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 Post subject: More tesujis in josekis
Post #1 Posted: Fri Feb 05, 2021 9:49 pm 
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I was exploring a big pile of KataGo semi-blindspots today, and there are a pretty dense cluster of uncommon tesuji and semi-AI-blindspots of them in this joseki line. Here they are posed as some puzzles. Most of them are human-understandable in retrospect, but still many moves are quite remarkable. Free free to take a guess, and check with a bot if you like. No guarantees that these are 100% accurate, maybe you will find another blind spot I should add to KataGo's training. :)

For reference, the parent joseki leading into all of these is the flying dagger pattern, but with the *outside* cut instead of the inside cut. The outside cut is much less complicated overall than the inside cut, but still has its share of fun stuff. The avalanche and taisha must have felt very sad to lose their top seats.

Click Here To Show Diagram Code
[go]$$Wc Overarching joseki - Outside cut (inside cut would be :w1: at "a")
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . 4 3 5 . . |
$$ | . . . . . . . . . . . . . . . X O . . |
$$ | . . . X . . . . . , . . . . a X O . . |
$$ | . . . . . . . . . . . . . 2 X O O . . |
$$ | . . . . . . . . . . . . . . 1 X X O . |
$$ | . . . . . . . . . . . . . . . . . X . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


----------------------------------------------------

So, first one. White can capture at "a", which threatens to win the capturing race, so black would want to respond at "b" to kill the corner. Then white can deal with black's 4 stones. But white has a better plan. What is it?

Click Here To Show Diagram Code
[go]$$Wc Problem 1 - White to continue and get black into trouble.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . X O O . b |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . . X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . . . O O O X . |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . . . 1 X X O . |
$$ | . . . , . . . . . , . . . . . 2 O X a |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


----------------------------------------------------

Next one. In a different variation, the capturing race happens in a different way. After :b2:, how should white proceed with this capturing race? White only has 3 liberties in the corner. Is white just dead?

Click Here To Show Diagram Code
[go]$$Wc Problem 2 - What can white do with this capturing race?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . 2 . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . X X X O O 1 |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X . |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . X . X X X O . |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]



----------------------------------------------------

Next one is a spoiler if you haven't thought about problem 2 yet.
Okay so yes white can make a ko using this clever empty triangle.

Click Here To Show Diagram Code
[go]$$Wc Tesuji!
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X . |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . X . X X X O 1 |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


So let's fight this ko.

Click Here To Show Diagram Code
[go]$$Bc Fight fight fight
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . 3 X 2 . . |
$$ | . . . . . . . . . . . . . . X O O . 1 |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X 4 |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . X . X X X O W |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Now, what is white's best ko threat?

Click Here To Show Diagram Code
[go]$$Bc Problem 3 - white to continue with a good threat
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . X X O . . |
$$ | . . . . . . . . . . . . . . X O O . X |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X C |
$$ | . . . . . . . . . . . . . . . O X O 5 |
$$ | . . . . . . . . . . . . X . X X X O O |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]




----------------------------------------------------

Problem 4 is also a spoiler for problem 2.
So, let's suppose black felt they didn't quite like the result of problem 3. Knowing the ko that white is planning to create, how can black mess with white's plans and make that ko a little more annoying for white?

Click Here To Show Diagram Code
[go]$$Wc Problem 4 - Black tesuji to make ko more challenging for white
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X . |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . X . X X X O W |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


----------------------------------------------------

Now, in a different variation things go like this. Luckily, white had the foresight to throw in the marked stone like 20 moves earlier. Yay.

Click Here To Show Diagram Code
[go]$$Bc Some other variation
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . X X X O O . |
$$ | . . . X . . . . . , . . . . W X O X . |
$$ | . . . . . . . . . . . . . X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . . . O O O X . |
$$ | . . . . . . . . . . . . . 5 . O X O . |
$$ | . . . . . . . . . . . . . . . X X O . |
$$ | . . . , . . . . . , . . . . . 1 O 4 2 |
$$ | . . . . . . . . . . . . . . . . 3 O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


So white can escape like so:

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



Now this one's just for fun. What should happen next? White to make a pretty shape, and black to respond with her own.

