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 Post subject: Behind the scenes of some endgame tesuji
Post #1 Posted: Sun Dec 29, 2019 5:19 pm 
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I'm re-reading 200 Endgame Problems. The first time round, many years ago, I went through it with a "spot the key move" attitude, and thought it was pretty easy. This time round, I'm setting the bar higher in terms of understanding why the key move is good, and seeing more of the variations, and I'm finding it much more challenging. Great to have a book that works on more than one level! I wonder if Shirae is trying to nudge us in the direction of effortful practice, in the same way that JF makes explicit in his variation-free Genjo-Chitoku?

Anyway, enough waffling. I'd like to take a dozen or so problems from the book and dig deeper, find the insights that aren't in the two solution diagrams per problem that you get. First up is part 1 problem 13.

Click Here To Show Diagram Code
[go]$$B Black to play
$$-----------------------+
$$ . . . . . . . . . . . |
$$ . . . . . O . . X X . |
$$ . O . . . O X X O O . |
$$ . . . . . O O O X . . |
$$ . . . . . . . . X . . |
$$ . . . . . . . O X . . |
$$ . . . . . . . . X . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Summary of book solution
Click Here To Show Diagram Code
[go]$$B Black to play
$$-----------------------+
$$ . . . . . . . a . . . |
$$ . . . . . O . c X X . |
$$ . O . . . O X X O O . |
$$ . . . . . O O O X b . |
$$ . . . . . . . . X . . |
$$ . . . . . . . O X . . |
$$ . . . . . . . . X . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]

Black a is the correct answer. Black b fails because it lets white squeeze at c. Black c fails less obviously: this is problem 14 in the book.

What's not discussed is this alternative move, a shape which appears as the solution to some later problems. What is white's reply to :b1: in the next diagram?
Click Here To Show Diagram Code
[go]$$B Black to play
$$-----------------------+
$$ . . . . . . 1 . . . . |
$$ . . . . . O . . X X . |
$$ . O . . . O X X O O . |
$$ . . . . . O O O X . . |
$$ . . . . . . . . X . . |
$$ . . . . . . . O X . . |
$$ . . . . . . . . X . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #2 Posted: Sun Dec 29, 2019 7:31 pm 
Gosei

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White's reply:
Click Here To Show Diagram Code
[go]$$
$$-----------------------+
$$ . . . . . . 1 . . . . |
$$ . . . . . O 2 . X X . |
$$ . O . . . O X X O O . |
$$ . . . . . O O O X . . |
$$ . . . . . . . . X . . |
$$ . . . . . . . O X . . |
$$ . . . . . . . . X . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


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

(hence black 1 is not the solution)

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #3 Posted: Mon Dec 30, 2019 5:05 am 
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Yes, that's it. Took me some effort to understand why it's actually a good result for white.

Next up, part 1 problem 30.
Click Here To Show Diagram Code
[go]$$B Black to play
$$-----------------------+
$$ . . . . . . . . . . . |
$$ . . . . . . . O X . . |
$$ . . O . . O . O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


This is what not to do:

Click Here To Show Diagram Code
[go]$$B The ordinary moves
$$-----------------------+
$$ . . . . . . 2 1 3 . . |
$$ . . . . . . 4 O X . . |
$$ . . O . . O . O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Here's the book solution:
Click Here To Show Diagram Code
[go]$$B Black gains ... how many points?
$$-----------------------+
$$ . . . . . 7 4 3 a . . |
$$ . . . . 8 1 5 O X . . |
$$ . . O . 2 O 6 O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]

Playing black, you might be tempted to connect at a now, to make sure :b7: doesn't get captured. But you should actually treat the position as gote, and probably shouldn't play a right away, depending on what else is on the board.

Now it might not be obvious at a glance that the solution is actually better than the ordinary moves. (At least, it wasn't obvious to me.) So this is a good counting exercise: how many points has black gained in the book solution compared with the ordinary moves?


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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #4 Posted: Mon Dec 30, 2019 10:57 am 
Gosei

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Black gains ...

Click Here To Show Diagram Code
[go]$$B The ordinary moves
$$-----------------------+
$$ . . . . x x 2 1 3 . . |
$$ . . . . x x 4 O X . . |
$$ . . O . x O x O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]

White 6 + 0 - 0 = 6 points

Click Here To Show Diagram Code
[go]$$Wm10 Black gains ... how many points?
$$-----------------------+
$$ . . . . 1 x 3 X 2 . . |
$$ . . . . O x x O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]

White 3 + 3 - 1 = 5 points
(3 territory + 3 black stones captured - 1 white stone captured)

Black gains 1 point

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #5 Posted: Mon Dec 30, 2019 11:17 am 
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@Gomoto: I think that Black gains more than that, because to capture the three stones, White has to take gote, but on the other hand Black can also take gote to save his three stones?

