DieterVerhofstadt/Solving problems

Sub-page of DieterVerhofstadt

Introduction

As an avid follower of the greatest of all go sites, gogameguru, I'm also weekly trying to solve their problems. At the time of writing this article, they're at 115 sets of easy, intermediate and hard problems. The levels have been well defined, because the easy ones require almost no thinking from me, the intermediate ones I will nearly always solve and the hard ones not very frequently or confidently.

However, I was not very satisfied with my approach of solving them. I'd solve them through trial and error way too often. Slightly better I'd read until I found a solution, often to find out there was an even better solution, also known as the solution. I realized I was not quite reading as I should, so I went back to the fundamentals of reading. I had written a page myself on how to read and then there is the fundamental on how to approach a life and death problem, which is dearly underestimated:

  1. surround the enemy (conversely, escape or break through)
  2. look for cuts in the position (conversely, stay connected)
  3. reduce the eye space (conversely, expand)
  4. play at the vital point (same)

There are two benefits of such a fundamental order of playing

  1. First of all, for the sake of solving problems, it is good to have a method.
  2. This particular order is guided by overall game principles
    1. If the enemy can escape, your own troops are cut and the first principle of the game is to stay connected
    2. If the local position is cut into two parts, each part needs to survive on its own, which is about twice as hard
    3. Small eyespaces are less likely to make two eyes. Moreover, if the kill fails, there is not much harm done and the opponent will live small.
    4. Also, in case a ko occurs elsewhere, reviving the position may be the result of a ko exchange. In such cases the damage is smaller if the opponent just lives by playing a vital point, then by escaping or enlarging the eye space, hence its territory.

Armed with this reinforced method, I tackled the problems at gogameguru again, and lo and behold, I did much better. Having such a method in place gives a lot of confidence. It also leads to an increased insight into the structure of a problem.

I decided to record my thoughts for each of these problems, so as to highlight the kind of decisions a player of my level takes when reading:

  1. which variations do I consider and why (reading width)
  2. when do I stop reading into the variation (reading depth)

I discovered the following heuristics with myself for these two decisions:

  1. for width, I prune variations which do not contribute to any of the above principles. Obvious examples are dame or the 1-1 point? when it is clearly not a vital point
  2. recognizing vital points is a major asset which a go player of my level should have
  3. for depth recognizing alive shapes? and dead shapes is a major end point
  4. symmetry or miai is an important pruning heuristic: if after your move two equivalent moves remain for the kill, you've killed
  5. recognizing a position which you assessed before but with another order of moves is another obvious pruning technique which plays an important but subconscious role
  6. for more complex problems, higher level L&D positions like the L-group or the door group can allow for faster evaluation
  7. lastly, there is specific intuition for a problem setting. Often problems are setup for a specific line of play. The position looks ordinary but for one aspect of it. You know that you're supposed to use that aspect to your advantage. This is not really valid in games, where a situation is rarely setup for you to think about something specific.

One of my mistakes is to emphasize the specificity of the problem and not be methodical about it. Now that I started practicing again, I find that being methodical first will give more insight about the position in its ordinary form, so that you get a better idea of how the specificity may work to your advantage.

Easy problems

[Diagram]

Easy problem 1

According to the method, I'm evaluating B1 first, which is the only move that reduces the eyespace. After W2 I stop because I see that a and b are equivalent points for making two eyes. This is not a solution.

Next I pick one of the vital points. My mind has a preference for the 1-2 points, since strange things happen there. W2 expands the eyespace and now B3 sets up a shortage of liberties if White were to play at a. Next I will consider a and b for W2 and see that B3 will each time be my answer. I also quickly notice that other variations will end in an almost filled 3-point eyespace.

For the sake of completeness, I also check B1 in the third diagram, to see that the atari at W2 makes two eyes. I also "see" that the exchange of a and b reverts to diagram 1 and as such is not worth analyzing again.

All in all, I'd give this problem a reading width of 5 variations, with a reading depth of 3 moves. There are 4 starting moves out of 7 which I don't consider or instantaneously dismiss.