Click Here To Show Diagram Code
[go]$$Wc Problem 5 - Pretty shapes, white first
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . X X X O O . |
$$ | . . . X . . . . . , . . . X . X O X . |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . X X O O X X X X |
$$ | . . . . . . . . . . . . O . O O O X . |
$$ | . . . . . . . . . . . . . X . O X O . |
$$ | . . . . . . . . . . . . . . . X X O . |
$$ | . . . , . . . . . , . . . . . X O O O |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Last edited by lightvector on Sat Feb 06, 2021 5:52 pm, edited 1 time in total.

This post by lightvector was liked by 2 people: Harleqin, Marcel Grünauer
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 Post subject: Re: More tesujis in josekis
Post #2 Posted: Sat Feb 06, 2021 4:57 pm 
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Problem 1: misread the ladder?

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 Post subject: Re: More tesujis in josekis
Post #3 Posted: Sat Feb 06, 2021 5:08 pm 
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Problem 4: I think you either have a white stone too much (the marked one) or a black stone too few (hane on the top).

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 Post subject: Re: More tesujis in josekis
Post #4 Posted: Sat Feb 06, 2021 5:53 pm 
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Thanks, fixed problem 4.

For problem 1, I'm not sure what you mean, but to clarify - white has something better than playing "a", black playing "b", and then capturing 4 stones in a ladder.

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 Post subject: Re: More tesujis in josekis
Post #5 Posted: Sun Feb 07, 2021 12:29 pm 
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Problem 1:

I meant the variation where White omits 'a' and directly plays the ladder with Q9. Black cannot capture at first, he also doesn't want to add more stones to the ladder since 'a' is sente anytime, but otherwise White can directly capture and gains an entire move. The ladder narrowly works for White.

If that's not the solution, I am too weak for this apparently. ^^

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 Post subject: Re: More tesujis in josekis
Post #6 Posted: Sun Feb 07, 2021 1:56 pm 
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If you are training out blindspots, you should also give some training to this position:

Click Here To Show Diagram Code
[go]$$Bc AI prefers A and doesn't immediately realize that 1 is often better.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . 1 a . X O . . |
$$ | . . . X . . . . . , . . . . . X O . . |
$$ | . . . . . . . . . . . . . X X O O . . |
$$ | . . . . . . . . . . . . . . O X X O . |
$$ | . . . . . . . . . . . . . . . . . X . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


This post by emerus was liked by 3 people: Harleqin, lightvector, Uberdude
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 Post subject: Re: More tesujis in josekis
Post #7 Posted: Sun Feb 07, 2021 3:28 pm 
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Answers!

Problem 1
Click Here To Show Diagram Code
[go]$$Wc Problem 1 - White to continue and get black into trouble.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . X O O . b |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . . X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . . . O O O X . |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . . . 1 X X O . |
$$ | . . . , . . . . . , . . . . . 2 O X a |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Answer: White has this unusual tesuji, even though white is in atari. If black plays "b" now, white captures 4 stones directly. This is far thicker than if white instead first captures "a", and then black "b", and the white takes the 4 stones with a ladder or net.
If black plays "c" now, white squeezes and still captures at least 4 stones ultra-thickly, it's similar.

Click Here To Show Diagram Code
[go]$$Wc Problem 1 - answer
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . X O O . b |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . . X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . . . O O O X . |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . . . O X X O . |
$$ | . . . , . . . . . , . . . . . X O X a |
$$ | . . . . . . . . . . . . . . . 3 c O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Okay what about the obvious resistance, where black comes out? If black runs, white plays out another step of the ladder-like shape, then captures. Now, black still has to come back to "b" to win the capturing race, but white is eating all 6 stones after that in a ladder. The marked black stone is *not* a ladder breaker.