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #6 Posted: Mon Dec 30, 2019 12:16 pm 
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jlt wrote:
@Gomoto: I think that Black gains more than that, because to capture the three stones, White has to take gote, but on the other hand Black can also take gote to save his three stones?



My understanding in this situation is that...

Since it is not sente to capture the stones or to save them, we can treat it as equally likely that black or white will get there first. So there's a 50% chance we get a situation like what Gomoto showed:
Click Here To Show Diagram Code
[go]$$Wm1 white first
$$-----------------------+
$$ . . . . 1 x 3 X 2 . . |
$$ . . . . O x x O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


And there's a 50% chance we get a situation like this:
Click Here To Show Diagram Code
[go]$$Bm1 black first
$$-----------------------+
$$ . . . . 2 X 3 X 1 . . |
$$ . . . . O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


(2 and 3 in the last diagram are white's privilege, so white may save it for later - e.g. ko threat or something)

Given that, to evaluate the value of territory here, you take 50% of the first total, which Gomoto already calculated (50% of 5 points = 2.5) and add it to 50% of the territory total you'd get for black going first (50% of -1 points = -0.5) and add them together for a total of 2 points. That'd give an overall gain of 6-2 = 4 points.


I'm bad at endgame calculations, so I'd be interested in having my analysis corrected, if there are errors.

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #7 Posted: Mon Dec 30, 2019 1:27 pm 
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Since I didn't study endgame theory seriously, it would be a miracle if my answer was correct, but here it is anyway. At least one of us is wrong.

Start from the book solution, and suppose White has no ko threats (one of my problems is that I don't know how to treat the ko). We count the score locally, so that the "wrong answer" in xela's post has score W+6.

Click Here To Show Diagram Code
[go]$$B (one white stone captured)
$$-----------------------+
$$ . . . . . X . X . . . |
$$ . . . . O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Consider the following positions :

Click Here To Show Diagram Code
[go]$$W Position W
$$-----------------------+
$$ . . . . 1 X . X . . . |
$$ . . . . O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$B Position B
$$-----------------------+
$$ . . . . . X . X 1 . . |
$$ . . . . O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$W Position WW
$$-----------------------+
$$ . . . . O . 1 X . . . |
$$ . . . . O . . O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$B Position WB=BW
$$-----------------------+
$$ . . . . O X . X 1 . . |
$$ . . . . O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$B Position WBB: B+1
$$-----------------------+
$$ . . . . O X X X X . . |
$$ . . . . O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$W Position WWW: W+7
$$-----------------------+
$$ . . . . O . O 3 1 2 . |
$$ . . . . O . . O X 4 . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$B Position WWB=WBW: W+5
$$-----------------------+
$$ . . . . O . O X 1 . . |
$$ . . . . O . . O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]



Click Here To Show Diagram Code
[go]$$B Position BB: B+3
$$-----------------------+
$$ . . . 2 1 X 3 X X . . |
$$ . . . 4 O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


White's score at the final positions is:

WWW=7, WWB=WBW=5, WBB=-1, BB=-3.
So WW=(WWW+WWB)/2=6
BW=WB=(WBW+WBB)/2=2
W=4
B=-0.5
(the book's position) = 1.75

On the other hand, the wrong answer had a score equal to 6. So compared to the wrong answer, the book answer gains 4.25 points.

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #8 Posted: Mon Dec 30, 2019 2:19 pm 
Gosei

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I am a simple man. With the optimal answer black gains at least 1 point. And there is the additional potential for even more gains (Related to the rest of the board position.)

That is enough endgame theory for my needs :-)

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #9 Posted: Mon Dec 30, 2019 2:33 pm 
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In pure area scoring, Black only gain sente

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #10 Posted: Mon Dec 30, 2019 3:10 pm 
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Gomoto wrote:
That is enough endgame theory for my needs :-)

Well, I'm posting these because I'm interested in endgame theory and want to learn more :-) It's not that I need more endgame theory though, what I really need is to not lose all those middlegame fights, but that's a different conversation...

So for this one I get the same as Kirby. Of course that doesn't mean I'm correct, I'm still learning this stuff too. My first impression of jlt's analysis was that in the 1-2-3 sequences, move 1 reverses. So the WWW and BB diagrams should never happen with correct play.

It's the same as the basic hane-connect:
Click Here To Show Diagram Code
[go]$$B Three-move sequence
$$ X X X O O O
$$ . . 3 1 2 .
$$ -------------[/go]

You'd never analyse the following position:
Click Here To Show Diagram Code
[go]$$B White to play
$$ X X X O O O
$$ . . . 1 2 .
$$ -------------[/go]

because for black to play 1 and then abandon the position is a loss for black. If black 1 goes on the board and both players are making the best moves, then you'll always see 1-2-3 as a unit.

