Solving life-and-death tsumegos by trial and error

Bill Spight · **#21**

Great, PeterPeter! :mrgreen:

PeterPeter wrote:

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.

You can be more specific.

As others have pointed out, taking note of the exact number of dame can be helpful. (I use the term, dame, because liberty is ambiguous.) Also, in terms of life and death, being cramped is a problem because there is not much space for Black to make two eyes.

So where are Black's potential eyes?

Click Here To Show Diagram Code: [go]$$B $$ | . . . . . . . . . $$ | . . . . . . . . . $$ | . . . . . . . . . $$ | . O . . . . . . . $$ | . . . . . . . . . $$ | . O O O . . . . . $$ | X X X O O O . . . $$ | . . W X X O. . . . $$ | a B . b . O . . . $$ ------------------[/go]

It looks like there is an eye at "a", thanks in part to :bc:

. Where is a second possible eye?

A brief inspection suggests that the second eye should include :wc:

. That being the case, Black needs to occupy or control point "b", else the eye will be false. Just thinking about eyes suggests "b" as the first move.

Does that move save the two Black stones and capture the :wc:

stone, forming the second eye?

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

Yes, thanks to :bc:

.

Because of its significance in forming the eye in the corner and in saving the two Black stones, I would say that :bc:

is a key feature of this position.

Bill Spight wrote:

When you were solving the position, which move looked best at first? Why? What was wrong with it?

Quote:

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.

Very often, when the opponent has a good play on a point, we also have a good play on that point. (In fact, it is a go proverb.

) If I had tried "c" first and discovered White's counter at "d", "d" would have been my next try.

Bill Spight wrote:

After Black's initial correct play, what is White's best play? (From an endgame point of view, OC.

)

Quote:

White should play at F.

Correct.

Although correct endgame is not part of a life and death problem, I think that it can be a good exercise to figure out the best endgame play. In a real game, it is part of the problem.

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

Bonus question. Where is Black's reply?

Bill Spight wrote:

Having solved the problem, can you go through the main variations quickly?

Quote:

Yes, playing D simplifies it a lot.

The lines starting with "c" and "b" are also main lines, IMO.

Bill Spight wrote:

Are you confident that you have a reply for every White response?

Quote:

Yes.

¡Bueno!

Bill Spight · **#22**

Here is a more difficult problem, as the Black 1-2 stone is missing.

Where can Black make two eyes?

Enjoy!

PeterPeter · **#23**

Bill Spight wrote:

So where are Black's potential eyes?

It looks like there is an eye at "a", thanks in part to :bc:

. Where is a second possible eye?

A brief inspection suggests that the second eye should include :wc:

. That being the case, Black needs to occupy or control point "b", else the eye will be false. Just thinking about eyes suggests "b" as the first move.

I thought this might be a good way to approach problems: predict where the eyes will be, then work from there. However, predicting likely eyes after the connections, captures, snapbacks etc have played out is not easy, with the added complication that both eyes must be genuine. It is not very intuitive.

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

In this problem, you rightly saw that the 1-1 corner point, and the enemy stone you had to capture, would become eyes. This seems like a good starting point for similar problems.

billywoods · **#24**

PeterPeter wrote:

predicting likely eyes after the connections, captures, snapbacks etc have played out is not easy, with the added complication that both eyes must be genuine. It is not very intuitive.

I think Bill did something subtly different from predicting likely eyes. Let's remove all the enemy stones and just look at the eyespace:

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

Here's a couple of ways of making eyes in it:

It should be fairly easy to see that all of the sensible formations you can make with two eyes involve this point:

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

Bill's slight leap of logic went: "so I need to capture the stone at circle. Ah, but not all captured stones become eyes! It's a real eye for black if and only if black controls all or all but one of the corners":

Click Here To Show Diagram Code: [go]$$B $$ | . . . . . . . . . $$ | . . . . . . . . . $$ | . . . . . . . . . $$ | . . . . . . . . . $$ | X Y X T . . . . . $$ | . . C X X . . . . $$ | . Y . T . . . . . $$ ------------------[/go]