Click Here To Show Diagram Code
[go]$$Bc Problem 1 - black loses more stones
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . X O O . b |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . . X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . . . O O O X . |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . . . O X X O . |
$$ | . . . , . . . . . , . . . 2 1 X O C 4 |
$$ | . . . . . . . . . . . . . . 3 O . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . B . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Problem 2
Click Here To Show Diagram Code
[go]$$Wc Problem 2 - What can white do with this capturing race?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . 2 . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . X X X O O 1 |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X . |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . X . X X X O . |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Answer: Make an empty triangle, preparing for a throw-in at "a" to get a ko.

Click Here To Show Diagram Code
[go]$$Wc Problem 2 - answer
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X a |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . X . X X X O 3 |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Problem 3:
Click Here To Show Diagram Code
[go]$$Bc Problem 3 - white to continue with a good threat
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . X X O . . |
$$ | . . . . . . . . . . . . . . X O O . X |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X C |
$$ | . . . . . . . . . . . . . . . O X O 5 |
$$ | . . . . . . . . . . . . X . X X X O O |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Answer: This is white's best ko threat:

Click Here To Show Diagram Code
[go]$$Wc Problem 3 - answer
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . X X O . . |
$$ | . . . . . . . . . . . . . . X O O . X |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . 1 O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X C |
$$ | . . . . . . . . . . . . . . . O X O B |
$$ | . . . . . . . . . . . . X . X X X O O |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Black has no threats big enough, so ends the ko. White continues by connecting out, *not* capturing. This is a fine result for white.

Click Here To Show Diagram Code
[go]$$Wc Problem 3 - continuation
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . X X O . . |
$$ | . . . . . . . . . . . . . . X O O . X |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . 3 1 O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X . |
$$ | . . . . . . . . . . . . . . . O X C X |
$$ | . . . . . . . . . . . . X . X X X C C |
$$ | . . . , . . . . . , . . . . . . O X 2 |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


The tricky part about this problem is that white must not play the threat below, even though it feels like the same threat except with less chance to turn into a dead loss.

Click Here To Show Diagram Code
[go]$$Wc Problem 3 - mistake
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . X X O . . |
$$ | . . . . . . . . . . . . . . X O O . X |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . b a O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . 1 O X X X X |
$$ | . . . . . . . . . . . . O . O O O X . |
$$ | . . . . . . . . . . . . . . . O X C B |
$$ | . . . . . . . . . . . . X . X X X C C |
$$ | . . . , . . . . . , . . . . . . O X 2 |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Because now, the only followup is for white to capture the two stones at "a". White does not end up with a stone at "b", which makes a significant difference for pressuring the black group at the top.


Problem 4
Click Here To Show Diagram Code
[go]$$Wc Problem 4 - Black tesuji to make ko more challenging for white
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X . |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . X . X X X O W |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Black has this amazing move!:

Click Here To Show Diagram Code
[go]$$Bc Problem 4 - answer
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . . O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X . |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . X . X X X O W |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . . O 1 |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


If white takes, then we have the same sequence, but when white starts the throw-in ko, white will be losing 4 stones here instead of 3. Obviously this is better for black.

Click Here To Show Diagram Code
[go]$$Bc Problem 4 - black ignores :w8: and captures 4 stones at the marked point
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . 5 X 4 . . |
$$ | . . . . . . . . . . . . . . X O O . 3 |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . 8 O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X 6 |
$$ | . . . . . . . . . . . . . . . O X O 7 |
$$ | . . . . . . . . . . . . X . X X X O O |
$$ | . . . , . . . . . , . . . . . . O C 2 |
$$ | . . . . . . . . . . . . . . . . . O 1 |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


If white responds on the other side, then...

Click Here To Show Diagram Code
[go]$$Bc Problem 4 - white tries the other way...
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . 5 X 4 . . |
$$ | . . . . . . . . . . . . . . X O O . 3 |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . . 8 O X O X X |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X 6 |
$$ | . . . . . . . . . . . . . . . O X O 7 |
$$ | . . . . . . . . . . . . X . X X X O O |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . . O 1 |
$$ | . . . . . . . . . . . . . . . . . . 2 |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Now black has a new alternative. Despite not being able to win the ko, black can answer white's threat.

