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 Post subject: Solving life-and-death tsumegos by trial and error
Post #1 Posted: Wed Mar 06, 2013 3:34 pm 
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At the level of life-and-death tsumegos that I am currently doing (around 15 kyu level, so it says), for most of them there are only a few reasonable first moves, and then all follow-up moves stay on one or two narrow paths until success or failure. Therefore, you can almost find your first move by trial and error. My question is: will this approach work with more advanced problems, or should I get into the habit of solving them by trying to understand the key features of each position first?

(I am talking about trial and error as in: mentally choose a reasonable-looking first move by trial and error, then read it through to a conclusion, and NOT randomly click everywhere (including follow-up moves) until it says Solved. Only about 20% of the time is my instinct for a solution so strong that I click without first reading it out.)

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #2 Posted: Wed Mar 06, 2013 3:57 pm 
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I think what you're calling "trial and error", most people just call reading. I don't think "understanding the key features" of a position can ever replace mentally checking each possible response from your opponent.

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #3 Posted: Wed Mar 06, 2013 3:59 pm 
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That sounds right to me. It won't work with more advanced problems right away, but by the time you finish your beginner problems and move to intermediate problems, you'll have much better intuitions about which moves to start with, and you'll be able to assess the follow-ups more quickly and accurately.

A few things to think about, though - when you say "all of the follow-up moves stay on one or two narrow paths", do you mean there are only one or two choices for each move, or only one or two choices that you think are reasonable? It makes sense to get into the habit, even once you're sure you have the answer, of trying at least one move that looks stupid, or to look at a sequence with the same moves, but in a different order. Sometimes the result is quite surprising - I'm sure you've encountered zwischenzug in another game...

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #4 Posted: Wed Mar 06, 2013 4:01 pm 
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The trial-and-error tree will soon get too large. You have to work on appreciating the character of the position. This will keep the size of the tree managable.

Of course, 'managable' is a relative concept. At least one pro has claimed to have read 100+ moves deep.

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #5 Posted: Wed Mar 06, 2013 4:04 pm 
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Hm, I am a bit confused by your using of trial and error but after reading your short little disclaimer I think you mean the "right" thing. That is, mentally playing out a sequence and only if you think you will end up with a good result it gets physical.

I tend to use trial and error when I just click at the first best move and after a few moves I can fairly easy see if this works or not. Well, not so efficient for training reading ^^

But yes, this approach stays the same. At least it did for me. You will learn the key features of certain shape automatically after solving a lot of problems because the same shapes (and therefore Tesujis, respectively vital points) keep reoccurring.

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #6 Posted: Wed Mar 06, 2013 4:05 pm 
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PeterPeter wrote:
At the level of life-and-death tsumegos that I am currently doing (around 15 kyu level, so it says), for most of them there are only a few reasonable first moves, and then all follow-up moves stay on one or two narrow paths until success or failure. Therefore, you can almost find your first move by trial and error. My question is: will this approach work with more advanced problems, or should I get into the habit of solving them by trying to understand the key features of each position first?

(I am talking about trial and error as in: mentally choose a reasonable-looking first move by trial and error, then read it through to a conclusion, and NOT randomly click everywhere (including follow-up moves) until it says Solved. Only about 20% of the time is my instinct for a solution so strong that I click without first reading it out.)


My own experience (3d EGF) is - trial & error YES - BUT in the head please !
If you just click - you will learn few from it.

You can train your first reflexes ('instinct') = narrowing down potential eye shape, hane + vitale points etc. - in such an order by doing many exercises.
Often I 'see' the possible THEMES and my work is to verify whether it works that way.
In a book problem that's easier, in a real situation it might not work or be another theme or a move misses etc.

When you can refrain from 'eating the Marshmallow' (google that metapher for psychology) AND you have solved a problem correctly, THEN you experience a moment of satori.

There are many good sites on senseis for a sound L&D-approach.

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #7 Posted: Wed Mar 06, 2013 4:14 pm 
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Here is an example, with black to move and live.

