Approaching a life and death problem the right way

    Keywords: Life & Death

It has been suggested that the content of this page should be merged with Approach in tsumego.


You know when you are dealing with a life and death problem (tsumego) if you ask yourself either one of the following questions:

  • Can I kill my opponent's group?
  • Is there a way my opponent can kill my group?

In order to answer these questions, it is a good habit to work systematically through all the possible moves that may work. A Kobayashi Koichi book or article may have recommended the following order:

Isolate the group from the center

If the group still has access to the center, it has a possibility to link up to friendly forces.

Reduce the eye space of the group under attack

The classic example is a hane, hence the proverb that there is death in the hane.

Look at the cuts

If there is a defect remaining in the group under attack, it may become a good deal easier to kill it if you manage to divide it into separate pieces. ("Divide and conquer".)

Placements

The rationale is that the placement will mess up the shape of the group under attack. However if you start with this technique, the group under attack may still have options of running to the center or becoming a bigger group, i.e. a group with more space to create eyes. This is why you should first look at isolating it and reducing the eye space.

--Stefan


The Professional Approach vs the Amateur Approach

To solve tsumego or real game problems, there is the professional approach as opposed to the amateur approach.

Amateurs have more or less the following approach:

Suppose we are to solve a tsumego:

  1. We look for the vital point;
  2. We look for a sequence, including the vital point, that kills or makes life;
  3. If we have found a sequence, we verify the branches of that sequence to see if it really works;
  4. We take that sequence as the solution.

In a real game, when our group is threatened, it goes something like this:

  1. We try to decide whether the group lives;
  2. If it lives, we mostly leave it;
  3. If it can live, we mostly play at the vital point in order to live;
  4. If we are not sure about its status, we mostly add an extra defensive move;
  5. If we have left it, we regularly come back to the problem to verify its status.

The professional approach is very different, or so I have been told.

Suppose they are to solve a tsumego. They:

  1. Take all possible moves into account, starting with the one most likely to be the best (the vital point);
  2. Explore each move, with all of its branches, successively, and evaluate the result (life/death, points gained, remaining aji, sente/gote);
  3. Take the sequence with the best result as the solution.

In a real game, when their group is threatened, they:

  1. Take all possible moves into account, starting with the one most likely to be the best (the vital point);
  2. Explore each move, with all of its branches, successively, and evaluate the result (life/death, points gained, remaining aji, sente/gote);
  3. Measure the local result against the global position.

For one thing, professionals have exactly the same approach to tsumego as to real game situations. For another, a professional reads until he knows exactly what is going on (locally) and knows the meaning of each move in each of the branches. Finally, once the problem has been read out, a pro never returns to verify the status. He'll only continue to perform the third step (weighing local result/global position) regularly.

We could try at least the professional approach in tsumego. If you continue to explore each possibility, even if you have found a solution, then you'll be surprised to find sequences that do the same thing as the one you already found, but with a better result in terms of points or aji. Moreover, exploring all moves, also the ones that don't work, does a great deal to your reading skills and your knowledge of shape.

-- Dieter Verhofstadt


Charles Matthews In real life, there is even more involved. There is a proverb 'play kikashi before living' (they may not be sente later). And there is a possibly conflicting piece of advice: live in a way that improves the position on ko threats.

It is even possible that you deliberately live in a way that allows seki later, for the sake of other aji. This came up in a famous consultation game where Kitani and Go Seigen made up one of the teams.

I think that where the status of a group depends on some aji on the outside - which is often the case - one cannot really just read the position once and leave it. Sounds like hoping for the best.


If the problem is to live and not just a capturing race, then a systematic way to solve life and death problems is to ask the following questions:

  1. Is there an eye point inside.
  2. Is there a point that divides the area into two rooms
  3. Expand your eye space to get more room.

At each step of the process start at 1) and work your way down until the problem is solved.

An example:

[Diagram]
Black to live (1121 from Go Problems)  
[Diagram]
An eye point  

B3 is also an eye point, but White plays W4 and it's ko. So let's change the last move that got us to ko. There is no point inside that divides the area to live in, into two 'rooms', so we skip step 2 and move on to step 3. Expand the eye space.

[Diagram]
 

But there's not enough room to live. So we've exhausted the steps, and need to fix the first move. There is no other eye point, so we choose a spot that divides the inside area into two rooms.
We have exhausted the possibilities that come from this B1. All end in death. Therefore we must reject this B1 and look for other moves for B1.

[Diagram]
Divide into two rooms  

B1 creates two small rooms within Black's group. As a result of B1 both W4 and B5 are eye points, so Black will play one of them (miai), and live.

[Diagram]
 

White can try some squeeze plays as well, but rather quickly we found the important points to solve this problem. The hardest point in a life and death problem is when you need to expand your eye space. A few tricks are necessary for that.



If the puzzle is to kill then use these steps instead:

  1. Is there an eye point inside?
  2. Is there a point that divides the area into two rooms?
  3. Squeeze the eye space to give him less room.

The hard part about killing is seeing how to squeeze best. Sometimes it involves very clever sacrifice.