But actually, jlt's diagrams are not quite the same thing, because the 1-2 exchanges there don't actually make the position worse for the first player, they just make the position no better. I think that in a whole-board position where the other moves are small enough that 1 is the best local move, then 2 would be sente, which is why you'd still treat 1-2-3 as a unit for counting purposes (although in practice you could play 1, leave it alone for a while, then do 2-3 later). So not technically a "reverse", but same effect.

I haven't read it yet, but I believe Robert Jasiek's Endgame 3 has some theory on "long sequences" which goes into this in more depth. And someone please tell me if I'm overthinking this.

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #11 Posted: Mon Dec 30, 2019 5:40 pm 
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You could actually analyze that position, xela; it is useful to know sometimes how much a lossy ko threat loses.


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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #12 Posted: Tue Dec 31, 2019 12:31 am 
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xela wrote:
Click Here To Show Diagram Code
[go]$$B White to play
$$ X X X O O O
$$ . . . 1 2 .
$$ -------------[/go]

because for black to play 1 and then abandon the position is a loss for black. [...]
I haven't read it yet, but I believe Robert Jasiek's Endgame 3 has some theory on "long sequences" which goes into this in more depth.


See https://lifein19x19.com/viewtopic.php?p=252422#p252422

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #13 Posted: Tue Dec 31, 2019 1:11 am 
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Still confused.

I think I understand why BB never happens. Is it true that BW must be followed by BWB and that WB must be followed by WBW. I still don't see why WWW cannot happen.


Well, I should really read some endgame books. I am currently working on tesuji but after that I should learn to count.

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #14 Posted: Tue Dec 31, 2019 2:12 am 
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Simple mistake way White has 6 points to baseline.
Tesuji variation White has 0 or 6 points depending who gets the gote. So currently worth 3. Black has 1 extra from throw in. So white net 3-1=2.
6-2=4. Black gained 4 points from the tesuji endgame.


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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #15 Posted: Tue Dec 31, 2019 7:58 am 
Honinbo

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jlt wrote:
Since I didn't study endgame theory seriously, it would be a miracle if my answer was correct, but here it is anyway. At least one of us is wrong.

Start from the book solution, and suppose White has no ko threats (one of my problems is that I don't know how to treat the ko). We count the score locally, so that the "wrong answer" in xela's post has score W+6.

Click Here To Show Diagram Code
[go]$$B (one white stone captured)
$$-----------------------+
$$ . . . . . X . X . . . |
$$ . . . . O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Consider the following positions :

Click Here To Show Diagram Code
[go]$$W Position W
$$-----------------------+
$$ . . . . 1 X . X . . . |
$$ . . . . O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$B Position B
$$-----------------------+
$$ . . . . . X . X 1 . . |
$$ . . . . O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$W Position WW
$$-----------------------+
$$ . . . . O . 1 X . . . |
$$ . . . . O . . O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$B Position WB=BW
$$-----------------------+
$$ . . . . O X . X 1 . . |
$$ . . . . O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$B Position WBB: B+1
$$-----------------------+
$$ . . . . O X X X X . . |
$$ . . . . O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$W Position WWW: W+7
$$-----------------------+
$$ . . . . O . O 3 1 2 . |
$$ . . . . O . . O X 4 . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$B Position WWB=WBW: W+5
$$-----------------------+
$$ . . . . O . O X 1 . . |
$$ . . . . O . . O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]



Click Here To Show Diagram Code
[go]$$B Position BB: B+3
$$-----------------------+
$$ . . . 2 1 X 3 X X . . |
$$ . . . 4 O X X O X . . |
$$ . . O . O O O O X . . |
$$ . . . O O X O O X . . |
$$ . . . . . X X X . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |[/go]


White's score at the final positions is:

WWW=7, WWB=WBW=5, WBB=-1, BB=-3.
So WW=(WWW+WWB)/2=6
BW=WB=(WBW+WBB)/2=2
W=4
B=-0.5
(the book's position) = 1.75

On the other hand, the wrong answer had a score equal to 6. So compared to the wrong answer, the book answer gains 4.25 points.


I have a little more confidence now that some other folks also got the same answer, so I'll give my interpretation as to why I have a different answer than this one:

1. Positions W and B are both possible sequences, equally likely to happen assuming neither are sente at the moment.

2. If both players are playing optimally, white wouldn't play as in Position W unless it's the biggest thing on the board. Because of that, if white plays the descent, as in Position W, it is *sente* for black to create Position WB=BW (just like it's sente for white to create position WB=BW if black did Position B at the start).

