Do you like curious positions (which will never happen in real game)? After a lot of effort I managed to build the following very strange one:

Click Here To Show Diagram Code

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

Assume area counting.
What is the best move?

I must be missing something, but here's my attempt:

If black plays at the 1-1 point in the lower right, the lower right is seki. Result: B+5.

If black plays at the 1-2 point to start the ko, then white immediately captures the ko. Black has no ko threats, so whatever black plays, white resolves the ko, living in the lower right. Result: W+5.

If black passes, and white plays at the 1-1 point to start the ko, black immediately captures the ko. White has no ko threats, so whatever white plays, black resolves the ko, capturing the lower right. Result: B+25.

If black passes, and white passes, the rules might say that this ends the game. Result: B+4.

If black passes, and white passes, and the rules don't say that this ends the game. Then black will still play 1-1 in the lower right, to increase his score by one. Result: B+5.

If you assume white will play optimally in all cases, black's best play is the 1-1 point in the lower right to make seki, resulting in B+5. If you assume that white is fallible and might make a mistake, and if the komi at least 5.5 so that black would lose with that just a seki, then maybe black's best play is to pass and hope that white makes the mistake of starting the ko.

Fine analysis EricBackus.
Are you sure of your count when black and whites passes?

No. I wasn't sure yesterday when I posted, and I'm even less sure now that you asked.

Seems like it would depend on the exact rules used?

Maybe I am wrong but my count for the initial position is the following:
black : 38 stones + 2 points for territory = 40 points
white : 32 stones + 2 points for territory = 34 points
=>B+6
Do you agree?

BTW EricBackus, did you also analyse a first black move in the upperright corner or a first white move in the left corner?

I have looked at this position and it has baffled me. Unless there is something very tricky in the rules like White can claim neutral points in the lower right which Black can't, I don't see the point of the problem.

Also the upper left and right seem irrelevant. Black is dead in the upper left and White is dead in the upper right. Either the author of the problem or me are missing something.

From your last post you seem to suggest the upper corners are seki?

No. That is the count if you assume all stones on the board are alive. But the upper left black stones and the upper right white stones are unconditionally dead. At least, that's how they look to me.

By my count:
black: 38 in main group including upper right corner, plus 3 in lower right seki = 41 points
white: 28 in main group including upper left corner, plus 9 in lower right seki = 37 points
=>B+4

I have to agree with Knotwilg, the upper left and right seem irrelevant. Maybe you meant to make them seki?

Click Here To Show Diagram Code

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

You say "Black is dead in the upper left and White is dead in the upper right." That is prefectly true in japanese rule due to the existence of the confirmation phase during which you can prove that.
But when you use area counting this confirmation phase does not exist. That means that, unless there is an agreement between the two players (in practice it is almost always the case), play must continue until the "potential dead" stones become effectively captured stones.
That is the point : if for example white plays in the upper left corner in order to effectively capture the black stones then white gives a ko threat to black and this ko threat can be use for the potential ko fight in the lower right corner.
If my interpretation is correct it is a very strange seki isn't it?

An application of https://senseis.xmp.net/?UnremovableKo#toc3

yes Herman, on this link you can find a position like the following:

Click Here To Show Diagram Code

[go]$$B
$$ --------------------
$$ |. X X O . O X . . |
$$ |O O X O O O X . . |
$$ |O O X O . O X . . |
$$ |. X X O O O X . . |
$$ |X X O O O X X . . |
$$ |O O O X X X X X X |
$$ |X X X X O O O O O |
$$ |X X X X O O X O . |
$$ |. X . X O . X X . |
$$ --------------------[/go]

White cannot play in the upper left corner without giving a good ko threat for black => seki

What is new in my position?

Click Here To Show Diagram Code

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

Here neither white nor black can kill the potential dead opponent group (the black group in the upper left corner or the white group in the upper right corner) to reach a better score than the seki. Did somebody already see such situation? For me this point is quite curious and strange.

How is it strange? Neither player can benefit from starting the ko, right?

If black tries then white just passes for and black gets the last dame with (if he remembers to play dame).

Click Here To Show Diagram Code

[go]$$B Black to play
$$ --------------------
$$ |. X X O O X X O 1 |
$$ |O X O . O X X O X |
$$ |O X O O O X X O X |
$$ |. X O . O X X O . |
$$ |X X O O O X X O O |
$$ |O O O X X X X X X |
$$ |X X X X O O O O O |
$$ |X X X X O O X O . |
$$ |. X . X O . X X 3 |
$$ --------------------[/go]

Does something different happen?