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | a b O X X O. . . .
$$ | . X c d e O . . .
$$ ------------------[/go]

To me, on an initial review, a, b, c, d and e are the moves that look like they might be solutions, and so worth reading.

So, I read them all in turn, until I can read one to an irrefutable solution. This is a bit time-consuming, but I get there in the end. Sometimes I dismiss the correct move too early, then have to re-consider it when I cannot get any of the other options to work.

I am not sure if this is practical with bigger or more complicated problems, where there might be twice as many reasonable-looking moves.

Do stronger players use any rules of thumb, or features of the position, to reduce my list of 5 down to 2 or 3?

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #8 Posted: Wed Mar 06, 2013 4:19 pm 
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Tommie wrote:
My own experience (3d EGF) is - trial & error YES - BUT in the head please !
If you just click - you will learn few from it.

Yes, absolutely, I tried to explain that.

Tommie wrote:
There are many good sites on senseis for a sound L&D-approach.

I had a look, but I could not see much on a general approach to these sorts of problems. Do you have a link?

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #9 Posted: Wed Mar 06, 2013 4:42 pm 
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PeterPeter wrote:
So, I read them all in turn, until I can read one to an irrefutable solution.

Absolutely the correct way to do it.

PeterPeter wrote:
Do stronger players use any rules of thumb, or features of the position, to reduce my list of 5 down to 2 or 3?

I doubt it. Here are my thoughts:

Let's try a first. a is quite an easy one to refute.

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | 1 C W X X O. . . .
$$ | T X C C . O . . .
$$ ------------------[/go]


Black has one eye in the corner. Where's the other eye going to be? It has to be at one of the circled points. A moment's thought will show you this atari:

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | 1 . W X X O. . . .
$$ | . X . 2 . O . . .
$$ ------------------[/go]

[/quote]

and so white captures two stones and none of those circled points belong to black any more. (Pushing in from the outside at :w2: also works.) So what about b or c, to give the marked white stone fewer liberties?

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | . 1 O X X O. . . .
$$ | . X . . . O . . .
$$ ------------------[/go]


White has no hope of making a dead shape inside black's group. There are only really three moves to consider: the descent (immediately obvious it doesn't work), the hane and pushing in from outside. Again, as before, both of the latter two work:

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | . 1 O X X O. . . .
$$ | . X 3 2 4 O . . .
$$ ------------------[/go]


Even though black captures, white can just connect, and the two stones are in atari, hence a false eye.

The problem here is coming from black's shortage of liberties. Those two stones have very little freedom to move due to the marked white stone. Let's see that in action once more with c:

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | . . O X X O. . . .
$$ | . X 1 2 . O . . .
$$ ------------------[/go]


White again can't hope to make a dead shape, so white has to capture the two stones. Check all the obvious points and you see easily that most fail. But white can play this throw-in and now black can't capture :w2: due to his shortage of liberties (it's a snapback). Here, pushing in from the outside doesn't work.

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | . . O X X O. . . .
$$ | . X . . 1 O . . .
$$ ------------------[/go]


This was one of your marked moves (e), but I'm sure it's obvious what's wrong with it! So there's only one left to consider:

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | . . O X X O. . . .
$$ | . X . 1 . O . . .
$$ ------------------[/go]


and indeed you can check that black does indeed get one eye in the corner, one eye on the side. Notice the double table shape, by the way.


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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #10 Posted: Wed Mar 06, 2013 4:46 pm 
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PeterPeter wrote:
My question is: will this approach work with more advanced problems

Of course the more complex the problems get the less brute force you want to apply, but you are doing things correctly for now. Once snapbacks and throw-ins and things like that are clear in your mind, you can worry about doing things more efficiently and spotting old familiar shapes. For now, just solve lots. The shapes will become more familiar in their own time. :)

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #11 Posted: Wed Mar 06, 2013 5:16 pm 
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Joaz Banbeck wrote:
At least one pro has claimed to have read 100+ moves deep.