3. Given #2, we can assume that whichever happens - Position W or Position B - the other player gets to play the sente move for free. I think some people say it's their privilege by some terminology.

4. Therefore, positions WW and WWW cannot happen if both players are playing optimally. So you don't need to consider them in the score evaluation.

5. In practice for amateur games, some folks may not play optimally. So maybe an amateur, as white, creates Position W before they need to. After they make their move, you can calculate starting from Position W and see if other places to play are bigger. E.g. maybe there's a 20 point move someplace else on the board. You can do that, and maybe they'd create position WW from that. But it doesn't matter, because you're still playing for the biggest points.


As usual, I'm open to critique in this analysis.

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #16 Posted: Tue Dec 31, 2019 12:39 pm 
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After watching the London New Year Tournament board 1 broadcasts in YouTube, I still wonder how these endgame discussions and the real games are so far apart.

Cheers,
Vesa


This post by Vesa was liked by: xela
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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #17 Posted: Tue Dec 31, 2019 5:02 pm 
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Wow, that got more interesting than I expected!

Next up, part 1 problem 53. I think this is easier, but I'm posting it because of a cute variation. And of course I could be wrong, there might be hidden depth here too.

Click Here To Show Diagram Code
[go]$$B Black to play
$$-------------------------+
$$ . . . . . . O . . . . . |
$$ . . . . . O X O O O . . |
$$ . . O O . . X X X X O O |
$$ . . . X O O X . . . X . |
$$ . . . X X X . . . X . . |
$$ . . . . . . . . . . . . |[/go]

Book solution:
Click Here To Show Diagram Code
[go]$$B Black to play
$$-------------------------+
$$ . . . . . a O b . . . . |
$$ . . . . 1 O X O O O . . |
$$ . . O O 2 3 X X X X O O |
$$ . . . X O O X . . . X . |
$$ . . . X X X . . . X . . |
$$ . . . . . . . . . . . . |[/go]

The book leaves us at this point, saying "if white connects at a, black throws in at b".

Question 1: how can white make ko?
Question 2: instead of :b3: in the solution diagram, what move might black try to avoid ko, and how does it fail?

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #18 Posted: Wed Jan 01, 2020 12:34 am 
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Ko:

Click Here To Show Diagram Code
[go]$$B
$$-------------------------+
$$ . . . . 4 . O . . . . . |
$$ . . . a 1 O X O O O . . |
$$ . . O O 2 3 X X X X O O |
$$ . . . X O O X . . . X . |
$$ . . . X X X . . . X . . |
$$ . . . . . . . . . . . . |[/go]


Black has a local ko threat at a.


Obviously many moves other than :b3: fail, but here is an unsuccessful attempt:

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

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #19 Posted: Wed Jan 01, 2020 12:58 am 
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Yes, that's the :b3: I was thinking of. For a moment I thought I'd improved on the book solution, but alas, no.

White can also resist this way, perhaps not the best reply but it amuses me that the throw-in no longer works:
Click Here To Show Diagram Code
[go]$$B Black to play
$$-------------------------+
$$ . . . . 3 4 O a . . . . |
$$ . . . . 1 O X O O O . . |
$$ . . O O 2 b X X X X O O |
$$ . . . X O O X . . . X . |
$$ . . . X X X . . . X . . |
$$ . . . . . . . . . . . . |[/go]

Now a and b are miai.

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 Post subject: Re: Behind the scenes of some endgame tesuji
Post #20 Posted: Wed Jan 01, 2020 1:06 am 
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Next, problems 49 and 50 of part 1 are a nice pair for practising your counting.

Click Here To Show Diagram Code
[go]$$Bc Black to play: 'a' or 'b'?
$$---------------------+
$$ . . . . . a b . . . |
$$ . . . . . . . . X . |
$$ . . O . O . O O X . |
$$ . . . . . O . X . . |
$$ . . . . . . . . X . |
$$ . . . . . . X . . . |
$$ . . . . . . . . . . |[/go]


Click Here To Show Diagram Code
[go]$$Bc Black to play: 'a' or 'b'?
$$---------------------+
$$ . . . . . a b . . . |
$$ . . . . . . . . X . |
$$ . O . O O O O O X . |
$$ . . . . X X . X . . |
$$ . . . . . . . . X . |
$$ . . . . . . . X . . |
$$ . . . . . . . . . . |[/go]


In both cases:
  • What's the best play for both sides after black a?
  • What's the best play for both sides after black b?
  • Which of a and b is best and by how many points?
Remember that the monkey jump is supposed to be sente. If you're looking at a gote sequence, think again about the choices for :b3:.
The book tells us which is best but doesn't do the counting. And the book also has this cute story about the name "monkey jump".

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