JoeSeki

George Caplan The method listed above is the method lectured on and endorsed by Yi Lun Yang 7dan who teaches in the U.S. and on line. In fact, it uses his precise terminology - particularly the term "eye point" which was invented, I believe, in collaboration with his students. If JoeSeki has another source for this text, I would be interested in knowing it.

This method has some real advantages. First, it organizes your reading and helps find correct solutions. Second, it discourages throw - ins untill they are absolutely necessary - avoiding lost points when we humans misread.


More Discussion (moved from tsumego)

Stefan: There are at least two approaches to tsumego.

The first approach is to solve the problem more or less 'on sight'. Speed is a concern - you typically spend 20 seconds or less on the problem (even if that implies not completely reading it out), decide on the right move for the situation, and check your move versus the correct answer. The purpose of this kind of study is to internalise a lot of different situations and get them in your head as working knowledge. A bit like developing reflexes when you learn how to drive a car. I use this kind of study to get to know the basic shapes better and work them faster in games (tripod group, anyone?), as well as to increase my tesuji-spotting capability.

The second approach is to take as much time as you need for a problem, but work it out systematically and don't look at the solution until you've convinced yourself you have completely read out all moves and countermoves (bonus points for working out the value of endgame sequences and how additional moves in the area influence the position). This takes a higher level of concentration. I use this kind of study to increase the accuracy and completeness of my reading (and frankly also to regain a bit the ability to focus, because the fast reflex-stuff makes me a tad sloppy in actual gameplay).

For the first approach I love taking a book a la Graded go problems for beginners and race from cover to cover. For the second approach I like the above mentioned [ext] goproblems.com. Solving problems there with a registered account gives you feedback in the form of a rating. And having a rating to maintain or boost tends to cause some of us to concentrate a little better... :-)


Dieter: I think it is very important to continue searching the various plausible moves, even if you have found the solution to a tsumego. This way one learns to know the shape even better. Also, even if "one" move works, there might be a better move. This is one of the themes in the Kanazawa Tesuji Series. I invite everyone to add possible moves that I haven't included and the reason why they fail.


DougRidgway: I've done a fair number of problems, including recently finished working through 1001LifeAndDeathProblems, and have some comments on how I do the tree search.

Move order matters. It's much easier to prove that the right solution works against all opposition than it is to find it, so starting out with the right answer saves time. If you don't know where to start, the order suggested above is good (isolate, reduce, then cuts and placements), and straightforward moves before fancy ones is good too. After a failure, try the opponent's successful moves.

The standard advice is to read each sequence once and only once, to completion, and then instantly recognize transpositions when they occur while reading future sequences. I'm not that strong, I find myself backtracking and retracing a lot.

Terminal states matter. Terminal states are where you can stop reading, either because one side got two eyes, ran out of liberties (and no under the stones shape is left), or you recognize the shape and know the result. Static recognition saves work and increases accuracy, and I'm sure stronger players are much better at it than me.

Know your ko assumptions. I.e., first assume that you will lose all kos -- this is optimism, you're assuming that you can live/kill without ko. Therefore, never read down a branch which involves you taking a ko, but the opponent always may. If you win, you have won without ko. If failure, then reverse the assumption, and try to win with ko. If you now succeed, then figure out what kind of ko it is, if a better ko is available, etc. Slavishly following this assumption fails when the final result involves a double ko, but these have to be recognized separately. When thinking about ko like this, local sequences never include ko threats or recaptures, which simplifies things considerably. This might be equivalent to assuming that first your opponent and then you are komaster.

Most problems that I get wrong are due to misevaluating terminal states, usually by missing a shortage of liberties; getting confused visualizing the stones during reading or failing to consider a key move at all is much rarer.

Bill: Let me just add a tip that I read about not too long ago. In a study of eye movements while attempting to solve tsumego problems laid out on a board, there was a significant difference between the eye movements of weaker players and stronger players. The weaker players tended to look at points to play stones. The stronger players tended to look at points to make eyes.


tapir: I doubt that this page is right about professional players approach to solve tsumego. Always reading out every move in every possible branch etc. (this is more like the brute-force computer approach isn't it?) I don't doubt that they read a lot and really fast, though :)

mike?: @tapir, how else can you attempt to read out the possible solutions unless if it's a shape that you recognize and have already read out in order to live/kill. Either way your inference to it being "brute-force" makes it sound difficult, which is incorrect -- it only requires practice to get a better understanding.

tapir: Well, I'm sure professional players read more, more accurate and faster... but I doubt they read all variations from all possible beginnings. Since this is what some beginners try to do... rather they discard more beginnings and variations they recognize shapewise or experience-wise as impossible and read the remaining much smaller tree out faster, more accurate etc. The page about reading contains the same argument btw. If you literally "read out everything" then there is no place for better understanding. Imho better understanding shows in reading the critical spots, exploring the relevant lines vs. reading all possible lines from all (even to the experienced player) obvious failing beginnings.

betterlife: Why on earth should a professional player explore each move with all its branches?

OneWeirdDude: Is there a part about playing tenuki once you realize the group you were trying to save is dead, so as to save a ko threat?


Approaching a life and death problem the right way last edited by betterlife on March 10, 2010 - 12:41
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