I heard that too, and it has always puzzled me. What does it mean?
- he read 100 moves along a singular branch? (i can do that too)
- he read 100 moves along 1 branch and this is how the game went (luck?)
- he read 100 moves along all the branches? was the position complex or just one-way street in yose? hard to imagine this happening in fuseki...
- and so on...

You can imagine plenty scenarios which would make this feat relatively easy or very difficult. Without knowing more, it is hard to judge if one pro reading 100+ moves deep is actually something amazing or something normal....

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #12 Posted: Wed Mar 06, 2013 6:11 pm 
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PeterPeter wrote:
Here is an example, with black to move and live.

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | a b O X X O. . . .
$$ | . X c d e O . . .
$$ ------------------[/go]

To me, on an initial review, a, b, c, d and e are the moves that look like they might be solutions, and so worth reading.

So, I read them all in turn, until I can read one to an irrefutable solution. This is a bit time-consuming, but I get there in the end. Sometimes I dismiss the correct move too early, then have to re-consider it when I cannot get any of the other options to work.

I am not sure if this is practical with bigger or more complicated problems, where there might be twice as many reasonable-looking moves.

Do stronger players use any rules of thumb, or features of the position, to reduce my list of 5 down to 2 or 3?


In the future, you will solve similar positions at a glance. :)

Now, since you have solved this problem, let me ask you a few questions.

    What are the key features of this position?
    When you were solving the position, which move looked best at first? Why? What was wrong with it?
    As you worked on this problem, did you pick up clues about where to make your first move?
    After Black's initial correct play, what is White's best play? (From an endgame point of view, OC. :))
    After Black's initial correct play, are there any White moves that are obviously useless? Why?
    Having solved the problem, can you go through the main variations quickly?
    Are you confident that you have a reply for every White response?

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #13 Posted: Wed Mar 06, 2013 9:16 pm 
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PeterPeter wrote:
Here is an example, with black to move and live.

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | a b O X X O. . . .
$$ | . X c d e O . . .
$$ ------------------[/go]

To me, on an initial review, a, b, c, d and e are the moves that look like they might be solutions, and so worth reading.

So, I read them all in turn, until I can read one to an irrefutable solution. This is a bit time-consuming, but I get there in the end. Sometimes I dismiss the correct move too early, then have to re-consider it when I cannot get any of the other options to work.

I am not sure if this is practical with bigger or more complicated problems, where there might be twice as many reasonable-looking moves.

Do stronger players use any rules of thumb, or features of the position, to reduce my list of 5 down to 2 or 3?


I do not understand how, but when I looked at this problem and your a-e, I immediately dismissed all but d without even really thinking about it. Some part of me recognized it as the only reasonable shape, and there was no conscious reading. It might be that I've internalized that problem, but I think there's also some kind of unconscious shape rules-of-thumb happening here.

edit. I'll add that this isn't something I've practiced, it's just the result of having done thousands of life-and-death problems.

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #14 Posted: Wed Mar 06, 2013 10:07 pm 
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PeterPeter wrote:
Here is an example, with black to move and live.

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | a b O X X O. . . .
$$ | . X c d e O . . .
$$ ------------------[/go]

... any rules of thumb, or features of the position, to reduce my list...


At first glance, I see this:

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . C . . . . . . .
$$ | . . . . . . . . .
$$ | . C C . . . . . .
$$ | C C C O O C . . .
$$ | . . O X X O. . . .
$$ | . C . d . O . . .
$$ ------------------[/go]


I think 'belly tesuji is what he wants'. Therefore, 'd' goes to the top of my list of candidates, on the theory that a good point for my opponent is a good one for me. After about 5 seconds of reading, I have assured myself that it works.
Next, I ask myself if I can get more territory by living with a different move. I analyze 'e' for about 1/2 second and conclude that it does not work.
I never consider 'a' or 'b' or 'c'.

The important point here is that I have an internal library of shapes, and when I look at a position, they jump out at me, as in the diagram above.

