After a lot of work I managed to build a position for which the win need a special strategy I have never seen before.
Can you solve the following problem:

AGA rules, komi 14.5

Click Here To Show Diagram Code

[go]$$B Black to play and win
$$ ------------------------
$$| . . . . O X O O O . X |
$$| O O O O O X O O O X X |
$$| X X X X X X X X O . X |
$$| . . . . . X X O . O O |
$$| . . . . . . X O O O O |
$$| . X . . . . X X X X X |
$$| X X X . . . X O O O O |
$$| O O X . . . X O . O . |
$$| . O X X X X X O O X O |
$$| X O O O O X O O X X X |
$$| . X X . O X O X . X . |
$$ -----------------------[/go]

Edit :look at https://lifein19x19.com/viewtopic.php?p=279399#p279399 for a far better problem.

May I ask the point of setting Komi to 14.5? Is it just to to ensure that a win vs loss depends on the solution?

It's funny. Another superko beast.

Basically the komi is here to help you. If black plays the correct sequence black will win, otherwise black will lose.
I could have only said "what is the best result for black" but in that case you have no clue to know if you are close to the solution.

Yes Dany it is a really a beast.
Assuming white is allowed to play "unuseful" moves (e.g. by using the double ko when it is not necessary) but is not allowed to play "bad" moves (a move which loses points), how many moves are necessary before black can make the decisive capture (I mean a capture which is not an exchange in the double ko in the bottom right corner or in the sending 2 return 1 sequence)?

I have just discovered a dual solution for the problem I showed in this topic. By just adding a black stone and a white stone in the upper left corner this dual issue is fixed:

AGA rules, komi 14.5

Click Here To Show Diagram Code

[go]$$B Black to play and win
$$ ------------------------
$$| X . O . O X O O O . X |
$$| O O O O O X O O O X X |
$$| X X X X X X X X O . X |
$$| . . . . . X X O . O O |
$$| . . . . . . X O O O O |
$$| . X . . . . X X X X X |
$$| X X X . . . X O O O O |
$$| O O X . . . X O . O . |
$$| . O X X X X X O O X O |
$$| X O O O O X O O X X X |
$$| . X X . O X O X . X . |
$$ -----------------------[/go]

After more work I have discovered the black attack is far stronger than what I believed initialy. As a consequence the win for black in my previous positions is not very interesting because almost any black moves (including a pass!) is winning.
Though the results I claimed are good it is not satisfactory and I have to change the position in order to have a quite interesting solution. Here it is with a more usual komi:

AGA rules, komi 6.5

Click Here To Show Diagram Code

[go]$$B Black to play and win
$$ ------------------------
$$| . O . O . O . O . O . |
$$| O O O O O O O O O O X |
$$| X X X X X X O . O . . |
$$| . . . . . X X O . O . |
$$| . . . . . . X O O O O |
$$| . X . . . . X X X X X |
$$| X X X . . . X O O O O |
$$| O O X . . . X O . O . |
$$| . O X X X X X O O X O |
$$| X O O O O X O O X X X |
$$| . X X . O X O X . X . |
$$ -----------------------[/go]

This time I am quite happy. The position seems quite simple, without weaknesses (with japanese rules it is even an endgame position) but with AGA rules, this apparently losing position is a winning one due to a very surprising sequence!
Take pleasure.

I think you mean "settled position".

I must be missing something, what is the number of prisoners on each side?
At first sight, assumming no prisoners, black has 22 points, white has 14, so with komi 6.5 black won already.

Yes Robert. I mean it is a position for which both players can easily decide to pass and go in the confirmation phase instead of playing the loop made of a single pass followed by an exchange in the double ko.

I assume AGA rules that means area counting. The number of prisoners is irrelevant.

As an example if

Click Here To Show Diagram Code

[go]$$B pass, pass, pass
$$ ------------------------
$$| . O . O . O . O . O 4 |
$$| O O O O O O O O O O X |
$$| X X X X X X O . O . 2 |
$$| . . . . . X X O . O . |
$$| . . . . . . X O O O O |
$$| . X . . . . X X X X X |
$$| X X X . . . X O O O O |
$$| O O X . . . X O . O . |
$$| . O X X X X X O O X O |
$$| X O O O O X O O X X X |
$$| 1 X X . O X O X . X . |
$$ -----------------------[/go]

black count : 38 stones + 24 territory = 62 points
white count : 45 stones + 12 territory = 57 points
with a 6.5 komi black loses the game by 1.5 points

If I'm right with my solution idea, it's a pretty nasty superko beast. A kind of "pass fight", and at the same time an example of the difference between situational superko and positional superko, isn't it?
And I think maaany moves are necessary before black can make the decisive capture...

You are 100% right jmeinh.
Do you think you have discovered the right sequence allowing to apply your idea?

Well, I think so.

The basic idea is correct and I confirm the SSK allows such sequence. Congratulation for that ajmeinh.
Unfortunetly the execution is not correct.

Is that really a problem?

Yes it is a problem

I see. Then my idea doesn't work as intended.

While not especially necessary, AGA still counts with prisoners as a convention.
Black to play, means an equal number of moves have been made.
43 White stones on the board
38 Black stones on the board
White has thus captured 5 more prisoners than black. Even in unlike event of an early pass in the game, player would still have to hand over a prisoner in AGA.

Yes hzamir, providing you count 5 more prisoners for white you can count by territory the initial position:

Click Here To Show Diagram Code

[go]$$B Black to play and win
$$ ------------------------
$$| T O T O T O T O T O T |
$$| O O O O O O O O O O Y |
$$| X X X X X X O T O T T |
$$| M M M M M X X O T O T |
$$| M M M M M M X O O O O |
$$| M X M M M M X X X X X |
$$| X X X M M M X O O O O |
$$| O O X M M M X O T O T |
$$| . O X X X X X O O X O |
$$| X O O O O X O O X X X |
$$| M X X . O X O X M X M |
$$ -----------------------[/go]

black : 25 territory = 25 points
white : 14 territory + 1 prisoner (upper right corner) + 5 prisoners (to reach the initial position) = 20 points
With a komi of 6.5 black loses by 1.5 points (same result under https://lifein19x19.com/viewtopic.php?p=279412#p279412)