This 'n' that

Bill Spight · **#621**

A difficult endgame position.

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

The outside region is Black's territory.

Enjoy! (If you can. :lol:

)

lightvector · **#622**

Since Bill said this was difficult, I'm guessing this might not be it for some reason, but it's still something?

gennan · **#623**

If I read it correctly, I'd call this a tsumego problem.

gennan · **#624**

My previous answer was wrong, white can live:

Bill Spight · **#625**

This is a modification of a position from a game, where White had one fewer dame and Black to play could kill. I realized that giving White a dame would make an interesting endgame position.

The main difficulty comes from the ko evaluation, depending on who is komaster. You may think of the komaster as having just enough sufficiently large ko threats to win the ko or kos that may arise in the position.

Bill Spight · **#626**

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, :b1:

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, :w1:

-

, 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, :w2:

is the other play in the mirror position. We can stop play after :w6:

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 :w6:

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, :b1:

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 :b1:

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, :w2:

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 :b5:

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 :b1:

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 :b1:

in this diagram also reverses.

After

the net result is ¼. Black wins.

So :b1:

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, :w5:

plays at 4 and wins. After :w9:

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 :w1:

in the first diagram dominates :w1:

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 :b2:

.

)

Bill Spight · **#627**

I have neglected this thread for too long.

Yes, I know that I have not dealt with the difficult ko position I posted, but this position, which may arise in theory, but I have never encountered across the board, is interesting in its own way, and not too difficult to evaluate.

Click Here To Show Diagram Code: [go]$$ Evaluate this corner $$ ---------------- $$ . . X O . . X | $$ . . X O O X . | $$ . . X O O O . | $$ . . X X X O O | $$ . . . . . X X | $$ . . . . X . . | $$ . . . . . . . |[/go]

Enjoy!

EdLee · **#628**

Hi Bill

Bill Spight · **#629**

Click Here To Show Diagram Code: [go]$$ Double throw-in ko $$ ---------------- $$ . . X O . . X | $$ . . X O O X . | $$ . . X O O O . | $$ . . X X X O O | $$ . . . . . X X | $$ . . . . X . . | $$ . . . . . . . |[/go]

Ed has shown the variations.

Either player can throw in to make a ko, but each player prefers that the other one do so, for two reasons. First, whoever throws in lets the opponent take the ko first; second, whoever throws in loses one point (of territory) by comparison with the opponent throwing in, because of the loss of the throw-in stone. (Black can force White to throw in first by playing on a 2-1 point and threatening to kill outright. But that move loses one point by comparison with White throwing in without that Black play.)

Once made, the ko is a typical size for direct kos in the corner, with a swing of 25 pts. Each play in the ko gains 8⅓ pts.

Black komaster

If there are no ko threats, Black is komaster of this ko, because of the fact that Black can force White to throw in first. At the end of the game, at temperature -1, where each play loses 1 point, Black can simply make and win the ko.

Click Here To Show Diagram Code: [go]$$B No seki $$ ---------------- $$ . . X O 5 1 X | $$ . . X O O X 2 | $$ . . X O O O 3 | $$ . . X X X O O | $$ . . . . . X X | $$ . . . . X . . | $$ . . . . . . . |[/go]

After

Black has 18 pts. in the corner, but has made 2 more plays than White, at a cost of 2 pts., so the corner is originally worth 20 pts. to Black.

Click Here To Show Diagram Code: [go]$$W White first $$ ---------------- $$ . . X O 4 . X | $$ . . X O O X 1 | $$ . . X O O O 2 | $$ . . X X X O O | $$ . . . . . X X | $$ . . . . X . . | $$ . . . . . . . |[/go]

If

throws in, Black gets 19 pts. in the corner, but has made only 1 extra move. Again, the corner is originally worth 20 pts.

But, even though Black is komaster, White does not have to accept this result, because at higher temperatures White can do better by playing elsewhere with :w3:

. Even at the dame stage :w3:

can fill a dame, for a net result of 19 pts. for Black instead of 20. Or suppose that :w3:

gained 5 pts. Then the net result would be 14 pts. for Black, 19 pts. in the corner minus 5 pts. elsewhere.

This illutrates the principle that normally the koloser should initiate the ko, in order to gain as much as possible by playing elsewhere in exchange for losing the ko.

How much can White gain by playing elsewhere in exchange for the ko? Suppose that the temperature is 10. Then when White throws in Black will not take and win the ko.

Click Here To Show Diagram Code: [go]$$W All yours $$ ---------------- $$ . . X O . 3 X | $$ . . X O O X 1 | $$ . . X O O O . | $$ . . X X X O O | $$ . . . . . X X | $$ . . . . X . . | $$ . . . . . . . |[/go]

,

elsewhere

The net result is 20 pts. for Black for the two moves elsewhere minus 6 pts. for White in the corner, or 14 pts., versus 19 pts. in the corner for taking and winning the ko minus 10 pts. for White elsewhere, or 9 pts.