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #15 Posted: Wed Mar 06, 2013 10:20 pm 
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Bantari wrote:
Joaz Banbeck wrote:
At least one pro has claimed to have read 100+ moves deep.


I heard that too, and it has always puzzled me. What does it mean?
- he read 100 moves along a singular branch? (i can do that too)
- he read 100 moves along 1 branch and this is how the game went (luck?)
- he read 100 moves along all the branches? was the position complex or just one-way street in yose? hard to imagine this happening in fuseki...
- and so on...

You can imagine plenty scenarios which would make this feat relatively easy or very difficult. Without knowing more, it is hard to judge if one pro reading 100+ moves deep is actually something amazing or something normal....


Easy, he just read the next 100 best moves ;-)

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #16 Posted: Wed Mar 06, 2013 10:29 pm 
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First of all: to join the chorus, yes, you are doing it right.

Shaddy wrote:
PeterPeter wrote:
Here is an example, with black to move and live.

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | a b O X X O. . . .
$$ | . X c d e O . . .
$$ ------------------[/go]

To me, on an initial review, a, b, c, d and e are the moves that look like they might be solutions, and so worth reading.

Do stronger players use any rules of thumb, or features of the position, to reduce my list of 5 down to 2 or 3?


I do not understand how, but when I looked at this problem and your a-e, I immediately dismissed all but d without even really thinking about it. Some part of me recognized it as the only reasonable shape, and there was no conscious reading. It might be that I've internalized that problem, but I think there's also some kind of unconscious shape rules-of-thumb happening here.

edit. I'll add that this isn't something I've practiced, it's just the result of having done thousands of life-and-death problems.


A never even entered my mind, and all other but d were ignored very quickly (but were considered for like 0,5 sec). Shows I'm weaker than Shaddy :P

Regarding rules of thumb:
When looking at the position, the very first thing that stands out is that the status of the two black stones and 1 white stone is unclear. So unless I play a move affecting those stones OR make a good enough sente move elsewhere, white will eat my two stones. If that happens -> no space for 2 eyes. I quite often (in complex problems, sometimes also in games as situation warrants) start by working out the statuses (count of liberties) of intertwined groups. It makes options clearer.

Second thing that stands out to me is the shape thing (Joaz brought it up better than I did while I was writing this).

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Post #17 Posted: Wed Mar 06, 2013 10:42 pm 
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(Somehow I remember seeing this exact problem a long time ago and finding it very difficult, and I can't for the life of me now remember why. I guess that's always the way.)

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Post #18 Posted: Thu Mar 07, 2013 12:31 am 
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PeterPeter wrote:
Here is an example, with black to move and live.

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | a b O X X O. . . .
$$ | . X c d e O . . .
$$ ------------------[/go]

To me, on an initial review, a, b, c, d and e are the moves that look like they might be solutions, and so worth reading.

So, I read them all in turn, until I can read one to an irrefutable solution. This is a bit time-consuming, but I get there in the end. Sometimes I dismiss the correct move too early, then have to re-consider it when I cannot get any of the other options to work.

I am not sure if this is practical with bigger or more complicated problems, where there might be twice as many reasonable-looking moves.

Do stronger players use any rules of thumb, or features of the position, to reduce my list of 5 down to 2 or 3?


I really wish that there were rules of thumb, but what the thumb offers is more like suggestions from a drunk buddy than rules. Some things he says may be reasonable, like the first thing he invariably slurs in a slightly too loud voice: "Count your LIBerties!"
Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | T O O O . . . . .
$$ | X X X O O O . . .
$$ | T T O X X O. . . .
$$ | . X . S S O . . .
$$ ------------------[/go]

Here I see one string with 3 and another with 2, and in this case, that makes me aware of a key feature of this problem: Liberties are short. His next sentiment is: "Eyes, eyes, it's all about EYes!" This leads me to make my first tests: if I make an eye right away (a or b) can my opponent stop me from making a second? In this case, the answer is yes, because in either case a white d will screw up the second eye. While this piece of advice proved valuable, I must add at this point that it's not as efficient as to eliminate a and b as all of the stronger players did simply by knowing "it won't work." The next piece of advice from my drunk thumb however is questionable: "You gotta CAPture that STone!" While this suggests a wrong move (c)and a right move (d), in more complicated problems, it often just proves to be lousy advice. Somewhat better are the musings of my stoned index finger: "shapes, man, shapes." He sees what Joaz saw (though presumably by legal means):

