ ---------------------------[/go]


However, people say that White should not capture at :w26: at early stages of the game (or that the joseki should be interrupted earlier) because there are usually bigger points elsewhere. I was a bit puzzled by this statement, since the difference between White capturing four stones and Black capturing four stones is 16 points, which is bigger than twice komi (14 points), so to convince myself I asked Katago(d) for clarification. Here is an artificial whole board position.

Click Here To Show Diagram Code
[go]$$Wc White to play
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . f . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . O X O O X X X . , . . . . . X . . . |
$$ | . O O X O X O X . X . . . . . . . . . |
$$ | . O X X X O O O X . . . . . . . . . . |
$$ | . . a c e . d b . . . . . . . . . . . |
$$ ---------------------------------------[/go]


After a few thousand playouts, Katago thinks that

  • f is 1.8 points better than a.
  • After the exchange a-b, f is 0.7 point better than c.
  • After the a-b-c-d, f is 4.7 points worse than e.

It seems Katago evaluates the first ko threat at 5.4 points and the second one at 1.1 point, but I am not sure this conclusion is valid, things are not clear in my mind. In any case, taking directly 4 stones off the board is significantly more valuable than needing a sequence of alternating plays to remove them.

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 Post subject: Re: To capture or not to capture?
Post #2 Posted: Fri Feb 21, 2020 3:17 am 
Honinbo

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jlt wrote:
I recently watched videos about this joseki

Click Here To Show Diagram Code
[go]$$Bc
$$ | . . . . . . . . . . . . .
$$ | . . 2 . . . . . . . . . .
$$ | . . . . . . . . . . . . .
$$ | . . . O 8 . . . . , . . .
$$ | . 0 4 3 6 1 . . . . . . .
$$ | . . 5 7 9 . . . . . . . .
$$ | . . . . . . . . . . . . .
$$ ---------------------------[/go]


Click Here To Show Diagram Code
[go]$$Bcm11
$$ | . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . .
$$ | . . . 9 0 . . . . . . . .
$$ | . 6 5 O O 1 . . . , . . .
$$ | . O O X O X 8 3 . 7 . . .
$$ | . . X X X . 2 4 . . . . .
$$ | . . . . . . . . . . . . .
$$ --------------------------[/go]


Click Here To Show Diagram Code
[go]$$Bcm21
$$ | . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . .
$$ | . . . X O . . . . . . . .
$$ | . O X O O X 5 1 . , . . .
$$ | . O O X O X O X . X . . .
$$ | . 4 X X X 2 O O 3 . . . .
$$ | . . 6 . . . . . . . . . .
$$ ---------------------------[/go]


However, people say that White should not capture at :w26: at early stages of the game (or that the joseki should be interrupted earlier) because there are usually bigger points elsewhere. I was a bit puzzled by this statement, since the difference between White capturing four stones and Black capturing four stones is 16 points, which is bigger than twice komi (14 points),


You are talking about the swing, although there is more to it that just taking stones. To compare it with, say, the first move in the game, you have to divide by two. The comparison, then, is between 14 pts. and 8 pts. plus.

Edit: I do not have an explanation for KataGo's evaluations.

Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . 1 . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . f . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . O X O O X X X . , . . . . . X . . . |
$$ | . O O X O X O X . X . . . . . . . . . |
$$ | . O X X X O O O X . . . . . . . . . . |
$$ | . . a c e . d b . . . . . . . . . . . |
$$ ---------------------------------------[/go]


How does KataGo compare :b1: with b, etc.?

_________________
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 Post subject: Re: To capture or not to capture?
Post #3 Posted: Fri Feb 21, 2020 3:47 am 
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Concerning your last question: according to Katago after a few thousand playouts,

:b1: is better than b by 0.5 point.
After b-a, :b1: is worse than d by 0.2 point.
After b-a-d-c, :b1: is worse than d by 5.7 points.


P.S. In the initial post, I indeed forgot to divide by 2. The difference between (White captures, Black passes, White to play) and (White passes, Black captures, White to play) is 16 points plus something, so White should capture when the cost of passing is less than about 8 points. On an empty board, the cost of passing is twice (fair komi), which is about 14 points.


This post by jlt was liked by: Bill Spight
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 Post subject: Re: To capture or not to capture?
Post #4 Posted: Fri Feb 21, 2020 7:00 am 
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I used a 40b256c network from KataGo that is in the middle of training right now, for around 50k playouts on each move.

Click Here To Show Diagram Code
[go]$$Wc Base position
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . f . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . i j . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . O X O O X X X . , . . . . . X . . . |
$$ | . O O X O X O X . X . . . . . . h . . |
$$ | . O X X X O O O X . . . . . . . . . . |
$$ | . . a c e g d b . . . . . . . . . . . |
$$ ---------------------------------------[/go]


  • Base position: B+3.2. White wants to play h (but f is also just as good).
  • After white a: B+5.0, so white lost about 2 points by playing in the lower left. Black now wants to play j (but i is also about as good).
  • After white a, black b: B+2.0, so black lost about 3 points by playing in the lower left. White now wants to play h (f is now judged between 0.5 to 1.0 points worse than h, or about 4% winrate).
  • After white a, black b, white c: B+3.0, so white lost about 1 point by playing in the lower left. Black wants to play i (but j is also about as good).
  • After white a, black b, white c, black d: B-3.0, so black lost about 6 points by playing in the lower left. White should just respond and capture at e. (white playing h would be about 3 points worse, playing f would be about 5.5 points worse).

So:

It is repeatedly the case that playing in the lower left is too small. The per-move value of the raw territory in the lower left is something like 9 points (8 points due to the capture swing, 1 from territory on the first line). Which is quite a bit too small for the opening. The reason why playing elsewhere is only often 1 or 2 points worse is that there is extra value beyond the 9 points in outside forcing moves and group safety from resolving the capture. So this all makes sense.

The a-b exchange costs black 1 point. The c-d exchange costs black another 5 points, at which point capturing is actually the largest move for white, white no longer wants to tenuki. Why?

Click Here To Show Diagram Code
[go]$$Bc Future forcing move
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . 1 . f . . . . . . . . . . . . |
$$ | . . . X O e . . . . . . . . . . . . . |
$$ | . O X O O X X X . , . . . . . X . . . |
$$ | . O O X O X O X . X . . . . . . . . . |
$$ | . O X X X O O O X . . . . . . . . . . |
$$ | . . a c . . d b . . . . . . . . . . . |
$$ ---------------------------------------[/go]


I'm pretty sure the answer is that KataGo senses that exchanging a-b in the lower left might in some variations reduce the effectiveness value of this forcing move when white resists by coming out at 'e', because black's stones down there have one fewer liberty. I'd be far from sure "1 point" is the right value for this, because it seems to me black can still follow with 'f' with about the same effect. So I don't entirely trust KataGo here, but it also seems plausible to me that it's right, there could well be variations where it matters.

And exchanging c-d further is very bad for black, now white wants to respond locally to finish the capture, and then black entirely loses out on this forcing move, which would be helpful in building the center and limiting white's left side.


This post by lightvector was liked by 6 people: Bill Spight, dfan, Dusk Eagle, dutchie, jlt, Kirby
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