Finally, let's overlay this onto the real diagram:

Click Here To Show Diagram Code: [go]$$B $$ | . . . . . . . . . $$ | . O . . . . . . . $$ | . . . . . . . . . $$ | . O O O . . . . . $$ | X Y X Q O O . . . $$ | . . W X X O . . . $$ | . Y . T . O . . . $$ ------------------[/go]

The marked point (where there is a white stone) must become an eye. So black must capture the white stone. Additionally, for it to become an eye, black must occupy at least three of the four triangle points (aka for white to make that eye false, white must occupy the remaining triangle point). This immediately tells you the only moves worth considering for both black and white: the point you both really want to occupy is the remaining triangle point, so try it first. But if you happened to try another point first in an attempt to capture the white stone, white's refutation probably starts by occupying that triangle point too.

I also liked peppernut's explanation: black's been cut. As you can see, there are lots of ways to think about the same problem.

PeterPeter · **#25**

billywoods wrote:

It should be fairly easy to see that all of the formations you can make with two eyes involve this point:

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

I am not sure about this. Is this not an equally valid way of getting 2 eyes?

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

I think a bigger clue is the fact that a white stone starts off occupying that point.

billywoods wrote:

The marked point (where there is a white stone) must become an eye. So black must capture the white stone. Additionally, for it to become an eye, black must occupy at least three of the four triangle points (aka for white to make that eye false, white must occupy the remaining triangle point). This immediately tells you the only moves worth considering for both black and white: the point you both really want to occupy is the remaining triangle point, so try it first.

That could be a really good clue: look at the diagonal points of each enemy stone in your eyespace area. I like it!

Bill Spight · **#26**

PeterPeter wrote:

That could be a really good clue: look at the diagonal points of each enemy stone in your eyespace area. I like it!

Actually, that's not a bad heuristic, even on a larger scale. The point is, OC, that you are attacking the stone or stones. Points that are diagonally related to defensive stones are often important. And it is not just the adjacent diagonals. For instance, after a one space jump from a single stone, the two stones are related along diagonal lines. (There is another go proverb that says that a one space jump is for defense, a knight's move for attack.)

Getting back to life and death problems, diagonals to your owns stones can be important, as well, because of eye potential.

billywoods · **#27**

PeterPeter wrote:

billywoods wrote:

It should be fairly easy to see that all of the formations you can make with two eyes involve this point:

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

I am not sure about this. Is this not an equally valid way of getting 2 eyes?

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

I think a bigger clue is the fact that a white stone starts off occupying that point.

Yes, fair point. The main thing to take away from what I said was: if you don't capture the white stone, you haven't got space for two eyes. You're right that I phrased it badly.

Bill Spight · **#28**

Some comments on my problem.

Click Here To Show Diagram Code: [go]$$B Black to play $$ | . . . . . . . . . $$ | . . . . . . . . . $$ | . . . . . . . . . $$ | . O . . . . . . . $$ | . . . . . . . . . $$ | . O O . . . . . . $$ | X X X O O O . . . $$ | . . W X X O. . . . $$ | . . . . . O . . . $$ ------------------[/go]

Where can Black make eyes?

That is not so obvious. We know from the previous problem that White can prevent the :wc:

point from becoming an eye. That does not leave much space.

PeterPeter · **#29**

Click Here To Show Diagram Code: [go]$$B Black to play $$ | . . . . . . . . . $$ | . . . . . . . . . $$ | . . . . . . . . . $$ | . O . . . . . . . $$ | . . . . . . . . . $$ | . O O . . . . . . $$ | X X X O O O . . . $$ | . . O X X O. . . . $$ | a b . . . O . . . $$ ------------------[/go]

Interesting that having a black stone on A is essential here, but was not even a candidate move when there was a black stone starting on B. No wonder that I sometimes stare at these puzzles for a while, not knowing where to start.