Click Here To Show Diagram Code
[go]$$Bc Problem 4 - black's new alternative
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . X X O . . |
$$ | . . . . . . . . . . . . . . X O O . X |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . 1 C C X O X X |
$$ | . . . . . . . . . . . . O X X O O X 4 |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X 2 |
$$ | . . . . . . . . . . . . . . . O X O C |
$$ | . . . . . . . . . . . . X . X X X O O |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . 3 O X |
$$ | . . . . . . . . . . . . . . . . . 5 O |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Black is thick enough on both sides to compensate white's winning the ko and killing the black group in the middle. Depending on the position, this may be quite playable for black.

Click Here To Show Diagram Code
[go]$$Bc Problem 4 - result
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . X X O . . |
$$ | . . . . . . . . . . . . . . X O O . X |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . X . . X O C C |
$$ | . . . . . . . . . . . . O X X O O C O |
$$ | . . . . . . . . . . . . . . O C C C C |
$$ | . . . . . . . . . . . . O . O O O C O |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . X . X X X O O |
$$ | . . . , . . . . . , . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . . X C X |
$$ | . . . . . . . . . . . . . . . . . X W |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


If black hadn't made the exchange, the only equivalent would be for Black to cut here and then finish with capturing at "a". Obviously for black to have gotten "b" for "c" exchange makes a huge difference in how much compensation the cut below at :b2: is getting for losing the ko.

Click Here To Show Diagram Code
[go]$$Wc Problem 4 - without the exchange
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . X X O . . |
$$ | . . . . . . . . . . . . . . X O O . X |
$$ | . . . . . . . . . . . . . X X X O O O |
$$ | . . . X . . . . . , . . X . . X O X X |
$$ | . . . . . . . . . . . . O X X O O X 3 |
$$ | . . . . . . . . . . . . . . O X X X X |
$$ | . . . . . . . . . . . . O . O O O X 1 |
$$ | . . . . . . . . . . . . . . . O X O . |
$$ | . . . . . . . . . . . . X . X X X O O |
$$ | . . . , . . . . . , . . . . . a O X . |
$$ | . . . . . . . . . . . . . . . . 2 O b |
$$ | . . . . . . . . . . . . . . . . . . c |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


There are of course complications depending on what the rest of the board looks like, if there are big threats. Or in some cases one of the players can delay the ko to try to make threats.


Problem 5:
Click Here To Show Diagram Code
[go]$$Wc Problem 5 - Pretty shapes, white first
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . X X X O O . |
$$ | . . . X . . . . . , . . . X . X O X . |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . X X O O X X X X |
$$ | . . . . . . . . . . . . O . O O O X . |
$$ | . . . . . . . . . . . . . X . O X O . |
$$ | . . . . . . . . . . . . . . . X X O . |
$$ | . . . , . . . . . , . . . . . X O O O |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Wc Problem 5 - Pretty!
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . X X X O O . |
$$ | . . . X . . . . . , . . . X . X O X . |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . X X O O X X X X |
$$ | . . . . . . . . . . . . O . O O O X . |
$$ | . . . . . . . . . . . . . X . O X O . |
$$ | . . . . . . . . . . . . . . 1 X X O . |
$$ | . . . , . . . . . , . . . . . X O O O |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Wc Problem 5 - Pretty!!
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . X O O . . |
$$ | . . . . . . . . . . . . . X X X O O . |
$$ | . . . X . . . . . , . . . X . X O X . |
$$ | . . . . . . . . . . . . O X X O O X . |
$$ | . . . . . . . . . . . X X O O X X X X |
$$ | . . . . . . . . . . . . O . O O O X . |
$$ | . . . . . . . . . . . . . X . O X O . |
$$ | . . . . . . . . . . . . 2 . O X X O . |
$$ | . . . , . . . . . , . . . . . X O O O |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O . . . . , . . . . . O . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Sadly, black's move in the last diagram might not actually be correct. But it's still pretty. :)


This post by lightvector was liked by 7 people: bernds, Bill Spight, gennan, Harleqin, MikeKyle, SoDesuNe, Uberdude
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