Exciting problem to decide a game

cyclops · **#21**

cyclops wrote:

No double snapback needed.

Well, this double snapback is nice but avoidable.

Click Here To Show Diagram Code: [go]$$Wc Next Wa, Bb $$ +--------------------------- $$ | . . . . X O b 1 5 O X . . $$ | . . . . X O . X . O X . . $$ | . . X X X O 9 a 2 O X . . $$ | . . X O O 6 7 4 3 O X X . $$ | . . X O . 8 0 X X X O X . $$ | . . X O . . X O O . O X . $$ | . . X O . . O . O O O X . $$ | . X X O . . O . O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

Uberdude · **#22**

cyclops found the double snapback, though his exchange of :w3:

for

was premature. Here's the rest of my solution with the net at :b3:

(which is rendered rather moot by ez4u's quicker solution of 3 at j16, but nevertheless has some rather nice sequences).

After the net white could play at :w4:

or

, for the latter see my previous post. So that leaves :w4:

as below, which means black gets to force at :b5:

and

. A key point to note here is the importance of starting at :b1:

: my initial idea on seeing this problem was to simply play black 1 at :b7:

, white answers at :b1:

, and then black tries to capture the top. However, these efforts come to nothing with only :b7:

in place. By following the proverb and sacrificing an extra stone, black gets 2 extra moves at :b5:

and

for free, which significantly help in the assault on the top.

Click Here To Show Diagram Code: [go]$$c Sacrifice an extra stone for extra kikashi $$ +--------------------------- $$ | . . . . X O . . . O X . . $$ | . . . . X O . c . O X . . $$ | . . X X X O . a b O X . . $$ | . . X O O . . . . O X X . $$ | . . X O . . . 3 7 X O X . $$ | . . X O . . 5 4 2 . O X . $$ | . . X O . . 6 1 O O O X . $$ | . X X O . . . X O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

So now black has to try to capture the 4 white stones, or at least harass them to reduce their eyespace and liberties so that the f16 cut then works. Moves at a or b were my first ideas, but neither of these come to much when white connects at c, for example as below (once black connects at a, white takes a liberty at b and black can't atari):

Click Here To Show Diagram Code: [go]$$cm9 Not working. $$ +--------------------------- $$ | . . . . X O . 6 4 O X . . $$ | . . . . X O . 2 3 O X . . $$ | . . X X X O 0 . 1 O X . . $$ | . . X O O 7 8 . 5 O X X . $$ | . . X O . 9 a X X X O X . $$ | . . X O . b X O O . O X . $$ | . . X O . . O . O O O X . $$ | . X X O . . O . O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

"Your opponent's key point is your key point" suggest black 9 at c from the 1st diagram. If white tries to cut this off, black succeeds in getting a ko.

Click Here To Show Diagram Code: [go]$$cm9 Ko, black success $$ +--------------------------- $$ | . . . . X O . . . O X . . $$ | . . . . X O . 1 6 O X . . $$ | . . X X X O 7 2 3 O X . . $$ | . . X O O . . 5 4 O X X . $$ | . . X O . . . X X X O X . $$ | . . X O . . X O O . O X . $$ | . . X O . . O . O O O X . $$ | . X X O . . O . O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

As white can't connect on top, he connects underneath. :b11:

threatens to throw in at j19 and capture in a connect-and-die. White can defend against this with g19 or j19, so black must be able to win against both.

Click Here To Show Diagram Code: [go]$$cm9 Pushing white down $$ +--------------------------- $$ | . . . . X O . 2 . O X . . $$ | . . . . X O . 1 . O X . . $$ | . . X X X O . . 3 O X . . $$ | . . X O O . . . . O X X . $$ | . . X O . . . X X X O X . $$ | . . X O . . X O O . O X . $$ | . . X O . . O . O O O X . $$ | . X X O . . O . O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

If white g19, black cuts at f16 and gets a seki; note how black has improved upon the 2nd diagram by denying white an eye.