[Diagram]

Easy Problem 2

In the second problem, the power of the method is revealed. B1 reduces eyespace, W2 keeps it maximal and B3 strikes at the vital point. Filling the space with a farmer's hat or something smaller.

Next, W2 tries at the vital point herself and White lives after B3.

So, B1 tries at the vital point in the 3rd diagram, W2 expands the space and B3 kills. This requires the insight that either White connects and we're back to a previous diagram, OR she does not connect and Black can cut to atari both chains.

For completeness, we can also explore the variation where B1 is played at 2-2 which leads to ko, an inferior result.

This problem has a width of 4 or 5 and a depth of 3 moves, at my level.

[Diagram]

Easy problem 3

Perhaps a beginner will start by capturing the white stone at a but I start by reducing the space at B1, considering that white stone as noise. W2 captures and makes miai of the circled points to make 2 eyes.

The 1-2 point has proven very successful in the first two problems and it looks like a vital point, so I try it. Indeed, after W2-B3 White is dead. But W2 at B3 would lead to ko. It becomes clear that this time the 1-1 point is vital.

So, I play B1 and make miai of a and b. This miai thinking has developed during the previous diagrams of this problem.

For completeness, capturing the isolated stone leads to a ko, which is in fact not trivial and should probably be added to the analysis.

This problem has width 4 to 5 and depth 3, which seems to be a standard metric for gogameguru's easy problems, matching them with my level.



As a conclusion, the method is not yet showing its power for a player like me in this section of problems. At the intermediate level, I will be confronted with more challenging problems, higher level concepts and a greater variety of pruning techniques.

Intermediate problems

Problem 1

[Diagram]
Intermediate problem 1  

This is a capturing race, 4 liberties against 4, with 1 shared liberty. Knowledge of capturing races reduces the possible first moves to 4, namely the liberties, because if Black plays elsewhere, White can go first. However there is one other option I will explore: a has the potential of increasing the liberties. Then there's also the liberties of the two black stones to consider.

Let's just start reading (in my head, what follows is just a recording of previous mental processes).

[Diagram]
Var 1  

I dismiss B1 immediately due to W2, wich escapes by playing on the vital point for a chain of three stones. Similarly I dismiss a because it doesn't prevent the escape and doesn't add to Black's strength. From this first attempt I'm starting to see a technique similar to the crane's nest tesuji but then including the edge of the board as a force.

[Diagram]
Var 2a  

This is the hardest variation to read. After B3 to W8, White has three liberties left and next will either capture at a or b. The exchanges of W2-B3 and W4-B5 can be switched. The crane's like tesuji has failed.

[Diagram]
Var 2b  

If B3 neglects to take a liberty, the race is 4-4 with White to play. I don't know if in real play White should crawl at a now or not.

[Diagram]
Var 3a  

The first success diagram is obtained after B1. White's move at W2 doesn't work anymore. An answer at W4 immediately is also quickly dismissed.

[Diagram]
Var 3b  

At first the capture of B1 with W4 looks unpromising but I'm reminded of the strength of black+circle in such a position. The capture at B9 is a familiar one. At this point I'm convinced I found the solution.

Incidentally B7 is the first time I consider the shared liberty. In other diagrams, especially for White, I don't even consider playing there, as is it opposes basic knowledge about capturing races.

[Diagram]
Var 4  

For completeness I verify B1-W2 to see no additional liberties are to be gained here. B3 makes an eye and defies the common sense that eyes win semeais which is non-trivial enough to include in the analysis.



For me this problem has width 9 and depth 10 (based on variation 2a). It uses pruning techniques based on knowledge of capturing races, counting liberties, previous problem solving to see the power of first line descent, symmetry and repetition.

Problem 2

[Diagram]
Var 1  

There are two moves that reduce the eye space. Let's start here and stop right there: White has two eyes.

[Diagram]
Var 2  

At first sight, W2 makes two eyes but then we spot the mouse stealing oil tesuji at B3, which may come as a surprise to a beginner and which gives the amateur the sense that this is what the exercise is all about. I assume pro players don't even have to think about this problem because they see the tesuji immediately and consider only B1.

Incidentally, myself I did not think about W2 at B3, because then B3 at W2 falsens an eye. Maybe I am actually taking this variation into account but I don't really visualize it.