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . ? ? ? ? ? . . .
$$ | ? ? ? O O ? ? . .
$$ | ? ? O X X O ? . . .
$$ | ? ? . d . O ? . .
$$ ------------------[/go]


and also this:
Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . ? . . . . . . .
$$ | . . . . . . . . .
$$ | . ? ? ? . . . . .
$$ | ? X X O ? ? . . .
$$ | ? C O X ? ?. . . .
$$ | . X C * ? ? . . .
$$ ------------------[/go]


In any case, while these digits may provide entertaining advice, success belongs to those who do the footwork.

_________________
Patience, grasshopper.

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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #19 Posted: Thu Mar 07, 2013 1:11 am 
Dies in gote

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PeterPeter wrote:
Here is an example, with black to move and live.

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | . O O O . . . . .
$$ | X X X O O O . . .
$$ | a b O X X O. . . .
$$ | . X c d e O . . .
$$ ------------------[/go]

To me, on an initial review, a, b, c, d and e are the moves that look like they might be solutions, and so worth reading.

Do stronger players use any rules of thumb, or features of the position, to reduce my list of 5 down to 2 or 3?


I think your mistake is in how you made the list of candidates in the first place. Let me explain ....

I think what you did was saw a block of 6 black stones with some incomplete eye shape, and looked at every move inside the eye shape that makes 2 eyes. Move 'a' creates an eye in the corner. Move 'e' creates an eye at 'd'. All these moves give Black the shape of 2 eyes.

However, that's not the important feature of the problem. The problem is that Black's been cut and he needs both halves to live. One half has only 2 liberties. If Black doesn't make a move to save these stones, White plays atari next move and the group dies.

I think you need to see this before assembling your list of candidate moves. You should see what's going on first before trying to live, because when you place your next stone you need to know what its job is. This way you can avoid considering at 'a' and 'e', because they don't help capture the cutting stone before White kills you.


This post by peppernut was liked by 2 people: gogameguru, Splatted
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 Post subject: Re: Solving life-and-death tsumegos by trial and error
Post #20 Posted: Thu Mar 07, 2013 2:06 am 
Lives with ko
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Bill Spight wrote:
Here is an example, with black to move and live.

Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . O . . . . . . .
$$ | . . . . . . . . .
$$ | f O O O . . . . .
$$ | X X X O O O . . .
$$ | a b O X X O. . . .
$$ | . X c d e O . . .
$$ ------------------[/go]


Now, since you have solved this problem, let me ask you a few questions.

What are the key features of this position?

Black is very cramped, and his 2 stones on the right are in danger.
Bill Spight wrote:
When you were solving the position, which move looked best at first? Why? What was wrong with it?
B and C were the first ones I looked at, as killing white's stone would both create space, and help connect. Both of them failed to white playing at D.
Bill Spight wrote:
As you worked on this problem, did you pick up clues about where to make your first move?
Only after exhausting B and C, and quickly ruling out E, did I seriously consider D. On a first review, D looked like it reduced eyespace. It took a while to see that it was the only move to save the 2 stones on the right.
Bill Spight wrote:
After Black's initial correct play, what is White's best play? (From an endgame point of view, OC. :))
White should play at F.
Bill Spight wrote:
After Black's initial correct play, are there any White moves that are obviously useless? Why?
White cannot save his stone, so any of ABC would be uselss, and E does nothing.
Bill Spight wrote:
Having solved the problem, can you go through the main variations quickly?
Yes, playing D simplifies it a lot.
Bill Spight wrote:
Are you confident that you have a reply for every White response?
Yes.

_________________
Regards,

Peter

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