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

springs to mind because it threatens

, making two eyes. We do not even think about branches from here.
- Click Here To Show Diagram Code
[go]$$B
$$ ------------------------
$$ . . . . X . 2 O X X . . .
$$ . O . O X 1 . X O . O O .
$$ . . . O X O O X O . . . .
$$ . . . O X O X X O . O . .
$$ . . . O X X X . O . . . .
$$ . . . O O O O O . . . . .
$$ . . . . . . . . . . . . .
$$ . . . . . . . . . . . . .[/go]

is forced. This position looks hopeless. Even "logically."

Why?
- Click Here To Show Diagram Code
[go]$$B
$$ ------------------------
$$ . . . . X . O O X X . . .
$$ . O . O X X 3 X O . O O .
$$ . . . O X W W X O . . . .
$$ . . . O X W X X O . O . .
$$ . . . O X X X . O . . . .
$$ . . . O O O O O . . . . .
$$ . . . . . . . . . . . . .
$$ . . . . . . . . . . . . .[/go]
The 3 stone White string is worth 1 eye, "logically". If

captures, . . .
- Click Here To Show Diagram Code
[go]$$B
$$ ------------------------
$$ . . . . X 5 W W X X . . .
$$ . O . O X X X X O . O O .
$$ . . . O X 4 . X O . . . .
$$ . . . O X . X X O . O . .
$$ . . . O X X X . O . . . .
$$ . . . O O O O O . . . . .
$$ . . . . . . . . . . . . .
$$ . . . . . . . . . . . . .[/go]

is nakade for 1 eye. Now the 2 stone White string is worth 0 eye, "logically". If

captures, . . .
- Click Here To Show Diagram Code
[go]$$B
$$ ------------------------
$$ . . . . X X . 6 X X . . .
$$ . O . O X X X X O . O O .
$$ . . . O X O . X O . . . .
$$ . . . O X . X X O . O . .
$$ . . . O X X X . O . . . .
$$ . . . O O O O O . . . . .
$$ . . . . . . . . . . . . .
$$ . . . . . . . . . . . . .[/go]

throws in for 0 eye. "Logically," 1 + 0 = 1, which is less than 2, so Black is dead.
The road not taken, the line not read:
- Click Here To Show Diagram Code
[go]$$B
$$ ------------------------
$$ . . . . X . 1 O X X . . .
$$ . O . O X 2 . X O . O O .
$$ . . . O X O O X O . . . .
$$ . . . O X O X X O . O . .
$$ . . . O X X X . O . . . .
$$ . . . O O O O O . . . . .
$$ . . . . . . . . . . . . .
$$ . . . . . . . . . . . . .[/go]

was not even considered, because it leads to this position, which is known to be dead.
That is a strange thing to say. If you do not even consider

, how do you see this position?

Be that as it may, I don't
think that I considered

.
- Click Here To Show Diagram Code
[go]$$B
$$ ------------------------
$$ . . . . X . 2 O X X . . .
$$ . O . O X . 1 X O . O O .
$$ . . . O X O O X O . . . .
$$ . . . O X O X X O . O . .
$$ . . . O X X X . O . . . .
$$ . . . O O O O O . . . . .
$$ . . . . . . . . . . . . .
$$ . . . . . . . . . . . . .[/go]
Next, what about this atari? Note that I stick with the same

. That's not a bad heuristic. If

countered other plays, maybe it will counter this one, too. And it does. I am still left with 1 eye plus 0 eye. Black is dead. (I did not actually add 1 + 0. I just know the eye value of each string, and that they do not add up.)
OK, time for the stupid play:
- Click Here To Show Diagram Code
[go]$$B
$$ ------------------------
$$ . . . . X 1 2 O X X . . .
$$ . O . O X . . X O . O O .
$$ . . . O X O O X O . . . .
$$ . . . O X O X X O . O . .
$$ . . . O X X X . O . . . .
$$ . . . O O O O O . . . . .
$$ . . . . . . . . . . . . .
$$ . . . . . . . . . . . . .[/go]
The light dawns! I already know that capturing does not work. 1 + 0 and all that. But I do not have to add.
- Click Here To Show Diagram Code
[go]$$B
$$ ------------------------
$$ . . . . X 1 2 O X X . . .
$$ . O . O X 3 5 X O 4 O O .
$$ . . . O X O O X O . . . .
$$ . . . O X O X X O . O . .
$$ . . . O X X X . O . . . .
$$ . . . O O O O O . . . . .
$$ . . . . . . . . . . . . .
$$ . . . . . . . . . . . . .[/go]

combines the two positions, so that they are not independent.

That means that the eye values do not just add.

makes a simultaneous capture, yielding this:
- Click Here To Show Diagram Code
[go]$$B
$$ ------------------------
$$ . . . . X X . . X X . . .
$$ . O . O X X X X O O O O .
$$ . . . O X . . X O . . . .
$$ . . . O X . X X O . O . .
$$ . . . O X X X . O . . . .
$$ . . . O O O O O . . . . .
$$ . . . . . . . . . . . . .
$$ . . . . . . . . . . . . .[/go]
The three point eye has an eye value of 1.5, and the two point half-false eye has an eye value of 0.5. 1.5 + 0.5 = 2, logically. Black is alive!
Now I know that

in this line is incorrect. (Without reading?

) I have to transpose

and

.
- Click Here To Show Diagram Code
[go]$$B
$$ ------------------------
$$ . . . . X 3 2 O X X . . .
$$ . O . O X 1 5 X O 4 O O .
$$ . . . O X O O X O . . . .
$$ . . . O X O X X O . O . .
$$ . . . O X X X . O . . . .
$$ . . . O O O O O . . . . .
$$ . . . . . . . . . . . . .
$$ . . . . . . . . . . . . .[/go]
Bingo!
Now I remember running across a simultaneous capture problem long ago. Too bad I had forgotten. The logic of simultaneous capture would have made this problem easy. It's magic. It's as though 1 + 0 = 2.

If I had been a depth first kind of guy, I would have solved this problem sooner. As you can see, I am not a breadth first kind of guy, either. I call what I do sideways search.

Note the value of assuming

. A line of play starting with two incorrect plays led to the solution.

You can see why I say that seeing is better than reading.

After some thought, I classified myself as a logical player. Even though I play by feel. Still, this problem was not easy for me. That's because of a flaw in my logic. The eye values did not add up. (Not that I added them consciously.

) The key was to combine the positions without adding.

And that I discovered by reading an illogical line of play.

I don't know if there is a moral to this story, but I thought it was worth sharing.

Edit: Afterthought. I found the heuristic of considering the same

valuable. But that was once I was into reading mode. Actually, except for the solution and the line I did not consider,

could have been a pass. But by then I had dropped out of evaluation mode. I was in calculation mode. If I had evaluated the positions correctly, I would have had to backtrack, instead of transposing. But it all worked out.