Click Here To Show Diagram Code: [go]$$Wcm12 White connects, black gets seki $$ +--------------------------- $$ | . . . . X O 1 O 7 O X . . $$ | . . . . X O . X . O X . . $$ | . . X X X O 5 . X O X . . $$ | . . X O O 2 3 . 6 O X X . $$ | . . X O . 4 8 X X X O X . $$ | . . X O . . X O O . O X . $$ | . . X O . . O . O O O X . $$ | . X X O . . O . O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

White could switch the connection of :w16:

to the cut below, but then black wins with a connect-and-die. Notice the crucial timing of :b17:

in the previous diagram and :b19:

below. It is not until white has chosen whether to cut or connect with :w16:

that black knows whether to connect at j16 or throw in at j19. If he does either of these before :w16:

white will choose the one which makes black's move the wrong one, and black will lose.

EDIT: actually :b17:

in the previous diagram can throw in and it is actually better, then he wins the semeai by 1 liberty instead of making a seki.

Click Here To Show Diagram Code: [go]$$Wcm12 White cuts, black wins by connect-and-die $$ +--------------------------- $$ | . . . . X O 1 O 8 O X . . $$ | . . . . X O . X 9 O X . . $$ | . . X X X O 6 . X O X . . $$ | . . X O O 2 3 . 0 O X X . $$ | . . X O . 4 5 X X X O X . $$ | . . X O . 7 X O O . O X . $$ | . . X O . . O . O O O X . $$ | . X X O . . O . O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

As an aside, notice the importance of the black kikashi at g14 taking a liberty which allows this sequence to work. This is why the net of black 3 way back at the start was key, if black simply plays as below then this sequence doesn't work (of course the net does give white the option of playing 4 at j15, but as shown in my previous post black wins that way too).

Click Here To Show Diagram Code: [go]$$c Not enough kikashi $$ +--------------------------- $$ | . . . . X O . . . O X . . $$ | . . . . X O . . . O X . . $$ | . . X X X O . . . O X . . $$ | . . X O O . . . . O X X . $$ | . . X O . . . 5 3 X O X . $$ | . . X O . . 6 4 2 . O X . $$ | . . X O . . . 1 O O O X . $$ | . X X O . . . X O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

So now for white j19. Again black cuts, and if white connects with :w16:

, black gets an exquisite double snapback (my favourite variation of this problem).

Click Here To Show Diagram Code: [go]$$Wcm12 White connects, black wins by double snapback $$ +--------------------------- $$ | . . . . X O 0 O 1 O X . . $$ | . . . . X O . X . O X . . $$ | . . X X X O 5 9 X O X . . $$ | . . X O O 2 3 8 7 O X X . $$ | . . X O . 4 6 X X X O X . $$ | . . X O . . X O O . O X . $$ | . . X O . . O . O O O X . $$ | . X X O . . O . O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

And if white cuts for :w16:

, black cuts and throws in:

Click Here To Show Diagram Code: [go]$$Wcm12 White cuts, ... $$ +--------------------------- $$ | . . . . X O 8 O 1 O X . . $$ | . . . . X O . X . O X . . $$ | . . X X X O 6 . X O X . . $$ | . . X O O 2 3 . . O X X . $$ | . . X O . 4 5 X X X O X . $$ | . . X O . 7 X O O . O X . $$ | . . X O . . O . O O O X . $$ | . X X O . . O . O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

White can't capture :b19:

or it's snapback, so black gets to capture the white stones on the right (in sente!):

Click Here To Show Diagram Code: [go]$$Wcm20 ... and dies $$ +--------------------------- $$ | . . . . X O X O O O X . . $$ | . . . . X O 2 X . O X . . $$ | . . X X X O X . X O X . . $$ | . . X O O 3 O . . O X X . $$ | . . X O 1 . O X X X O X . $$ | . . X O . O X O O . O X . $$ | . . X O . . O . O O O X . $$ | . X X O . . O . O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

There are a few other resistances for white to try, such as the fancy wedge below. If black falls for the bait and ataris, white wins:

Click Here To Show Diagram Code: [go]$$Wcm12 Fancy wedge, black tricked $$ +--------------------------- $$ | . . . . X O . O 1 O X . . $$ | . . . . X O . X . O X . . $$ | . . X X X O 4 3 X O X . . $$ | . . X O O 2 5 6 . O X X . $$ | . . X O . 7 . X X X O X . $$ | . . X O . . X O O . O X . $$ | . . X O . . O . O O O X . $$ | . X X O . . O . O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

Instead black must calmly connect. Even though it looks like white's wedge fixed the cutting point at g17 in sente, black still can force a shortage of liberties by throwing-in there.

Click Here To Show Diagram Code: [go]$$Wcm12 Fancy wedge refuted 1 $$ +--------------------------- $$ | . . . . X O . O 1 O X . . $$ | . . . . X O 9 X 0 O X . . $$ | . . X X X O 8 3 X O X . . $$ | . . X O O 2 5 . 4 O X X . $$ | . . X O . 6 7 X X X O X . $$ | . . X O . . X O O . O X . $$ | . . X O . . O . O O O X . $$ | . X X O . . O . O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

Click Here To Show Diagram Code: [go]$$Wcm12 Fancy wedge refuted 2 $$ +--------------------------- $$ | . . . . X O . O 1 O X . . $$ | . . . . X O 0 X . O X . . $$ | . . X X X O 8 3 X O X . . $$ | . . X O O 2 5 . 4 O X X . $$ | . . X O . 6 7 X X X O X . $$ | . . X O . 9 X O O . O X . $$ | . . X O . . O . O O O X . $$ | . X X O . . O . O X X X . $$ | . X O O . O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]

In conclusion, black has many beautiful ways to win; I hope you enjoyed this problem as much as I did

ez4u · **#23**

@ Uberdude

Excellent problem!

Were you using clocks in the actual game? If so, how much time did you have left and how long did it take you to read out the situation? Do you think that you had read out all the essentials before playing or did you "go for it", knowing that you would lose if you passed?

Uberdude · **#24**

This was played on OGS (http://www.online-go.com/games/board.php?boardID=271713) so 1 day per move clocks :lol:

. The question of whether white needed to defend once the dame were filled had been sitting there for quite a while, and I didn't think he did (I had considered h13 as well as j15 as the starting move, but had not spotted the net of black 3 (nor your black 3). I actually thought an endgame ko (which I would lose) would decide the game, but had miscalculated and white found a move order that meant he filled the ko without fighting it, so it was only when white passed that I re-read this problem (knowing I was losing by 0.5) and found the net. I did play out variations, and spent over an hour on it. I had found all the variations I posted and was 95% confident it worked when I started the sequence (hence not looking for an alternative to black 3).

Uberdude · **#25**

I am going to write up this problem for the British Go Journal, using L19 as the typesetting mechanism for transfer to the editor as it's easy to make diagrams, so that's why the voice of the following posts is a bit strange.

Uberdude · **#26**

The following problem is adapted from a recent game of mine. It is black to play. White could have played a defensive move to fix the bad aji as the dame were being filled, but then he would have lost by half a point (the game was played under Japanese rules). Therefore any gain counts as a success for black: capturing some stones, seki or ko.

Click Here To Show Diagram Code: [go]$$c Black to play $$ ---------------------------- $$ | . . . . X O . . . O X . . | $$ | . . . . X O . . . O X . . | $$ | . . X X X O . . . O X . . | $$ | . . X O O . . . . O X X . | $$ | . . X O . . . . . X O X . | $$ | . . X O . . . . . . O X . | $$ | . . X O . . . . O O O X . | $$ | . X X O . . . X O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

This problem is rather difficult: you probably need to be a high dan player to solve it in your head. However, I suggest that you try for a while, and then explore variations on a board before looking at the answers: there are many beautiful tesujis, snapbacks, and connect-and-dies hidden within as rewards for the determined traveller.

A few hints:
1) Add a second stone and sacrifice both.
2) My solution relied on the dango in the lower left not being an eye, but someone else found another solution that works regardless.