[Diagram]
Var 3  

Being the apparent vital point, what happens when B1 is played here right away? W4 catches a stone, or else of Black a then White will capture three to make an eye.



This gives this problem a width of 3 to 4 and a depth of about 6 (if we go until the capture of three in var 3), without any particular pruning, which would rather put it into the easy category, however the tesuji is not beginner's material.

Problem 3

[Diagram]
Var 1  

When things start feeling easy, it's probably that you are improving. It's surprising how fast this methodical thinking affects my solving ability. Expanding the eyespace is only possible at B1, then W2 makes miai of capturing at a or b to reduce Black to one eye.

[Diagram]
Var 2  

So, B1 here is an obvious next candidate, because the enemy's key point is yours. But W2 again reduces to one eye.

[Diagram]
Var 3  

Next we try removing the troublesome stone, but W2 forces B3 and W4 falsens the second eye.

[Diagram]
Var 4  

Eventually, B1 here is the solution. It forces W2, next B3 captures 2 stones and makes miai of a and white+circle for the second eye.



Width is 4, depth is 4. Pruning is done by recognition of eyes and equivalence. This was quite an easy problem.

Hard problems

[Diagram]
Hard problem 1  

The hard problems at gogameguru are indeed hard for me. When I attempted them again methodically, I missed the first one. Let's have a look.

[Diagram]
Var 1  

There's only one way to expand the eyespace: B1. However, this will meet with W2 and Black dies.

[Diagram]
Var 2  

Covering the weakness exposes the vital point at W2.

[Diagram]
Var 3  

Playing on this vital point is answered with W2. These are all mental preparations for the real solution, which I can sense must use the weakness at a. I know that cutting stones at the second line may yield a gain in tempo.

[Diagram]
Var 4  

This is the basic solution and I must admit I stopped reading here. I missed the real issue of this problem, which was not about tempo gain.

[Diagram]
Var 5  

Blinded by the capture of two stones, I missed the fact that W6 captures the rest of the group and Black has only one eye. There's more to this problem.

[Diagram]
Var 6  

B3 here works in the same fashion as var 4, but it has another purpose too, in case White resists as in var 5.

[Diagram]
Var 7 (B7@B1)  

Thanks to B3, Black can now atari at B9 to make a second eye, if White swallows the rest of the group with W6 and W8.

[Diagram]
Var 8  

More interesting even is W4 here. After B7, a will make a second eye, or b will move White in a connect and die.

[Diagram]
Var 9  

The same structure can be applied right after B1, so I don't really consider this move.



This problem has a width of minimum 8 and a depth of 9. I'm sure pros will prune heavily here, based on repeated arguments and known tesujis like the snapback. They will probably skip the mental preparation and dive right into var 7 as the main line.

Problem 2

[Diagram]
Var 1  

There's again only one way to expand the space. After W4, which sets up a snapback, Black will come too late to atari at a. However, we can see that this is the specificity of the problem and we must use this weakness to gain tempo.

[Diagram]
Var 2  

It's not at B3 here. White can even play W4 at a, a side variation.

[Diagram]
Var 3  

Incidentally, it's only a quick verification to see that B1 here is not an option.

[Diagram]
Var 4  

There doesn't seem to be any option but playing the tempo gaining move right away and read what happens next. If W2 falls for it, then Black has created a position where a would be self atari for White.

[Diagram]
Var 5  

Again, there's more than gaining tempo to this problem. If W2 reduces the space, B3 captures the group due to the shortage of liberties at a. I think B5 is a move not easily spot by players who've just been brought up with mental pictures like the chapel.

[Diagram]
Var 6  

I needed to read this one too.

[Diagram]
Var 7  

This inverts the order and can be evaluated early.



Width is 7, depth is about 7. Pruning through liberties, known shapes and repetition.

Problem 3

[Diagram]
Var 1  

When approaching this problem methodically, B1-W2 ends in a simple and dull position. This is because I know that the corner is one eye. In fact ...

[Diagram]
Var 2  

It is almost impossible for me not to see B1 at this vital point. After B3, Black is safe: the liberty count is 3 against 2 and there is an eye in the corner.