Bill Spight · **#30**

PeterPeter wrote:

Click Here To Show Diagram Code: [go]$$B Black to play $$ | . . . . . . . . . $$ | . . . . . . . . . $$ | . . . . . . . . . $$ | . O . . . . . . . $$ | . . . . . . . . . $$ | . O O . . . . . . $$ | X X X O O O . . . $$ | . . O X X O. . . . $$ | a b . . . O . . . $$ ------------------[/go]

Interesting that having a black stone on A is essential here, but was not even a candidate move when there was a black stone starting on B. No wonder that I sometimes stare at these puzzles for a while, not knowing where to start.

In such a tight space, if Black to live occupies either "a" or "b", the other one almost has to be an eye, or part of one.

My main point in talking about these relationships is not that I think you should know them before tackling these problems, but that you can learn them from doing the problems, or from playing games. Especially if you review them afterwards.

PeterPeter · **#31**

billywoods wrote:

It's a real eye for black if and only if black controls all or all but one of the corners"

I have been using another definition of a real eye, that I think is logically very sound, but not that easy to apply in practice. Something along the lines of it being a real eye if none of the stones that surround it can be put in atari. I might be better of using something simpler, even if it only works 99% of the time. (Not saying this is the case here; I don't know.)

Bill Spight · **#32**

PeterPeter wrote:

billywoods wrote:

It's a real eye for black if and only if black controls all or all but one of the corners"

I have been using another definition of a real eye, that I think is logically very sound, but not that easy to apply in practice. Something along the lines of it being a real eye if none of the stones that surround it can be put in atari. I might be better of using something simpler, even if it only works 99% of the time. (Not saying this is the case here; I don't know.)

Defining an eye is not easy.

The topic has generated much discussion on Sensei's Library.

Here is a cute example from http://senseis.xmp.net/?TwoEyeFormation .

Click Here To Show Diagram Code: [go]$$B Two-eye-formation with four black strings $$ . . . . . . . . . . . . . . . . . $$ . . . O O . . . . . . . O O . . . $$ . . . O . O O O O O O O . O . . . $$ . . . O O O X X X X X O O O . . . $$ . . . . O X X O O O X X O . . . . $$ . . . . O X O . O . O X O . . . . $$ . . O O O X O O O O O X O O O . . $$ . . O X X . X X X X X . X X O . . $$ . . O X O X O O O O O X O X O . . $$ . O O X O X O . O . O X O X O O . $$ . O X X O X X O O O X X O X X O . $$ . O X O O O X X X X X O O O X O . $$ . O X O . O O O O O O O . O X O . $$ . O X O O X X X X X X X O O X O . $$ . O X X X X O O O O O X X X X O . $$ . O O O O O O . . . O O O O O O . $$ . . . . . . . . . . . . . . . . .[/go]

OC, such formations are rare.

There are eyes that count for independent life and those that do not. As a practical rule of thumb, these are the types of eyes that count for independent life.

Click Here To Show Diagram Code: [go]$$B Single point eyes $$ . . . . . . . . . . . . . . | $$ . . . . . . . . . . . . . . | $$ . . B X B . . . . . . . B X | $$ . . X C X . . . . . . . X C | $$ . . . X B . . . . . . . B X | $$ . . . . . . . . . . . . . . | $$ . . . . . . . . . . . . . . | $$ . . . . . . . . . . . . B X | $$ . . . . . . . . . . . . X C | $$ ----------------------------[/go]

(From http://senseis.xmp.net/?Eye )

The points indicated by :bc:

are occupied or controlled by Black. Note that Black controls one diagonal of the corner eye, two diagonals of the side eye, and three diagonals of the center eye.

You might also be interested in this page. http://senseis.xmp.net/?TopologicalLife

daal · **#33**

I'd like to continue this thread, because I am interested in how we look at and understand the points in a shape that may or may not become eyes. Here is a random and relatively simple sample problem taken from Logan's Go Problem & Pro Game Journal:

Click Here To Show Diagram Code: [go]$$B Black to play $$ | . . . . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ | . . O . . . . . . . . $$ | O O . . . . . . . . . $$ | O X O O . . . . . , . $$ | . X X X O O . . . . . $$ | . . . X X O . O . . . $$ | . . . . . . . . . . . $$ ----------------------[/go]

My first thought is that the triangled points can never become eyes, which leaves me to look for them within the 7 shaded points.