Incidentally, this demonstrates an aspect of Japanese rules I prefer over AGA. It is much more satisfying for a game to be decided by a problem like this than the randomness of dame parity.

Uberdude · **#27**

If black is to accomplish anything, it should be clear it will be by utilising his two cutting stones, white's marked cut and trying to capture white's four stones in the top right. The first move to consider would be simply extending as below, but once white defends at :w2:

black can try capturing white's 4 stones at the top (for example with a), but nothing quite works (white answers at b).

Click Here To Show Diagram Code: [go]$$ $$ ---------------------------- $$ | . . . . X O . . . O X . . | $$ | . . . . X O . b . O X . . | $$ | . . X X X O . a . O X . . | $$ | . . X O O C . . . O X X . | $$ | . . X O . . . . 1 X O X . | $$ | . . X O . . . . . . O X . | $$ | . . X O . . . 2 O O O X . | $$ | . X X O . . . X O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

If black is to be successful in his assault on the top, he will need more than a single stone in sente to help him. Therefore he pulls out his other cutting stone first, intending to sacrifice it to get additional forcing moves before attacking the top. White has to make the empty triangle at :w2:

: if she plays atari on the other cutting stone black gets a snapback. Next :b3:

makes a net from which white has two ways to escape.

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

If white captures the single stone, black cuts again aiming to squeeze white. If white simply captures the single stone to avoid snapback, black squeezes and the pushes down at a and white is captured (if white jumps to b black throws in at c).

Click Here To Show Diagram Code: [go]$$ $$ ---------------------------- $$ | . . . . X O . b c O X . . | $$ | . . . . X O . . . O X . . | $$ | . . X X X O . . a O X . . | $$ | . . X O O . . . 5 O X X . | $$ | . . X O . . . X 4 X O X . | $$ | . . X O . . . . O . O X . | $$ | . . X O . . . X O O O X . | $$ | . X X O . . . X O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

White might try putting in the atari of :w6:

first, but black still squeezes and with a-i white's on a one-way street to death.

Click Here To Show Diagram Code: [go]$$ $$ ---------------------------- $$ | . . . . X O h f c O X . . | $$ | . . . . X O e b d O X . . | $$ | . . X X X O g a 6 O X . . | $$ | . . X O O i . 7 X O X X . | $$ | . . X O . . . X O X O X . | $$ | . . X O . . . 9 O 8 O X . | $$ | . . X O . . . X O O O X . | $$ | . X X O . . . X O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

After black's cut of :b5:

white might try breaking out with two ataris but black doesn't save the second stone but instead catches white in a lovely connect-and-die.

Click Here To Show Diagram Code: [go]$$Wm6 $$ ---------------------------- $$ | . . . . X O . . 6 O X . . | $$ | . . . . X O . . 4 O X . . | $$ | . . X X X O . . 2 O X . . | $$ | . . X O O . . 1 X O X X . | $$ | . . X O . . . X O X O X . | $$ | . . X O . . . 3 O 5 O X . | $$ | . . X O . . . X O O O X . | $$ | . X X O . . . X O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

Given that the above succeeds for black, white can try as below which looks better for a while as white gets to connect along the top...

Click Here To Show Diagram Code: [go]$$ $$ ---------------------------- $$ | . . . . X O . . . O X . . | $$ | . . . . X O . 0 8 O X . . | $$ | . . X X X O . 9 7 O X . . | $$ | . . X O O . . 6 X O X X . | $$ | . . X O . . . X O X O X . | $$ | . . X O . . . . O . O X . | $$ | . . X O . . . X O O O X . | $$ | . X X O . . . X O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

...and then captures to avoid snapback. However, black again squeezes, and then cuts. White has to live at :w18:

(or black plays there and white dies very quickly) which allows black to play :b19:

to take away white's eyes of the group which he has cut off in sente. Black doesn't have an eye either though, so this is a seki (verification left to the reader). This is why I mentioned earlier that white's dango in the lower left was relevant: if she had an eye then black would be dead.