[Diagram]
Var 3  

The real question is this diagram and where to play B5. If a then b wins the capturing race. This danger on the outside may be a blind spot.

[Diagram]
Var 3 (continued)  

So, Black needs to keep on the liberty pressure. B5 is the correct move. After B7, a and b are auto-atari for White, while the liberty count with respect to the right part is still in Black's favour (3-2).

[Diagram]
Var 4  

Although methodically appropriate, I will probably not even consider this variation.



Width is maximum 5. Depth is 7. This would rather classify it as an intermediate problem, also because the pruning is more about liberties than anything. What really makes this problem challenging is the impact of the inside on the outside, i.e. the blind spot referred to above.


Hard problem 119

[Diagram]
Black to kill  

[ext] The hard problem at GGG was particularly challenging. Here's a systematic approach.

Clearly, White has the potential to create one eye at a and another at the bottom. If Black takes time to destroy the one at a, White may create two eyes at the bottom and in the corner. The aji of the marked stones will play a major role.

Apart from a, attractive starting moves are b to d. The retracted e has some appeal because this is a difficult problem, so we must perhaps include some ideas that don't feel intuitive at first. On second thought e may be precisely the way to deal with aforementioned aji. I exclude the hane at f immediately because it is ridiculed by a.

It is also worth noting that a and b together falsen the circled eye.



Let's tackle this methodically,

  • reducing eyespace first
  • playing the vital point next
[Diagram]
Reduce eyespace 1  

Reducing the eyespace results in life, after W6 makes an eye and renders the circled point into an eye as well.

  • Can we play B5 at W6? No, because then White will atari at B5 in sente, due to the aji.
  • Can we play B3 at W6? Let's see.
[Diagram]
Reduce eyespace 1b  

White forces and lives: there are true eyes left and right of W8.

[Diagram]
Reduce eyespace 2  

The enemy's key point is yours: B1 looks like both a vital point and a reduction of eyespace. This must be the move! Alas, the aji comes to life again. B9 and B7 are forced.

  • Can we resist with B5? No, the capture is sente to capture another stone.
  • Can we resist with B3? No, in that case there was no point in playing B1.
[Diagram]
Reduce eyespace 3  

The keima of B1 looks promising, but if White simply plays the vital point W2 again, it's all over.



All three intuitive ways to reduce the space in the corner have failed. Maybe we must kill the eye first and wait what White will do in the corner?

[Diagram]
Two eyes in the corner 1  

Annoyingly, we must answer at B5. Perhaps we can avoid that?

[Diagram]
Two eyes in the corner 2  

This was the variation that made it all explode for me. It boils down to a J-group with an extra hane, because White a is sente. But I didn't know the status of this group, so I had to read all variations of this structure and it became too much for me. Well, it's alive, as it appears.

[Diagram]
Reducing the eyespace 4  

My intuition initially offered me the awkward looking move B1 and it turns out to be right. If W2 takes the vital point again, B3 will make miai of a and b. The variation b deserves another diagram:

[Diagram]
Reducing the eyespace 4  

B7 reduces the space and exploits the weakness at B9. After W10, Black kills at a.

  • Can W8 be at B9? No, Black will strike at a.
  • Can W6 be at W10? No, Black will play B7 at W6 and Black needs two moves to live.



Coming up with B1 in this problem is hard. Systematically looking at the problem leads to major variations, especially if one is unfamiliar with the variants of the J-group.

A strong amateur or pro will be familiar with most of the shapes in this problem. They will probably concentrate on how to take care of the aji and come up with B1 more easily.

[Diagram]
White's dead.  

Timm: I think what makes the problem hard is that it's not obvious (I mean really obvious, for me at least) that this shape is dead. The fear of White b above is what keeps us away from the kosumi. Good to know !

p.s. I like to think to such problems aim as being to “reduce White to one eye in sente, to be able to remove the obvious (but double-gote) eye.” With this sente issue in mind, it becomes easier to see that the tobi and keima are less likely to work.


DieterVerhofstadt/Solving problems last edited by Timm on June 23, 2014 - 20:22
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