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[go]$$B corner
$$ ------------------
$$ | . O . . . . . . .
$$ | 2 O X X . . . . .
$$ | . O O X . . . . .
$$ | O a O X . . . . .
$$ | 1 X O X . . . . .
$$ | X O O X . . . . .
$$ | b X X X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

In L&D problems like these, I have always liked this as the more stylish solution. It omits the brute exchange of A for B, which is incidental to the solution. is the real vital point. As such, it is an application of Charles Matthews' 1-2-3 principle. Esthetically, it applies the "beauty of omission".

However ...

After Black has a ko threat at B which threatens to kill the whole White group. White's ko threat at A merely threatens to capture 3 stones.

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[go]$$B corner
$$ ------------------
$$ | . O . . . . . . .
$$ | 4 O X X . . . . .
$$ | . O O X . . . . .
$$ | O 2 O X . . . . .
$$ | 1 X O X . . . . .
$$ | X O O X . . . . .
$$ | 3 X X X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

here applies "force before living". If Black doesn't answer it, White can capture 3 stones and live, so that is no longer necessary. If Black does answer, White got rid of the unbalanced ko threat situation mentioned above.

This solution is therefore the better one and I may have to re-evaluate my "aesthetics".

Oops, you highlight here an interesting point concerning the 1-2-3 principle.
Here you MUST NOT apply this 1-2-3 principle simply because the conditions to apply this principle are not fullfilled : if white plays at 2 instead of "a" then black CAN answer immediatly at b forcing white to play at "a" with the same result as the brute force. By playing at 2 white OFFERS black the choice between the result of the brute force or other moves. In such situation it is clear that applying the 1-2-3 principle is a mistake.
IOW before applying the 1-2-3 principle you have to verify that after the immediate 3 (instead of 1) your opponent cannot force immediatly the exchange 2 for 1.
For me it is not relevant to look for the following ko threats or whatever, the 1-2-3 principle MUST simply NOT be applied here.

This depends on the ko that you expect. White wouldn't only be eliminating a ko threat for black but also a threat for white. The white threat maybe looks insignificant but it could be sente, black could take the ko first and it could be heavier for black.

If you don't expect a big ko then this is a moot point. Either player can eliminate this threat at the last moment if the ko is small enough.

Usually, ko threat considerations depend on the following:

1. If there a ko coming.
2. Are there other ko threats.

If there is a ko coming then you need to do what is right for the kind of ko that you see coming. If there is no ko or it is small one (that allows us to eliminate this threat if we need to) then it doesn't matter. Unless there is a specific ko that we expect then we just don't know who will be able to use the ko threat in the example. Also, if there are other ko threats then the one in the example might not change anything.

Maybe I should ask my opponent before choosing my move. "Any plans for a big ko?"

That sounds like when someone buys gas every time they take the car out and says things like: "How was I supposed to know if I needed gas? Ask the car!? Only if the car could talk."

Sometimes it is anything except learning when something is needed or not.

No it doesn't sound like that. You can easily predict if you will need gas depending on the trip you plan. You can't predict if you will run into a big ko, except towards the endgame. Yes, you can avoid big kos later on, but that's adapting to the position, while this is about preparing for potential positions.

I don't understand your point here. Size of ko threats don't matter in evaluating a position, if you don't expect a big ko to come up?

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

If you consider that the above sequence is forced then, as I explained in my previous post, you cannot apply the 1-2-3 principle and you must not replace the move by a move at
If however the result of the game depends on a big ko elsewhere then the sequence above is no more forced. The only concerned for both players is the number of black ko threats in the corner and the 1-2-3 principle is irrelevant. In this situation the sequence above gives black two ko threats (the and moves) but this result is bad for black. The correct black sequence is

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

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[go]$$B
$$ ------------------
$$ | . O . . . . . . .
$$ | X O X X . . . . .
$$ | . O O X . . . . .
$$ | O O O X . . . . .
$$ | 6 . O X . . . . .
$$ | 5 O O X . . . . .
$$ | O X X X . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

and black gets three ko threats.

You see the point?

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

By choosing to begin by this move the number of black ko threats is only two. In this case the Knotwilg vital point is very fine isn't it?

I have a feeling I may be completely missing the point here - so the following may be completely offtrack (and sorry if so) , but 2 points I'd make about the preceding discussion are:

- Each player has some agency in whether a big Ko comes up in the game. There are no guarantees, but it should hopefully be possible to find a line that avoids a big Ko if you don't want one (if you can't, then your opponent was probably going to outplay you somewhere in the game anyway)

- Playing too tightly or solidly in your game because a big Ko may somehow come up in a way you can't as yet envisage is likely to lead to some very strange distortions and inefficiencies in your game.


Vaguely related anecdotally, I remember reading in an old Go World in the 1980s some professional saying that the difference in strength between themself and Cho Chikun (then multiple title holder) was illustrated by the fact that by the time they had worked out the position was a Ko, Cho had already assessed the balance of Ko threats. I took it from this that handling Ko is kind of an key index or reflection of your overall strength.

I can try to explain.

Ko threats matter for ko. If there won't be a ko then ko threats don't matter that much. And if the ko threat isn't useful for the ko that does occur then that ko threat isn't something important.

The example position is potentially complex. Maybe that wasn't intended. I think what is important is firstly if both players can eliminate the ko threat in sente later or not, and secondly if it is likely that this ko threat will be needed by either player. I would expect that it is likely that the player that takes first in any ko will try to eliminate this threat first and therefore it would often not matter in the end which player eliminates the threat or when.

Of course there are situations when allowing ko threats changes something. If you recognize those situations then you can eliminate or create ko threats in time. Just for fun I found this example of how a ko arose in the opening and the threats were something that was left by a very common joseki. That joseki leaves some big threats, in that way it is a good example of what can happen if you leave big ko threats. Since you can find this same joseki in so many games it is also an example of why leaving ko threats often isn't very important. http://ps.waltheri.net/database/game/28236/

Also for possible wider entertainment purposes as an example of what can happen if you leave big ko threats hanging, there is the game below from 1987 which features large ko aji from very early in the game.

As explained by Matthew Macfadyen in the British Go Journal, in an article entitled "The Value of Two Moves in a Row" (BGJ 90):


"White refuses to protect his group at 28, and insists on counter-attacking with 44-48 instead of running away. In the result to 77 his group is killed with the following proviso: White can, at any time, play atari above 63, and then take the ko in the corner. Black will then have one free move to prepare himself before White makes a ko threat which Black will have to ignore. Effectively, then, White can play two moves in a row and can choose any time in the game to do it".

[Spoiler alert: the sword of Damocles ko threat finally appears in the moves around 230]

The following position is expected to hignlight the properties of the position in the upper right corner analysed by Knotwilg. OC a big ko is necessary. I hope I have not misunderstood his ideas!

Komi 7.5 Black to play and win.

Very nice and not trivial. BTW, you mean "upper left", I think.

My previous example hightlighted some of your ideas but not the last one above : "A" merely threatens to capture 3 stones.
This last point is not easy but eventually I succeed (I hope!) with the following more complex example:

Komi 7.5 Black to play and win.

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

BTW it is quite interesting, for the understanding of the position in the upper left corner, to see why I did not put the marked black stone at "a"