My thought process is: if white captures those 3 stones he’ll be connected and cutting me.
If I capture those 4 white stones I’ll be connected and alive.
So it’s all about who captures first.
The single black stone on second line makes it all more complicated. If that stone was connected, black would be unconditionally alive in the corner and could think only about the best way to surround the 4 white stones.
But if white cuts that stone, he could almost make an eye, which would take many more moves to kill…
It took me a LONG time to solve this one (As a reference I am about 3kyu). I was in fact very proud of being able to solve it today on the first try when it came up in the tsumego app. So Gia should probably take it easy, these problems are of quite different difficulties and some are quite hard!
I see that a Tsumego ending with “ko” confused you. Maybe most of the tsumego you found were just live / die, but more advanced ones often have “ko” as the best (and thus correct) answer. Sometimes there are even various different kos possible, and the solution is to make the “best” ko!
Tsumego ask for the best move in a local situation. That is a bit tricky because, the best move in a local situation might actually depend on the global situation, so some kind of “typical case, rule of thumb” assumption must be made.
Thus, the standard tsumego assumption is that results are ordered like this (from best to worst, from the point of view of the one trying to live. Of course if you are trying to kill, the list is reversed).
Living with two eyes is the best possible result (usually tsumego accept any solution that lives, but often one can dig even more and study more carefully if desired: a move might live with only 2 points, while a slightly different one lives with 4 points for example, and thus normally the best move is the one that lives larger. Similarly, two moves might live with identical points but one leaves behind no ko threats and would be preferred to one that leaves ko threats, etc).
Living in seki (this might be considered a special case of the above fine distinction… as it would be “living with 0 points” instead of living with actual points. It just happens that this one is often distinguished by tsumego, and creating seki when two-eyes-life is possible is not considered a correct solution of the tsumego).
Creating a ko fight for the life of the group (in a real game, depending on many factors and ko threats in the whole board, the player trying to live might prefer an all-or-nothing ko rather than live in just seki with 0 points… but that is the rare exception. Most of the time, the better move is to create seki, and not risk ko. Thus, although it is not universally the best local move, tsumegos typically have this assumption that creating ko when you could have lived in seki is wrong, because most of the time it is indeed a worse move).
Just dying is obviously the worst possible outcome.
About point 3), quite often you have two sequences that create ko, but changing who takes the ko first: in that case, it is better to play the sequence where you take the ko first, as that is basically like having one more ko threat.
Also, ocassionally there are advanced tsumego where more than one kind of ko can be created (like, direct ko vs an approach ko). This gets more case by case but as a general rule, you want the ko that is more favorable to you (you need less moves to win it / your opponent needs more moves to win it).
So back to your example, the solution to that problem is ko, so we get “number 3” in our previous scale. A better result according to our “scale” cannot be achieved, so in this case this is the answer, create a ko. This is an additional difficulty of tsumego where you don’t get the “best” result in the scale (which is either perfect two-eye-life / perfect clean kill, depending on who you play): You still have to keep reading to check that there isn’t another initial move that get’s you an even better result!
Yes, that seems like ko. Black cannot kill white in time unless he wins some ko fight, thus black will have to ignore some white move somewhere else to be able to kill. That is obviously worse than killing unconditionally without giving white any free move, thus justifying the “scale”.
In this problem’s solution, black can capture white unconditionally, no need to fight ko.
To check that something depends on a ko, you can imagine that your opponent has the superpower to ignore the ko rule (but you don’t). If you still kill then your solution does not depend on ko,but if this power makes the kill fail then the solution depends on the ko fight. Here it is easy to see that if white has this imaginary superpower, black cannot take at T5 and thus there is no way to capture white before she captures black. In fact in this position,if white had played T5 directly instead of O6, it would not even be ko: white would live directly.
One more comment: in this one you posted a month ago, the solution is ko. Now that you have seen the solution, It is a great exercise to check ALL other possible initial black moves (arguably you should have done that too in order to solve the tsumego),and verify thay they are all worse: white can live directly, no ko at all, with the other moves. With this one it is at least ko. The key thing to understand is that ko is locally ALWAYS better than the direct no ko result, it does not depend on winning it: if you win it great,that would have been imposible to achieve and kill white if you played the other moves that have no ko. But EVEN if you still lose the ko, as a result of the ko fight, white will have to ignore one of your ko threats to come back here and live. So that ignored ko threat is an extra free move, compared to the other options that fail without even ko. The extra benefit depends on how poweful the ignored ko threat was, but even if it is just a small move, it is a free move, thus better
As a rough value of a life on ko. You can estimate it as half the points if the life was granted without ko. Just for a simple evaluation
(because the ko threats are going to start to vanish when they are of the same size of the ko and because playing two consecutive moves will then be of the same size too)
It is a semeai with 3 vs 3 liberties. So black needs to keep white down to 2 liberties.
It might be a ko, but did you consider this move 5 for black (to keep white’s cutting stones down to 2 liberties without a ko)?:
Perhaps you can try to read out if this works?
If you mean the value of making the move, “2/3 of the normal value” is a better estimate
More precisely, when you have a normal unsettled group without ko, such that the score is A if white plays and B if black plays, then you can imagine that “right now” the score is (A+B)/2, the average of both. So the extra “gain” of making a move is half the difference, |B-A|/2, for whomever plays to kill/live.
When the situation is a direct ko with the “endpoints” still having score A and B, the value of each move is now |B-A|/3, because there are now “three steps” instead of “two steps” to jump from situation A to situation B. So in a normal unsettled group without ko, your group is “half dead”. If your group instead can be made alive in a single move, but the opponent can create a ko with his move, then your group is “a third dead” (and each net move that anyone invests in the position, “moves” the group’s status 1/3 of its way towards one of the alive/dead endpoints).
The following picture shows this for a very late “1-stone ko”, but the same principle holds for a larger group that lives or dies depending on a ko:
By the same principle, the value of each move in a two-stage-ko is 1/4 of the difference of the endpoints:
Hm, I think I made a mistake in move order, because this white counter seems to work for white:
So by 1-2-3 reading, my 2nd attempt is for black to start at the point that counters my 1st attempt:
And then read from there, and you would also need to consider white 2 at 3:
The longest branch (strongest resistance by white) of my solution has 17 moves before white is captured. So I’d say the reading depth of this problem is probably challenging for strong kyus, and maybe also for lower dans who don’t do much reading practice. Probably too much for @Gia’s level (no offense intended).
I also made some mistakes while solving it. My 1st intuition was in the right direction, but I was sloppy, because I was underestimating the problem intially, so I didn’t check all of white’s options for resistance carefully.
