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 Post subject: Re: This 'n' that
Post #621 Posted: Sun Jun 09, 2019 8:23 am 
Lives in sente

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

Click Here To Show Diagram Code
[go]$$B main line?
$$ ------------------------
$$ . X . 1 3 4 2 . O . . . .
$$ . X . O . O . O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]


Click Here To Show Diagram Code
[go]$$B white only does this with a ton of ko threats
$$ ------------------------
$$ . X 4 1 2 . 3 . O . . . .
$$ . X 5 O . O . O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]


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 Post subject: Re: This 'n' that
Post #622 Posted: Sun Jun 09, 2019 9:09 am 
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If I read it correctly, I'd call this a tsumego problem.

Click Here To Show Diagram Code
[go]$$B kill in ko?
$$ ------------------------
$$ . X 4 3 2 . 1 . O . . . .
$$ . X 5 O . O . O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]


White cannot connect:

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[go]$$W white fails
$$ ------------------------
$$ . X O 1 O 2 X . O . . . .
$$ . X X O . O . O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]


So it bocomes a ko:

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[go]$$W white fails
$$ ------------------------
$$ . X O 2 O . X . O . . . .
$$ . X X O . O 1 O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]

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 Post subject: Re: This 'n' that
Post #623 Posted: Sun Jun 09, 2019 9:20 am 
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My previous answer was wrong, white can live:

Click Here To Show Diagram Code
[go]$$B live
$$ ------------------------
$$ . X . 2 4 3 1 . O . . . .
$$ . X . O . O . O O X . X .
$$ . X X O O X O O X X . . .
$$ . . . X X X X X . . . . .
$$ . . X . . . . . X . . . .[/go]


So 2 seems to be the vital point and I now think that lightvector's answer is correct (white gets 3 points less in his solution).


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 Post subject: Re: This 'n' that
Post #624 Posted: Sun Jun 09, 2019 10:20 am 
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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. :)

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 Post subject: Re: This 'n' that
Post #625 Posted: Mon Jun 10, 2019 10:42 am 
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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 :b3: 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: - :w3:, 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]


:b1: 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 :b3: 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 :w6: 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 :b4: 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 :w7: 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:. :))

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— Winona Adkins

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 Post subject: Re: This 'n' that
Post #626 Posted: Thu Jul 11, 2019 8:19 pm 
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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! :D

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Post #627 Posted: Thu Jul 11, 2019 9:12 pm 
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Hi Bill :)
Quote:
Click Here To Show Diagram Code
[go]$$
$$ ---------------
$$ . . X O . . X |
$$ . . X O O X . |
$$ . . X O O O . |
$$ . . X X X O O |
$$ . . . . . X X |
$$ . . . . X . . |
$$ . . . . . . . |[/go]
Very confusing for me. :blackeye:
Click Here To Show Diagram Code
[go]$$B B option to start ko (W takes first)
$$ ---------------
$$ . . X O . . X |
$$ . . X O O X . |
$$ . . X X O O 1 |
$$ . . . , X O O |
$$ . . . . X X X |
$$ . . . . . . . |[/go]
Click Here To Show Diagram Code
[go]$$B W ko(a) option (B takes first); B kills with (a)
$$ ---------------
$$ . . X O b a X |
$$ . . X O O X 1 |
$$ . . X X O O . |
$$ . . . , X O O |
$$ . . . . X X X |
$$ . . . . . . . |[/go]
Click Here To Show Diagram Code
[go]$$W W starts ko (B takes first)
$$ ---------------
$$ . . X O . . X |
$$ . . X O O X 1 |
$$ . . X X O O . |
$$ . . . , X O O |
$$ . . . . X X X |
$$ . . . . . . . |[/go]
Click Here To Show Diagram Code
[go]$$W B option to kill(a)
$$ ---------------
$$ . . X O 1 . X |
$$ . . X O O X a |
$$ . . X X O O . |
$$ . . . , X O O |
$$ . . . . X X X |
$$ . . . . . . . |[/go]


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 Post subject: Re: This 'n' that
Post #628 Posted: Sat Jul 13, 2019 4:55 am 
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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 :b5: 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 :w1: 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]

:b2:, :b4: 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]

:w4:, :b5: 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]

:w3:, :b4: ko threat and reply, :w5: takes ko back. :b6:, :b8: 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. :)

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 Post subject: Re: This 'n' that
Post #629 Posted: Thu Aug 01, 2019 9:08 am 
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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!

