Precision, please

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Bill Spight
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Precision, please

Post by Bill Spight »

A new endgame beastie. :)
Click Here To Show Diagram Code
[go]$$ New beastie
$$ -------------------------------------
$$ , X O O O O O O O . O O . O . O X X ,
$$ , X O . . . . O . O O . O O O . O X ,
$$ , X O . . . O O X O . X O X O O O X ,
$$ , X X X X X X X X X X X X X X X X X ,
$$ , , , , , , , , , , , , , , , , , , ,[/go]
(By convention, the Black stones are alive.)

1) How much territory, on average, does White have?

2) How much does a play gain, on average?

Please be precise.

Enjoy! :D
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Knotwilg
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Re: Precision, please

Post by Knotwilg »

First calculation:

1) White has on average 2817/512 = 5.501953125
2) First play gains 545/512 = 1.064453125
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Bill Spight
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Re: Precision, please

Post by Bill Spight »

Knotwilg wrote:First calculation:

1) White has on average 2817/512 = 5.501953125
2) First play gains 545/512 = 1.064453125
Thanks. :)
I think the gain is less than 1, however.
Edit: Correction.
Now I think it's greater than 1. :oops:
Last edited by Bill Spight on Fri May 01, 2020 11:11 am, edited 2 times in total.
The Adkins Principle:
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— Winona Adkins

Visualize whirled peas.

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Bill Spight
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Re: Precision, please

Post by Bill Spight »

Failure 1
Click Here To Show Diagram Code
[go]$$B Failure
$$ -------------------------------------
$$ , X O O O O O O O C O O C O C O X X ,
$$ , X O . . 2 C O . O O . O O O C O X ,
$$ , X O . . 1 O O X O . X O X O O O X ,
$$ , X X X X X X X X X X X X X X X X X ,
$$ , , , , , , , , , , , , , , , , , , ,[/go]
If :b1: then :w2: gets 5½ pts. on average.

If White does not reply:
Click Here To Show Diagram Code
[go]$$ White does not reply
$$ -------------------------------------
$$ , X O O O O O O O . O O . O C O X X ,
$$ , X O . . 3 . O . O O . O O O C O X ,
$$ , X O . . 1 O O X O . X O X O O O X ,
$$ , X X X X X X X X X X X X X X X X X ,
$$ , , , , , , , , , , , , , , , , , , ,[/go]
After :b3: White has 3¼ pts. on average.

:w2: and :b3: each gains 1⅛ pts. on average. :w2: is too good. :b1: can do better.
The Adkins Principle:
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— Winona Adkins

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Re: Precision, please

Post by dany »

Click Here To Show Diagram Code
[go]$$c
$$ -------------------------------------
$$ |, X O O O O O O O . O O . O . O X X ,|
$$ |, X O . . . . O . O O . O O O . O X ,|
$$ |, X O 1 . . O O X O . X O X O O O X ,|
$$ |, X X X X X X X X X X X X X X X X X ,|
$$ |, , , , , , , , , , , , , , , , , , ,|[/go]
Last edited by dany on Fri May 01, 2020 4:54 am, edited 1 time in total.
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Knotwilg
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Re: Precision, please

Post by Knotwilg »



Second attempt: White has 821/256 on average; a play gains 245/256 on average
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Bill Spight
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Re: Precision, please

Post by Bill Spight »

Knotwilg wrote:

Second attempt: White has 821/256 on average; a play gains 245/256 on average
Black can play better. :)
Edit:
So can White. ;)
The Adkins Principle:
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— Winona Adkins

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Re: Precision, please

Post by Bill Spight »

Difference game for White's first play.

The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

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Re: Precision, please

Post by dany »

1) White has on average 1307/256 = 5.10546875
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Bill Spight
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Re: Precision, please

Post by Bill Spight »

I am afraid my hint gave the impression that the answers have a large denominator. That may not be the case. :)
The Adkins Principle:
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— Winona Adkins

Visualize whirled peas.

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Knotwilg
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Re: Precision, please

Post by Knotwilg »

Bill Spight wrote:I am afraid my hint gave the impression that the answers have a large denominator. That may not be the case. :)
You have not commented on that aspect before. Me too I get a 256 denominator. It's not the hint that set me up for it, but the problem composition, which suggests the two false eyes are unsettled points, depending on follow-up play.

If it were only about the big eye where the action is, then why the complex problem composition with two real eyes at the tail?
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Bill Spight
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Re: Precision, please

Post by Bill Spight »

Knotwilg wrote:
Bill Spight wrote:I am afraid my hint gave the impression that the answers have a large denominator. That may not be the case. :)
You have not commented on that aspect before. Me too I get a 256 denominator.
So did I, and that's when I posted the problem. But I was mistaken. :oops:
It's not the hint that set me up for it, but the problem composition, which suggests the two false eyes are unsettled points, depending on follow-up play.

If it were only about the big eye where the action is, then why the complex problem composition with two real eyes at the tail?
I was inspired by a similar position I ran across in a pro endgame. I thought that the false eyes (Edit: technically, half eyes) made for a cool problem. :cool: This position is slightly simpler than the game position. The half eyes are still significant. :)

BTW, the game is in the GoGoD collection. 2018-07-19u.
Last edited by Bill Spight on Sat May 02, 2020 6:12 am, edited 1 time in total.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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Bill Spight
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Re: Precision, please

Post by Bill Spight »

Difference game for Black's first play. :)

The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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Bill Spight
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Re: Precision, please

Post by Bill Spight »

Another difference game.

Warning, this one gives a big hint.

The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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dany
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Re: Precision, please

Post by dany »

Click Here To Show Diagram Code
[go]$$c
$$ -------------------------------------
$$ |, X O O O O O O O . O O . O . O X X ,|
$$ |, X O . . . . O . O O . O O O . O X ,|
$$ |, X O a . b O O X O . X O X O O O X ,|
$$ |, X X X X X X X X X X X X X X X X X ,|
$$ |, , , , , , , , , , , , , , , , , , ,|[/go]
In such positions, often the best play is asymmetric.
So I think: a - the best for black, b - the best for White. But I was wrong - a the best for the both.
Bill Spight wrote:Warning, this one gives a big hint.
...
Now we have a simpler problem than the original
Click Here To Show Diagram Code
[go]$$c
$$ -------------------------------------
$$ |, X O O O O O O O . O O . O . O X X ,|
$$ |, X O . . . . O . O O . O O O . O X ,|
$$ |, X O O X . O O X O . X O X O O O X ,|
$$ |, X X X X X X X X X X X X X X X X X ,|
$$ |, , , , , , , , , , , , , , , , , , ,|[/go]
1) White has on average 83/16 = 5.1875
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