Click Here To Show Diagram Code: [go]$$B shaded $$ | . . . . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ | . . O . . . . . . . . $$ | O O . . . . . . . . . $$ | O X O O . . . . . , . $$ | T X X X O O . . . . . $$ | ? ? ? X X O . O . . . $$ | ? ? ? ? T . . . . . . $$ ----------------------[/go]

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

What I'm curious about is what happens next in your minds. Do you imagine the space being divided for example at b or e? Do you see certain points as being easier to protect, for example at d or c? Do you visualize a black stone for example at b or e and find the shape pleasing? Do you visualize the damage a white stone might do for example at e destroying the potential for the adjacent points of d, b and f to become separate eyes?

I'm guessing that any stronger player will respond: none of the above - my pattern recognition instantly saw that either b or e would create a living shape, both serving to protect eyes at d and c. Perhaps a more difficult problem could illustrate your thought process better?

In any case, my original thought was that it would be great if I could start my search for the correct sequence by seeing the best possible eyes just pop out at me, and select moves that keep these particular eyes viable. Is this a useful or useless approach?

Click Here To Show Diagram Code: [go]$$B particularly good eye potential? $$ | . . . . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ | . . O . . . . . . . . $$ | O O . . . . . . . . . $$ | O X O O . . . . . , . $$ | . X X X O O . . . . . $$ | . . C X X O . O . . . $$ | C . . . . . . . . . . $$ ----------------------[/go]

Cassandra · **#34**

What about "seeing" some shapes you might want to prevent ?

Click Here To Show Diagram Code: [go]$$B bulky five I $$ | . . . . . . . . . . . $$ | . . O . . . . . . . . $$ | O O . . . . . . . . . $$ | O X O O . . . . . , . $$ | . X X X O O . . . . . $$ | ? T ? X X O . O . . . $$ | ? ? . . . . . . . . . $$ ----------------------[/go]

Click Here To Show Diagram Code: [go]$$B bulky five II $$ | . . . . . . . . . . . $$ | . . O . . . . . . . . $$ | O O . . . . . . . . . $$ | O X O O . . . . . , . $$ | . X X X O O . . . . . $$ | . ? ? X X O . O . . . $$ | ? T ? . . . . . . . . $$ ----------------------[/go]

PeterPeter · **#35**

On this subject, I stumbled upon this page on Sensei's which is very helpful:

http://senseis.xmp.net/?PlacementPrinciples

Bill Spight · **#36**

Click Here To Show Diagram Code: [go]$$B Wrong way $$ | . . . . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ | . . O . . . . . . . . $$ | O O . . . . . . . . . $$ | O X O O . . . . . , . $$ | 3 X X X O O . . . . . $$ | 2 4 5 X X O . O . . . $$ | . 1 . . 6 . . . . . . . $$ ----------------------[/go]

Shaddy · **#37**

Bill Spight wrote:

Click Here To Show Diagram Code: [go]$$B Wrong way $$ | . . . . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ | . . O . . . . . . . . $$ | O O . . . . . . . . . $$ | O X O O . . . . . , . $$ | 3 X X X O O . . . . . $$ | 2 4 5 X X O . O . . . $$ | . 1 . . 6 . . . . . . . $$ ----------------------[/go]

5 at 6 lives.

Bill Spight · **#38**

Shaddy wrote:

Bill Spight wrote:

Click Here To Show Diagram Code: [go]$$B Wrong way $$ | . . . . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ | . . O . . . . . . . . $$ | O O . . . . . . . . . $$ | O X O O . . . . . , . $$ | 3 X X X O O . . . . . $$ | 2 4 5 X X O . O . . . $$ | . 1 . . 6 . . . . . . . $$ ----------------------[/go]

5 at 6 lives.

Oops!

Well, the caption is correct.

Solving life-and-death tsumegos by trial and error

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