Hi.

Suppose one has a tsumego and there are two solutions which only differ in one respect, viz. that one of the solutions leaves a ko-threat, while the other solution doesn't leave a ko-threat. So for instance, either both solutions end in a sente move, or both solutions end in a gote move, etc.
Can one imagine a situation where the solution that leaves a ko-threat is still to be preferred over the solution that doesn't leave a ko-threat?

Sometimes the solution given by a tsumego can sill be suboptimal depending on the rest of the board. E.g. when the tsumego involves a superko where one might decide to let one's opponent capture the group that is at stake in the tsumego, to avoid one's opponent being able to achieve a N.R. game result under Japanese rules, when one would still win the game if one sacrifices the group at stake in the tsumego.

greetings and thanks in advance for any feedback, Niek

I would say you should take the one that doesn't leave a ko threat. As with all things in go, you need specific examples to talk about though.

Some things to consider, in approximate order of importance:

1. Status of the group (alive, dead, ko)
2. Sente
3. Number of points of territory
4. Remaining endgame moves
5. Creating or fixing aji on the outside
6. Difficulty of the toughest line of resistance
7. Ko threats

So there are many very good reasons to play a line that leaves lots of ko threats. But like Oren says, context is key. This is especially true when living isn't enough to win, in which case a slightly more profitable ko may be preferable to a less profitable unconditional solution. Or if there is a large ko remaining on the board, eliminating ko threats may be more important than a few points of territory.

You seem to be asking something different, though, which is, "does the importance of ko threats depend on the rule set?" The answer is no. Whether you're using superko or Japanese, you want to leave as few ko threats as possible.

Here are two specific examples from the gochild tsumego site:

---------
Dong-Dong grouping > (1) ~10k_6350 > (6) 20k~10k > (4) > 5653

http://eidogo.com/#1Rfa7OX

----------

Dong-Dong grouping > (1) ~10k_6350 > (6) 20k~10k > (4) > 5693

http://eidogo.com/#1EWDj7wB

----------

In problem 5653, there is a single solution, but it involves a superko. Presumably,
if black can win the game despite losing the group at stake in the tsumego, he
should not play according to the solution given, but let white capture the group,
because if he does try to save the group, white gets a chance to achieve a N.R.
result for the game under Japanese rules (because of the superko).

In problem 5693 there are three possible solutions given. One of them, the third solution, doesn't leave any ko-threats (B17, A17, A16, A15, C15, A18, A14, A16, A12)
and another, the first solution (B17, A17, A14, A16, A12),
does seem to leave a clear ko-threat (C15 for white).
So I was wondering if the solution that doesn't leave a ko-threat is superior to the one that does and whether the remaining second solution (B17, A17, A16, A15, A14) might also be inferior compared to the solution that doesn't leave a ko-threat, or whether that solution is simply an abbreviation of various alternative solutions that don't leave any ko-threat either
like (B17, A17, A16, A15, A14, A18, C15, A16, A12) and
(B17, A17, A16, A15, A14, A18, A12, A16, C15).

Problem 5363 ends as a seki. You can use it as a semi-infinite source of ko threats, but almost all the time you can call it a seki.

On the second solution there is a ko threat left on the first two solutions and the third has none.

It's good to find all the answers if you can.

If ko is not a consideration for the second problem, it does not matter whether Black throws in or not.

Click Here To Show Diagram Code

[go]$$B No throw-in
$$ ----------------
$$ | . . . . . . . .
$$ | . O O . . . . .
$$ | 2 1 X O O O . .
$$ | 4 O X X X X O .
$$ | . O 6 X . X O .
$$ | 3 X 7 X X O . .
$$ | . X X O O . O .
$$ | 5 X O . . . . .
$$ | O O O . O . . .
$$ | . . . , . . . .[/go]

If ko is a consideration, White will save until near the end, as it leaves a number of ko threats for Black.

Click Here To Show Diagram Code

[go]$$B Throw-in
$$ ----------------
$$ | . . . . . . . .
$$ | 4 O O . . . . .
$$ | 2 1 X O O O . .
$$ | 3 O X X X X O .
$$ | 6 O 7 X . X O .
$$ | 5 X . X X O . .
$$ | . X X O O . O .
$$ | 9 X O . . . . .
$$ | O O O . O . . .
$$ | . . . , . . . .[/go]

fills at 3.