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Post #630 Posted: Thu Aug 01, 2019 3:40 pm 
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:study:
Click Here To Show Diagram Code
[go]$$W
$$ ------------------
$$ | . . . X . . . . .
$$ | . O 1 X . . . . .
$$ | . . . X . . . . .
$$ | . O X , . . . . .
$$ | . O X . . . . . .
$$ | . O X . . . . . .
$$ | . O X . . . . . .
$$ | X X X . . . . . .
$$ | . . . . . . . . .[/go]


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 Post subject: Re: This 'n' that
Post #631 Posted: Thu Aug 01, 2019 6:49 pm 
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Thanks, Ed. :)

What is the result?

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Post #632 Posted: Thu Aug 01, 2019 8:53 pm 
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Hi Bill :)
:blackeye:
Click Here To Show Diagram Code
[go]$$W dead
$$ -------------------
$$ | . 2 3 X . . . . .
$$ | 7 O 1 X . . . . .
$$ | 5 4 6 X . . . . .
$$ | 8 O X , . . . . .
$$ | . O X . . . . . .
$$ | . O X . . . . . .
$$ | . O X . . . . . .
$$ | X X X . . . . . .
$$ | . . . . . . . . .[/go]
Click Here To Show Diagram Code
[go]$$W ko?
$$ ------------------
$$ | 7 2 4 X . . . . .
$$ | 6 O 1 X . . . . .
$$ | 5 . 3 X . . . . .
$$ | . O X , . . . . .
$$ | . O X . . . . . .
$$ | . O X . . . . . .
$$ | . O X . . . . . .
$$ | X X X . . . . . .
$$ | . . . . . . . . .[/go]
Click Here To Show Diagram Code
[go]$$W Life
$$ ------------------
$$ | . 2 4 X . . . . .
$$ | 3 O 1 X . . . . .
$$ | . . 5 X . . . . .
$$ | . O X , . . . . .
$$ | . O X . . . . . .
$$ | . O X . . . . . .
$$ | . O X . . . . . .
$$ | X X X . . . . . .
$$ | . . . . . . . . .[/go]
:study:

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 Post subject: Re: This 'n' that
Post #633 Posted: Thu Aug 01, 2019 9:21 pm 
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Hi, Ed.

What else? :)

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Post #634 Posted: Thu Aug 01, 2019 9:52 pm 
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Hi Bill,
Reverts to another var:
Click Here To Show Diagram Code
[go]$$W
$$ -------------------
$$ | . 4 . X . . . . .
$$ | 5 O 1 X . . . . .
$$ | . 2 3 X . . . . .
$$ | . O X , . . . . .
$$ | . O X . . . . . .
$$ | . O X . . . . . .
$$ | . O X . . . . . .
$$ | X X X . . . . . .
$$ | . . . . . . . . .[/go]

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 Post subject: Re: This 'n' that
Post #635 Posted: Fri Aug 02, 2019 2:30 am 
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Hi, Ed.

What else? :)

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Post #636 Posted: Fri Aug 02, 2019 6:45 pm 
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Bill Spight wrote:
Hi, Ed.

What else? :)


Are you referring to the variation where black goes for ko, white repeatedly declines, captures a farmer's hat, and dies due to shortage of liberties? :study: :)

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Post #637 Posted: Fri Aug 02, 2019 7:50 pm 
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Hi, lightvector. :)

That's certainly an important variation.

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Post #638 Posted: Sun Aug 04, 2019 1:43 am 
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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: - :b6: 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]


:w5: 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]


:b10: 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

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Post #639 Posted: Mon Aug 05, 2019 12:02 am 
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Thanks, Bill.