It seems to me that the white pass (move 2) and black 3 are not good moves.
Let's take black 3. It seems better to play

Click Here To Show Diagram Code

[go]$$B Black to play
$$ --------------------
$$ |. X X O O X X O 1 |
$$ |O X O . O X X O X |
$$ |O X O O O X X O X |
$$ |. X O . O X X O 3 |
$$ |X X O O O X X O O |
$$ |O O O X X X X X X |
$$ |X X X X O O O O O |
$$ |X X X X O O X O . |
$$ |. X . X O . X X . |
$$ --------------------[/go]

so that white cannot still kill the upper left corner due to the potential ko in the lower left corner

OK, I think I see what you mean.

Probably the continuation is not like this either, it is too many branches for me, it is also same result (right?) as if black plays the 1-1 point to begin with

Click Here To Show Diagram Code

[go]$$B Black to play
$$ --------------------
$$ |2 X X O O X X O 1 |
$$ |O X O . O X X O X |
$$ |O X O O O X X O X |
$$ |. X O . O X X O . |
$$ |X X O O O X X O O |
$$ |O O O X X X X X X |
$$ |X X X X O O O O O |
$$ |X X X X O O X O 3 |
$$ |. X . X O . X X 4 |
$$ --------------------[/go]

Click Here To Show Diagram Code

[go]$$Bm5 B+5(?)
$$ --------------------
$$ |. X X O O X X O . |
$$ |2 X O . O X X O 6 |
$$ |. X O O O X X O . |
$$ |1 X O . O X X O 4 |
$$ |X X O O O X X O O |
$$ |O O O X X X X X X |
$$ |X X X X O O O O O |
$$ |X X X X O O X O 3 |
$$ |. X . X O 5 X X O |
$$ --------------------[/go]

Correct sequence Kvasir.

In addition you can verify that white can also choose the following

Click Here To Show Diagram Code

[go]$$B Black to play
$$ --------------------
$$ |. X X O O X X O 1 |
$$ |O X O . O X X O X |
$$ |O X O O O X X O X |
$$ |. X O . O X X O . |
$$ |X X O O O X X O O |
$$ |O O O X X X X X X |
$$ |X X X X O O O O O |
$$ |X X X X O O X O . |
$$ |. X . X O . X X 2 |
$$ --------------------[/go]

Nice - halfway the analysis I had already forgotten about the non-existence of the confirmation

As soon as you have discovered a strange position you can often build a problem where the first move of the solution could be a very strange move. Here it is:

Area counting. Komi 5.5

Click Here To Show Diagram Code

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

I like this kind of problem.

Area counting. Komi -6.5 (negative)

Click Here To Show Diagram Code

[go]$$W White to play and win
$$ +-------------------+
$$ | . X X X O O X O . |
$$ | O X X O . O X O O |
$$ | O X X O O O X O . |
$$ | . X X O . O X O O |
$$ | X X X O O . X X O |
$$ | O O O O X X X X X |
$$ | X . X X X O O O O |
$$ | X X X X O O X O . |
$$ | . X . X O . X X . |
$$ +-------------------+[/go]

Maybe I miss something because it seems simple and in addition I see two solutions.
The point is the following : to win white must capture the black group in the upper left corner. By capturing this group immediatly, white gives black a ko threat and black will capture the white stones in the bottom right corner. It remains only the two dame between the white and black living groups in the center. To win white has only to occupy these two dame which is quite simple: instead of forcing black to begin a ko, white can simply begin herself this ko:

Click Here To Show Diagram Code

[go]$$W White to play and win
$$ +-------------------+
$$ | . X X X O O X O . |
$$ | O X X O . O X O O |
$$ | O X X O O O X O . |
$$ | . X X O . O X O O |
$$ | X X X O O 3 X X O |
$$ | O O O O X X X X X |
$$ | X 5 X X X O O O O |
$$ | X X X X O O X O 2 |
$$ | . X . X O 4 X X 1 |
$$ +-------------------+[/go]

I think white can also win by beginning in the upper left corner but the short sequence above is obviously simpler.

After finally understanding the point about the rules , I think this version is very nice!

_________________
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21