If ko is a consideration, Black may leave as a ko threat, at the risk of White getting a reverse sente there. If the ko is small enough to occur after in the first diagram (or with some complex kos), Black will prefer it.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Yes. And not just ko situations. It is not that uncommon for two plays to be alike except for ko threats, and for correct play to differ depending upon the ko possibilities.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Correctness of tsumego answers can depend on ko threats, just as with other factors such as size of territory and follow-up endgame moves. However, a tsumego problem is usually a local position so in a real game it could happen that the overall position has an effect that wouldn't be considered in a tsumego problem.

But is it possible to distinguish somehow between tsumego where one might reject
answers that leave a ko-threat because there are superior answers that don't leave a ko-threat
as opposed to other tsumego where one might accept both answers that leave a ko-threat
as well as other answers that don't leave a ko-threat?

I reckon one might try to maintain consistency among a collection of tsumego problems by trying
to avoid the impression that answers that leave a ko-threat are sometimes arbitrarily accepted
or rejected. So perhaps one can think of criteria that would be a good guideline to decide whether
or not a solution that leaves a ko-threat ought to be accepted as an alternative for a solution
that doesn't leave a ko-threat.

Likewise, one might accept or reject a solution that involves a seki, when another solution involves
a group that is alive without seki. Usually one probably would prefer to be alive without seki,
but does that mean that one should always reject seki solutions to a tsumego when there are also
solutions that don't involve a seki? Again, to avoid the situation that people get the impression that
seki solutions are somewhat arbitrarily accepted or rejected as alternatives for non-seki solutions.

I think you're overthinking this a bit. It's a go problem and often there are multiple correct answers. In a game the most important thing is going to be life/death and then points/ko threats. If the problem is a ko, the goal is to gain the most favorable ko by losing as little as possible if the ko is lost and by getting to take first when possible.

Seki will be worse pointwise than having two eyes, so that should be your goal. If you can't meet that goal, go for seki. After that, I would try to live with most points possible. The ko threats generated is likely going to be the last thing you will worry about.

So I would say yes, there are in game considerations other than points and/or ko threats. If you find some different solutions, and how they differ; I would say that's an excellent thing.

_________________
Revisiting Go - Study Journal
My Programming Blog - About the evolution of my go bot.

Well, overthinking, I dunno. The reason I'm thinking about this is because I often solve tsumego at gochild. Sometimes I see there is an additional solution and I mention this on the forum. But then I hear that the additional solution isn't accepted because it leaves a ko-threat. Yet, in other exercises, alternative solutions that leave ko-threats are accepted. So it remains unclear to me what governs the decision to accept or reject alternative solutions that leave ko-threats. Personally I think it would be best to accept all solutions, but it would also be nice if one would be notified of the fact that a solution leaves a ko-threat to indicate that it's likely one might prefer one of the other solutions that doesn't leave a ko-threat. At the moment, usually when I see that an additional solution that has a ko-threat is accepted while there are other solutions that don't leave a ko-threat, I report this on the forum and the solution that leaves a ko-threat is removed. But in the example involving ko-threats I've mentioned in this thread, it's not entirely clear if there might be a reason to reject one of the three solutions given because it is inferior
due to leaving a ko-threat while other solutions don't leave a ko-threat.

Ok, but ko possibilities might not be present at the moment you encounter the tsumego-pattern in the context of a game, yet later in the game a ko-situation might arise that affects the question of how to handle the tsumego pattern optimally. So unless the rest of the board is settled, I reckon it's not just actual ko possibilities that might play a role, but also potential ko possibilities that might arise later on in the game.

Then it's just an issue in the consistency of a web page. If either solution results in the desired life/death I would accept it. I wouldn't disallow a solution due to ko threats.

If the problem is ko, then the order of ko should be taken into account.

Tsumego are not about ko threats. For one's own stones, life is best (and seki is a form of life), ko is next best, death is worst. Reverse that for the opponent's stones.

Ko threats are important in real games. As a rule, if two lines of play are otherwise acceptable, but one yields more ko threats on balance for you, you should pick that line. But there are exceptions. To decide between alternatives, you usually have to see the rest of the board. Which tsumego problems do not show.

BTW, by ko possibilities I meant what you are calling potential ko possibilities as well as what you are calling actual ko possibilities.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.