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Post #640 Posted: Mon Aug 19, 2019 8:42 am 
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On winrate estimates, territory estimates, margins of error, and the last play

OC, as humans we are used to territory estimates, but we are past the hype about how top bots think differently, and better than humans, in some mysterious way about the probability of winning the game. Unless we are talking about certain situations such as the 5x5 board, where we know that the probability is 100% that Black wins with perfect play, and even reasonably good play, or the late endgame where we can figure out perfect play, or a pro vs pro game where one player leads by, say, 50 pts. and the largest play gains 10 pts., there is no a priori knowable probability of winning the game. A posteriori, we could have a position played to the end many times by certain players, or by players of comparable levels, and get winrate estimates thaty way, but we do not know how well those winrates would generalize, and to whom. In general, as the skill of the players decreases towards random play, the winrates get closer to 50%. And the bots do not estimate winrates in that manner, anyway. The mystery of winrates is baked into the cake. We really do not know enough about the factors involved. Perhaps there will be a Ph.D. dissertation about winrates in the near future. :) (BTW, I have found another example where Elf is way wrong about the value of a play by a top player — Dosaku in this case. More later. :))

My purpose here is not to casts doubt on winrate estimates. They are useful. It was the hype that got me started, but that has pretty well blown over. One problem that still remains is that of their margins of error. If a top bot estimates, given sufficient playouts — and we don't know how many that is, either —, that one play has a winrate 10% worse than that of the bot's top choice, we can be pretty sure that it is a mistake. OTOH, if the winrate estimate is only 2% worse, we have little assurance that it is an error. I have recently downsized my margin of error for Elf to 4%, but that is still an educated guess. Nobody has worked out the margins of error for winrate estimates, and I doubt if anybody is going to do so anytime soon. The margin of error may be important for a human attempting to interpret winrate estimates, but any bot that picks a play with a smaller winrate estimate, given sufficient playouts, is likely to play worse. And today's bots are written to win games, not analyze positions.

Now, when we can actually work out territory estimates, we can determine the margins of error. For example, if a gote gains 5 pts., its margin of error is 5 pts., as well, since we do not know who will make the play. Assuming correct play, that is. If the players make mistakes, the margin of error could be greater. But the gain is not a territory estimate, it is something that we find out when we make the estimate. Now, some bots make territory estimates as well as winrate estimates. This is good, but, AFAIK, they do not yet estimate the margin of error of the territory estimates. In terms of the whole board the gain from making the largest gote or reverse sente is the temperature. If we are going to use territory estimates, we need temperature estimates, as well.

That brings me to the topic of the last play. If I am 1 pt. behind and make a play that gains 3 pts., then I am 2 pts. ahead. The opponent might still win. But if my play was the last play of the game, then I win. Such a situation would be unusual, because the temperature would drop from 3 to 0, and such a large temperature drop is unusual in go. The average drop in temperature between moves is less than 1 pt. It is probably less than 0.1 pt. But larger temperature drops do occur. For instance, suppose that after my play the temperature dropped by 2 pts., i.e., to 1 pt. Then I would still (very likely) win, since I would be 2 pts. ahead and the best my opponent could do would be to gain 1 pt., not enough to catch up. (A very unusual ko situation could still give her the win, since the margin of error for ko positions is greater than their temperature.) The play just before a significant temperature drop is also called a last play.

In fact, one of the traditional dogmas of go is that of getting the last big play of the opening. Now, what that play is is not well defined, but good players can usually sense it, and sense the related temperature drop, as well. Unless the bots prove that it is hokum, which I don't think they will. ;) In fact, I have found an example where I think the bots back up the idea of a significant temperature drop in the opening. :D It has to do with the 5-3 approach to the 3-4 point.

Now, humans have known, or at least strongly suspected, that the 5-3 approach to the 3-4 point is not as big, as a rule, as the original 3-4 play itself. Certainly by the 19th century the idea was that, usually at move 4, White should play the 5-3 approach to a 3-4 stone before occupying an empty corner, even though occupying the empty corner was better objectively, because White needed to complicate the game to overcome Black's advantage. Today, with komi, the empty corner beckons, although approaching a 3-4 stone, even at move 2, is not unknown. Writing in the mid-20th century, even Takagawa could not unequivocally say that the approach at move 2 was a mistake. Obviously, the 3-4 makes more territory, on average, but the 5-3 has more influence towards the center and the side. Which is better? Probably the 3-4, but quien sabe?