Click Here To Show Diagram Code: [go]$$Bm11 $$ ---------------------------- $$ | . . . . X O . 8 . O X . . | $$ | . . . . X O . O O O X . . | $$ | . . X X X O 2 X X O X . . | $$ | . . X O O 7 1 3 X O X X . | $$ | . . X O . . . X O 6 O X . | $$ | . . X O . . . 5 O 4 O X . | $$ | . . X O . . . X O O O X . | $$ | . X X O . 9 . X O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

So from these variations, we can conclude that :w4:

capturing the single stone fails, so instead must be as below. Black keeps up getting as many forcing moves as possible by blocking at :b5:

(white can't answer at 7 or else black plays one above for the now familiar snapback). White captures 2 stones, but we can now see that black has vastly improved upon the first diagram as he has two extra stones at 3 and 5 as support for the attack on the top.

Click Here To Show Diagram Code: [go]$$ $$ ---------------------------- $$ | . . . . X O . . . O X . . | $$ | . . . . X O . c . O X . . | $$ | . . X X X O . a b O X . . | $$ | . . X O O C . . . O X X . | $$ | . . X O . . . 3 7 X O X . | $$ | . . X O . . 5 4 2 . O X . | $$ | . . X O . . 6 1 O O O X . | $$ | . X X O . . 8 X O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

So now black has to try to capture the 4 white stones, or at least harass them to reduce their eyespace and liberties so that the marked cut then works. Moves at a or b were my first ideas, but neither of these come to much when white connects at c, for example as below (once black connects at a, white takes a liberty at b and black can't atari due to his lack of an eye whilst white does have one).

Click Here To Show Diagram Code: [go]$$Bm9 $$ ---------------------------- $$ | . . . . X O . 6 4 O X . . | $$ | . . . . X O . 2 3 O X . . | $$ | . . X X X O 0 . 1 O X . . | $$ | . . X O O 7 8 . 5 O X X . | $$ | . . X O . 9 a X X X O X . | $$ | . . X O . b X O O . O X . | $$ | . . X O . . O . O O O X . | $$ | . X X O . . O . O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

"Your opponent's key point is your key point" suggest black 9 at c from the previous diagram. If white tries to cut this off, black succeeds in getting a ko.

Click Here To Show Diagram Code: [go]$$Bm9 $$ ---------------------------- $$ | . . . . X O . . . O X . . | $$ | . . . . X O . 1 6 O X . . | $$ | . . X X X O 7 2 3 O X . . | $$ | . . X O O . . 5 4 O X X . | $$ | . . X O . . . X X X O X . | $$ | . . X O . . X O O . O X . | $$ | . . X O . . O . O O O X . | $$ | . X X O . . O . O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

As white can't connect on top, he connects underneath. :b11:

threatens to throw in and capture in a connect-and-die. White can defend against this by connecting to either side, so black must be able to win against both. The variations are similar, to stop this rather long solution getting longer I will only show one.

Click Here To Show Diagram Code: [go]$$Bm9 $$ ---------------------------- $$ | . . . . X O . 2 . O X . . | $$ | . . . . X O . 1 . O X . . | $$ | . . X X X O . . 3 O X . . | $$ | . . X O O . . . . O X X . | $$ | . . X O . . . X X X O X . | $$ | . . X O . . X O O . O X . | $$ | . . X O . . O . O O O X . | $$ | . X X O . . O . O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

Having squished white against the edge without an eye, black cuts, and if white connects with :w16:

black gets an exquisite double snapback (my favourite variation of this problem).