The threshold temperature is 8⅓ pts. If Black takes and wins the ko the net result will be 19 - 8⅓ = 10⅔ pts., while if Black lets White win the ko the net result will be 16⅔ - 6 = 10⅔ pts. It does not matter who wins the ko.

When the temperature is above 8⅓ and Black is komaster, we may regard this ko to be worth 10⅔ pts. for Black. In thermography this is called the mast value, since the mast of the thermograph of this position rises vertically above temperature 8⅓ at the territorial value of 10⅔.

White komaster

Click Here To Show Diagram Code: [go]$$B White komaster $$ ---------------- $$ . . X O 8 1 X | $$ . . X O O X 2 | $$ . . X O O O 3 | $$ . . X X X O O | $$ . . . . . X X | $$ . . . . X . . | $$ . . . . . . . |[/go]

,

ko threat and reply, :w6:

takes ko back, :b7:

elsewhere

When the koloser, Black, initiates the ko at temperature, t, the net result for Black will be t - 7, up to temperature 8⅓. The mast value is 8⅓ - 7 = 1⅓ pts. for Black. That is 9⅓ pts. less than the mast value when Black is komaster, so who is komaster makes a big difference.

Quirk of the Nihon Kiin rules

The 1989 Nihon Kiin rules do not allow White to be komaster at temperature -1, since the only threat to take a ko back is to pass. So before stopping play White will need to initiate the ko at temperature 0.

Click Here To Show Diagram Code: [go]$$W White first $$ ---------------- $$ . . X O . 7 X | $$ . . X O O X 1 | $$ . . X O O O 2 | $$ . . X X X O O | $$ . . . . . X X | $$ . . . . X . . | $$ . . . . . . . |[/go]

,

ko threat and reply, :w5:

takes ko back. :b6:

,

dame or pass

The net result will be 6 pts. for White instead of 7. And that means that Black only has to initiate the ko above temperature 1.

Mean value

Somewhat surprisingly, this position has a mean value. Hyperactive positions typically do not. Let us use the method of multiples.

As we have noted, it is a disadvantage to let the opponent take the throw-in stone, but Black can force White to throw in first. That means that when Black plays first in a pair of these positions, Black can score 12 pts. in the pair, with White playing last, for a mean value of 6 pts. per position. The same goes with any number of pairs. But when White plays first Black can take the throw-in stone and score 13 points in the pair, with White playing last. However, with another pair Black plays first in the second pair, and first in any other pairs. With N pairs the result will be 12N + 1 for Black. As we figure mean values the mean value is 6 pts. for Black.

Bill Spight · **#630**

I just dug up this tsumego I composed a while back.

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

Enjoy!

EdLee · **#631**

Bill Spight · **#632**

Thanks, Ed.

What is the result?

EdLee · **#633**

Hi Bill

Bill Spight · **#634**

Hi, Ed.

What else?

EdLee · **#635**

Hi Bill,

Bill Spight · **#636**

Hi, Ed.

What else?

lightvector · **#637**

Bill Spight wrote:

Hi, Ed.

What else?

Bill Spight · **#638**

Hi, lightvector.

That's certainly an important variation.

Bill Spight · **#639**

OK, here we go.

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

Ed's play, :w1:

, is correct. Then :b2:

-

makes an approach ko.

Click Here To Show Diagram Code: [go]$$Wc Direct ko $$ ------------------ $$ | . 5 . X . . . . . $$ | 4 O 1 X . . . . . $$ | 7 2 3 X . . . . . $$ | 6 O X , . . . . . $$ | . O X . . . . . . $$ | . O X . . . . . . $$ | . O X . . . . . . $$ | X X X . . . . . . $$ | . . . . . . . . .[/go]

makes a direct ko, which on average is not as good as the approach ko.

Click Here To Show Diagram Code: [go]$$Wc White dies $$ ------------------ $$ | 9 5 . X . . . . . $$ | 4 O 1 X . . . . . $$ | 8 2 3 X . . . . . $$ | 6 O X , . . . . . $$ | 7 O X . . . . . . $$ | . O X . . . . . . $$ | . O X . . . . . . $$ | X X X . . . . . . $$ | . . . . . . . . .[/go]

This is lightvector's line.

Click Here To Show Diagram Code: [go]$$Bcm10 White dies, continued $$ ------------------ $$ | O O . X . . . . . $$ | . O O X . . . . . $$ | 1 3 O X . . . . . $$ | . O X , . . . . . $$ | O O X . . . . . . $$ | . O X . . . . . . $$ | 2 O X . . . . . . $$ | X X X . . . . . . $$ | . . . . . . . . .[/go]

is the vital point. :w11:

makes a one point eye. But then :b12:

makes a Golden Cock Stands on One Leg shape, which White cannot take because of damezumari.

----

My most difficult tsumego, I think. It was inspired by a problem by emeraldemon. See https://lifein19x19.com/viewtopic.php?t=2271

EdLee · **#640**

Thanks, Bill.

This 'n' that

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