Life In 19x19

-Edit - I got a bit confused with my diagrams in my first post so this is the correction version.

I have just started learning using the Interactive Way to Go website (it's so good!) and solve Tsumego on my phone, but the app I use doesn't really explain why a certain shape is the correct solution. Here is the problem from the Hactar Go Lite phone app.

White to play.

Click Here To Show Diagram Code

[go]$$Wc
$$ +-------------------+
$$ | O X . O . . . . .
$$ | O X X X X X X X O
$$ | O O O O O O O O .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ +-------------------+[/go]

I finally arrive at the solution:

Click Here To Show Diagram Code

[go]$$Wc
$$ +-------------------+
$$ | O X . O 3 . 2 1 4
$$ | O X X X X X X X O
$$ | O O O O O O O O 5
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ +-------------------+[/go]

I'm guessing that White needs to stop Black from forming two eyes and living. So why is the above correct? Because I can see that Black has two eyes, one big one of the left and a small one on the right. Maybe I have completely misunderstood the point of this tsumego or the concept of forming eyes. Assuming that Black wants to form two eyes, could it then play either a or b? It looks okay to me.

Click Here To Show Diagram Code

[go]$$Wc
$$ +-------------------+
$$ | O X a O 3 b 2 1 4
$$ | O X X X X X X X O
$$ | O O O O O O O O 5
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ +-------------------+[/go]

Hi Libcat,

B has only one real eye, and is dead.

(a) and (b) are two liberties, not two eyes.
(c) is a False Eye.

Click Here To Show Diagram Code

[go]$$B Black Dead shape
$$ +--------------------
$$ | a O O b X c X . . .
$$ | X X X X X X O W . .
$$ | O O O O O O . . O .
$$ | . . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$W Black Dead shape
$$ +---------------------
$$ | . O O . X 2 X 1 . .
$$ | X X X X X X O O . .
$$ | O O O O O O . . O .
$$ | . . . . . . . . . .[/go]

As an exercise, try to prove to your satisfaction that B cannot form two real eyes with this shape:

Click Here To Show Diagram Code

[go]$$B Black Dead shape
$$ +--------------------
$$ | . O O . X X X O . .
$$ | X X X X X X O O . .
$$ | O O O O O O . . O .
$$ | . . . . . . . . . .[/go]

Did you mean to make 9x9 boards in your diagrams ?
... because your diagrams are open-ended on the right edge.
If your diagrams are supposed to be 9x9, then in your second diagram,
your at J7, in reply to J9, is correct.

In the diagrams here, I made the boards bigger than 9x9,
and in reply to , W extends toward the right with .

The problem makes sense now, with the better diagrams. I removed your other thread, since it was confusing.

@EdLee Hello and thank you!

EdLee wrote: Did you mean to make 9x9 boards in your diagrams ?
... because your diagrams are open-ended on the right edge.
If your diagrams are supposed to be 9x9, then in your second diagram,
your at J7, in reply to J9, is correct.

In the diagrams here, I made the boards bigger than 9x9,
and in reply to , W extends toward the right with .

Yes, I did not even realise this until checked my phone again. Here is the screenshot. It looks like everything was supposed to be happening on the top right of a 19x19 board, so technically yes, 9x9. I hadn't thought about this up till now, but clearly where the tsumego takes place/board size makes a huge difference! Sorry for missing that big detail.

I will have to check my understanding of all the concepts you linked to - especially false eyes since they don't look appear obvious to me.

EdLee wrote: As an exercise, try to prove to your satisfaction that B cannot form two real eyes with this shape:

$$B Black Dead shape
$$ +--------------------
$$ | . O O . X X X O . .
$$ | X X X X X X O O . .
$$ | O O O O O O . . O .
$$ | . . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B Black Dead shape
$$ +--------------------
$$ | . O O . X X X O . .
$$ | X X X X X X O O . .
$$ | O O O O O O . . O .
$$ | . . . . . . . . . .[/go]

ARGH okay yes, I see. Thanks again.

Kirby wrote:The problem makes sense now, with the better diagrams. I removed your other thread, since it was confusing.

Thank you! (I don't know what the etiquette is here i.e, do I 'like' your reply? No idea, but either way I'm grateful)

libcat wrote:... false eyes since they don't appear obvious to me.

The easiest way to understand a false eye is to ask yourself how it will eventually resolve. ( Works for lots of other shapes too, FWIW )

If you look at the example used above...

Click Here To Show Diagram Code

[go]$$B False eye
$$ +--------------------
$$ | . O O . X C B O . .
$$ | X X X X X X O O . .
$$ | O O O O O O . . O .
$$ | . . . . . . . . . .[/go]

you can realize that,sooner or later, ONE player must play BOTH of the circled points.

In other words, this:

Click Here To Show Diagram Code

[go]$$B Not in this universe
$$ +--------------------
$$ | . O O . X B W O . .
$$ | X X X X X X O O . .
$$ | O O O O O O . . O .
$$ | . . . . . . . . . .[/go]

...sharing of the two points cannot ever exist. Try it on a board to prove it to yourself.
Even if both players cooperate, you can't get there from here.

So, eventually it must end like this:

Click Here To Show Diagram Code

[go]$$B Dead with one eye
$$ +--------------------
$$ | . O O . X B B O . .
$$ | X X X X X X O O . .
$$ | O O O O O O . . O .
$$ | . . . . . . . . . .[/go]

...or this:

Click Here To Show Diagram Code

[go]$$ Dead with one eye
$$ +--------------------
$$ | . O O . X W W O . .
$$ | X X X X X X O O . .
$$ | O O O O O O . . O .
$$ | . . . . . . . . . .[/go]

BTW, I'm assuming in this post that you know basic dead/live shapes, and therefore you know that this:

Click Here To Show Diagram Code

[go]$$B Basic dead shape
$$ +--------------------
$$ | . O O . X O .
$$ | X X X X X O .
$$ | O O O O O O .
$$ | . . . . . . .[/go]

..is dead.

This is not the first time that the issue has been discussed.

For a slightly different statement of the issue, have a look at this: viewtopic.php?f=11&t=16767