Click Here To Show Diagram Code: [go]$$Wm12 $$ ---------------------------- $$ | . . . . X O 0 O 1 O X . . | $$ | . . . . X O . X . O X . . | $$ | . . X X X O 5 9 X O X . . | $$ | . . X O O 2 3 8 7 O X X . | $$ | . . X O . 4 6 X X X O X . | $$ | . . X O . . X O O . O X . | $$ | . . X O . . O . O O O X . | $$ | . X X O . . O . O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

And if white cuts for :w16:

, black cuts and throws in:

Click Here To Show Diagram Code: [go]$$Wm12 $$ ---------------------------- $$ | . . . . X O 8 O 1 O X . . | $$ | . . . . X O . X . O X . . | $$ | . . X X X O 6 . X O X . . | $$ | . . X O O 2 3 . . O X X . | $$ | . . X O . 4 5 X X X O X . | $$ | . . X O . 7 B O O . O X . | $$ | . . X O . . O . O O O X . | $$ | . X X O . . O . O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

As an aside, notice the importance of the marked black stone taking a liberty which allows this sequence to work. This is why the net of black 3 way back at the start was key, if black simply plays as below then this sequence doesn't work (of course the net does give white the option of playing 4 breaking out above, but we've shown black wins that way too).

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

To continue, white can't capture :b19:

or it's snapback, so black gets to capture the white stones on the right (in sente!):

Click Here To Show Diagram Code: [go]$$Wm20 $$ ---------------------------- $$ | . . . . X O X O O O X . . | $$ | . . . . X O 2 X . O X . . | $$ | . . X X X O X . X O X . . | $$ | . . X O O 3 O . . O X X . | $$ | . . X O 1 . O X X X O X . | $$ | . . X O . O . O O . O X . | $$ | . . X O . . O . O O O X . | $$ | . X X O . . O . O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

There are a few other resistances for white to try, such as the fancy wedge below. If black falls for the bait and ataris, white wins as black only has one eye inside, and white is safely connected.

Click Here To Show Diagram Code: [go]$$Wm12 $$ ---------------------------- $$ | . . . . X O . O 1 O X . . | $$ | . . . . X O . X . O X . . | $$ | . . X X X O 4 3 X O X . . | $$ | . . X O O 2 5 6 . O X X . | $$ | . . X O . 7 . X X X O X . | $$ | . . X O . . X O O . O X . | $$ | . . X O . . O . O O O X . | $$ | . X X O . . O . O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

Instead black must calmly connect. Even though it looks like white's wedge fixed the cutting point in sente, black still can force a shortage of liberties by throwing-in there for another connect-and-die.

Click Here To Show Diagram Code: [go]$$Wm12 $$ ---------------------------- $$ | . . . . X O . O 1 O X . . | $$ | . . . . X O 9 X 0 O X . . | $$ | . . X X X O 8 3 X O X . . | $$ | . . X O O 2 5 . 4 O X X . | $$ | . . X O . 6 7 X X X O X . | $$ | . . X O . . X O O . O X . | $$ | . . X O . . O . O O O X . | $$ | . X X O . . O . O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

But that's not the end of it! When I posted this problem online, someone found an alternative solution. It is better in that it works even if white has an eye in the lower left and is elegant in its simplicity, but is worse in that its denouement is not a double snapback! Rather than playing the net for black 3, he takes a liberty as below in the key shape point for setting up the squeeze.

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

If white cuts, black pushes down and white has to capture the 2 stones somehow, such as :w6:

. But black continues squeezing and then plays 11, making miai of a and b. White 4 at b ends up very similar with black 11 being the key point of creating miai to capture some stones. White 4 blocking at black 5 is answered at b and ends up as the one-way road to death of the 4th diagram.

Click Here To Show Diagram Code: [go]$$Wm4 $$ ---------------------------- $$ | . . . . X O . . 6 O X . . | $$ | . . . . X O . . 4 O X . . | $$ | . . X X X O . . 2 O X . . | $$ | . . X O O a 8 . X O X X . | $$ | . . X O . . . . 1 7 O X . | $$ | . . X O . . 3 b O 5 O X . | $$ | . . X O . . . X O O O X . | $$ | . X X O . . . X O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

White's strongest resistance is the rather silly looking empty triangle of 6, but again a and b end up as miai. This variation reveals why this alternative black 3 is better than the net: with the net black had already made the exchange of :b9:

for

before white played at 6, which meant white 6 was atari and he was able to connect underneath with 7, and black only won because of the seki that resulted later. By keeping the 9-10 exchange in reserve until it is needed, white is denied this opportunity so is dead even with an eye instead of a dango in the lower left.