In the 17th century the 5-3 approach to the 3-4 stone was common at move 2. Did the players think that the 5-3 stone was objectively not quite as good? Maybe so, but Dosaku played a number of games as White where he played the 5-3 in all four corners, playing it as the first play in empty corners. Did he think that the 5-3 was objectively as good as, or better than, the 3-4? Obviously, he was extremely skilled at utilizing the influence of the 5-3, but would he have played it to occupy an empty corner if he were playing against himself?

Well, Elf has an opinion, expressed in terms of winrates. What does Elf say?

In a game against Yasui Chitetsu (GoGoD 1671-08-25a) Dosaku played the 5-3 approach as :w2: against Chitetsu's 3-4 :b1:, a very common opening at the time. Elf estimates that the approach loses 5½% versus a 4-4 play in an empty corner. (I don't regard winrate estimates as precise enough to warrant reporting tenths of a point difference near 50%. Half point precision is good enough, IMHO. :)) Next, Chitetsu played :b3: as a two space pincer against :w2:, which was also common back then. Elf regards :b3: as a 4% winrate error. (Within decades human players had dropped the :b3: pincer, which indicates that they also had come to regard it as an error. When both bots and humans think a play is a mistake, it probably is. ;)) Dosaku played :w4: on the 5-3 in the adjacent corner closest to :b3:. Elf considers it a 7% error. OK, Elf considers the 5-3 to be a mistake, whether as an approach to the 3-4 or as the first play in an empty corner. What does this have to do with the last play, if anything?

OK. Today's bots consider the corners to be worth more, by comparison with the sides, than humans. In the late 20th century we were starting to see humans devalue the sides by a little bit. For instance, the sanrensei was devalued, but the nirensei was still considered good. Even today, the bots like the nirensei. ;) But we see plays on the side that top humans played without a second thought regarded as losing 10% by today's top bots. Shoulder hits, side attachments, or other plays against enclosures are usually considered to be bigger than extensions on the side. This represents a big difference in opening theory. IOW, the temperature of the corners remains hotter than the temperature of the sides for longer than we humans have thought. A temperature drop is coming up. ;)

GoGoD 1665-00-00a, Aoki Guseki (W) vs. Dosaku. :w4: plays the 5-3 approach instead of occupying the last empty corner. Elf estimates a winrate loss of 6½%.

GoGoD 1667-12-05b, Castle Game, Honinbo Doetsu (W) vs. Yasui Chitetsu. :w2: is a 5-3 approach, estimated loss of 5½%, :b3: plays on the 3-4 in an open corner. :w4: approaches on the 5-3. Estimated loss: only 2%. :o (But there are two empty corners.)

GoGoD 1669-07-16, Dosaku (W) vs. Doetsu. :w2: is a 5-3 approach. Estimated winrate loss: 6½%. :b5: is a 5-3 approach. Estimated winrate loss: 2%. (Two empty corners.) :w8: is a 5-3 approach instead of occupying the last empty corner. Estimated winrate loss: 7½%.

If I were writing an article or thesis, I would OC, examine many instances, either of actual games, or of computer generated positions. And I have looked at more games than I report here. The number of empty corners seems to matter to the winrate loss estimate of the 5-3 approach. Here is my hypothesis as to why.

Winrate loss estimates depend, not only upon the play made, but upon the alternative, presumably best, play. The value of the 5-3 approach in each corner is approximately the same in each case, I assume. Then the difference in winrates reflects the difference in the value of occupying an empty corner, assuming that that is the best play. When there is only one empty corner, that difference is around 6½% in terms of winrates. But when there are two empty corners, they are miai, if not exactly so. And then the difference is pretty much the loss in the corner of the 5-3 approach versus the play after the two corners are occupied, which comes to around 2%. The difference of around 4½% reflects a temperature drop after the last empty corner is occupied. Occupying the last empty corner is significant.

When there are three empty corners, there is some uncertainty about who will get to occupy the last empty corner, at least as bots calculate winrates. That uncertainty reduces the winrate estimate of the loss of the 5-3 approach by around 1½%.

OC, if I did the research I could get better estimates, and there may be other factors to consider. :) But I think these results are suggestive. There does seem to be a last play effect in the opening, namely occupying the last empty corner. It comes earlier than humans have thought, but there may be another significant temperature drop a bit later on at the threshold of the middle game, and yet another at the cusp of the endgame. :)

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