- Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . O O O O O O O O .
$$ . O X . . . . . O .
$$ . O X O O . . O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]
Outside stones are safe.
Evaluate the position.
This is an ambiguous position, a 2 move distant sente where each move gains 1 pt. Its count is -7.
What is the best play by each side?
- Click Here To Show Diagram Code
[go]$$B
$$ . . . . . . . . . .
$$ . O O O O O O O O .
$$ . O X . . 4 2 . O .
$$ . O X O O 3 1 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]
OC, since the position is ambiguous,

and

are not sente. The result is a local score of -7.
- Click Here To Show Diagram Code
[go]$$W
$$ . . . . . . . . . .
$$ . O O O O O O O O .
$$ . O X . . . 3 . O .
$$ . O X O O 1 2 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]
The sequence,

-

, gains one pt., for a local score of -8.
----
What about the other plays? Let's use difference games to compare plays.
- Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 2 . X X .
$$ . X O . . 3 . . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 6 4 . O .
$$ . O X O O 5 1 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]

is the recommended play,

is the other play in the mirror position. We can stop play after

because the local temperature has dropped below 1. Black has 6 + 1¼ = 7¼ pts. and White has 7 pts., for a net result of ¼. Black is ahead and has the move, so Black wins.
- Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 6 2 X X .
$$ . X O . . 4 5 . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 3 . . O .
$$ . O X O O 1 . O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]
We can stop after

because the left sides are mirrored and the right sides have temperatures less than 1. The left sides are miai and equal. Black has 1 pt. on the right and White has ½ pt., for a net result of ½. Black wins.
Since both moves result in a win for the first player, They should be incomparable. In which case, which to play depends upon the rest of the board. But actually,

in the second game is a mistake, unless the ko situation makes it a good ko threat or there is some other ko consideration. We have actually run across this kind of problem before in this thread, with the mistake that Dieter (Knotwilg) discovered in Sakata's
Tesuji and Anti-Suji of Go. The point is that

in the second diagram reverses. (See
https://senseis.xmp.net/?Reversible ) That is, White has a local play that produces a position that is at least as good for White as the original position.
- Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X . . X X .
$$ . X O . . . . . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 2 . . O .
$$ . O X O O 1 . O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]
In this case,

is just such a play.

How can we tell that this position is at least as good for White as the original position? Well, the original position is mirrored on the top, so we already have a difference game set up. If Black to play cannot win, then this position is at least as good for White as the original. (Remember, the original difference game is worth 0.)
- Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 3 4 X X .
$$ . X O . . . 5 . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 2 . . O .
$$ . O X O O 1 . O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]
We can stop after

because the local temperature is below 1. Black has 8 pts. and White has 7¼, for a net result of ¾. But White to play can round down to 0, so Black does not win.
When a play reverses the rule is to keep going locally. In the worst case that means playing inside territory or simply giving up 1 pt.
- Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 6 4 X X .
$$ . X O . . 7 5 . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 2 . . O .
$$ . O X O O 1 3 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]
So

makes a local play in the bottom position, after which White plays first in the mirror position. The net result is ½, which White to play can round down to 0. Because

reverses, Black does not win.
- Click Here To Show Diagram Code
[go]$$
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 4 . X X .
$$ . X O . . 5 . . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 6 2 . O .
$$ . O X O O 3 1 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]
It turns out that

in this diagram also reverses.

After

the net result is ¼. Black wins.
So

in the last diagram is correct, and the other play is not.

We could have reached the same conclusion by noticing that the wrong play is a losing sente. But I wanted to revisit reversal with difference games.

Now what about White's play in the original position?
- Click Here To Show Diagram Code
[go]$$W
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 3 2 X X .
$$ . X O 8 7 5 . . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 9 6 . O .
$$ . O X O O 1 4 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]
If

plays at 5,

plays at 4 and wins. After

the net result is -1½. Black can round that up to -1, but White wins.
- Click Here To Show Diagram Code
[go]$$W
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 2 3 X X .
$$ . X O . . 7 5 . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 6 . . O .
$$ . O X O O 4 1 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]
After

the left side is miai, and the net result is -½, which Black can round up to 0. White does not win.
So

in the first diagram dominates

in the second diagram. However, it turns out that both plays reverse, so with correct play we get this comparison.
- Click Here To Show Diagram Code
[go]$$W
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 5 4 X X .
$$ . X O . . 6 . . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . . 3 . O .
$$ . O X O O 1 2 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]
So with correct play we get this diagram, which is a jigo.
- Click Here To Show Diagram Code
[go]$$W
$$ . . . . . . . . . .
$$ . X X X O O O O O .
$$ . X O X X 4 5 X X .
$$ . X O . . . 6 . X .
$$ . X X X X X X X X .
$$ . O O O O O O O O .
$$ . O X . . 3 . . O .
$$ . O X O O 2 1 O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]
And this diagram, which is also jigo.
So both plays are correct, as long as White recognizes that each one reverses and continues locally. OC, White could make a mistake. The difference game compares the mistakes and prefers the play with the smaller mistake. Did you notice the reversal? Neither did I.

(OC, we would have in a game after

.

)
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Everything with love. Stay safe.