Click Here To Show Diagram Code: [go]$$Wm4 $$ ---------------------------- $$ | . . . . X O . . . O X . . | $$ | . . . . X O . 4 3 O X . . | $$ | . . X X X O . 8 2 O X . . | $$ | . . X O O b 0 7 X O X X . | $$ | . . X O . . . 6 1 X O X . | $$ | . . X O . . a 9 O 5 O X . | $$ | . . X O . . . X O O O X . | $$ | . X X O . . . X O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

In conclusion, black has many beautiful ways to win; I hope you enjoyed this problem as much as I did. I find it remarkable that such an exquisite problem arose naturally in a game (http://www.online-go.com/games/board.php?boardID=271713).

cyclops · **#28**

Uberdude wrote:

...... I hope you enjoyed this problem as much as I did. .......

Yes, I did. And I spent way too many hours on it in which I saw many of your variations, but not all.
( I didn't see why white shape in the bottom left was important. )
Still I doubt B needs the double snapback. For example in

Click Here To Show Diagram Code: [go]$$Wm12 $$ ---------------------------- $$ | . . . . X O 0 O 1 O X . . | $$ | . . . . X O . X . O X . . | $$ | . . X X X O 5 9 X O X . . | $$ | . . X O O 2 3 8 7 O X X . | $$ | . . X O . 4 6 X X X O X . | $$ | . . X O . . X O O . O X . | $$ | . . X O . . O . O O O X . | $$ | . X X O . . O . O X X X . | $$ | . X O O . O O O X X . . . | $$ | . X O O O X X X . , . . . | $$ | . X O O O X . . . . . . . | $$ | . X X X X X . . . . . . . | $$ | . . . . . . . . . . . . . | $$ ----------------------------[/go]

he could play 17 above 16 as well.

But most of all I liked your skillful explanations and diagrams, clarifying it even for this 7 kyu. :bow:

NoSkill · **#29**

Robert linked me here so i have a question:

Click Here To Show Diagram Code: [go]$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . . . X O . 7 . O X . . . . . . . . | $$ | . . X X X O . 8 9 O X . . . . . . . . | $$ | . . X O O . . . . O X X . . . , . . . | $$ | . . X O . . . 5 3 X O X . . . . . . . | $$ | . . X O . . 6 4 2 . O X . . . . . . . | $$ | . . X O . . . 1 O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Isnt this a ko?

Uberdude · **#30**

NoSkill wrote:

Isnt this a ko?

Yes, but both sides have made mistakes ( :b3:

and

).

NoSkill · **#31**

Uberdude wrote:

NoSkill wrote:

Isnt this a ko?

Yes, but both sides have made mistakes ( :b3:

and

).

I dont see how 3 is a mistake, punish it please

Uberdude · **#32**

NoSkill wrote:

Uberdude wrote:

NoSkill wrote:

Isnt this a ko?

Yes, but both sides have made mistakes ( :b3:

and

).

I dont see how 3 is a mistake, punish it please

As ever, reading is important. Either read moves on the problem yourself, or read my comprehensive answer above in this thread.

NoSkill · **#33**

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

This ?

Or :

Click Here To Show Diagram Code: [go]$$c Black to play $$ --------------------------------------- $$ | . . . . X O 6 O 7 O X . . . . . . . . | $$ | . . . . X O . X 8 O X . . . . . . . . | $$ | . . X X X O 5 . 9 O X . . . . . . . . | $$ | . . X O O 1 2 . . O X X . . . , . . . | $$ | . . X O . 3 4 X X X O X . . . . . . . | $$ | . . X O . . O O O . O X . . . . . . . | $$ | . . X O . . . X O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Uberdude · **#34**

In the first diagram, :w2:

is a mistake, :w4:

in the second.

Exciting problem to decide a game

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