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 Post subject: Komaster concept for hypothetical play
Post #1 Posted: Thu Nov 28, 2019 12:21 pm 
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I hope the title is clear enough. :) This is an idea I have had in the back of my mind for quite a while. I had not thought everything through when I saw lightvector's thread on his Japanese style rules for KataGo, and I thought I would bring the idea up. So as not to hijack his thread, I thought I would move the komaster discussion here.

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 Post subject: Re: Komaster concept for hypothetical play
Post #2 Posted: Thu Nov 28, 2019 12:24 pm 
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Copied from lightvector's thread.

Bill Spight wrote:
As for evaluating kos that remain on the board after the main play or arise in an encore, I am considering a variant of Berlekamp's komaster rule. By that rule if the komaster takes a ko (or plays in a superko) she must immediately resolve the ko or superko. My variant is to allow the opponent to reply instead of having the komaster make more than one move at her turn.

Consider Moonshine Life. One player uses a double ko or other ko threat to take the Moonshine Life, but leaves the ko mouth open. Berlekamp's rule forces the player to fill the ko, thus allowing the opponent to capture.

Consider double ko seki. Berlekamp's original rule would allow one player to take one of the kos and then take the opponent's group on the same turn. My modification allows the opponent to take the other ko. Then the komaster must fill the ko she just took and it is she who loses a group. Under this rule neither player will attempt to be komaster for the double ko seki, and so neither will take the ko.

Consider an approach ko. One player can claim to be komaster and resolve the ko, the other player cannot do so under the modified rule because the opponent will be able to capture her stones in the ko.

Consider a ten thousand year ko. One player will be able to resolve the ko safely, the other player will not. Only the first player can be komaster and will be allowed to resolve the ko.

Consider the J89 anti-seki. Each player is able to resolve the ko as komaster, so it should be resolved before any encore.

There is no pass for ko rule. Instead you allow one player or other to attempt to be komaster. The komaster does not need to make any ko threat and the koloser cannot do so. Play is hypothetical. Since the koloser is allowed to reply when the komaster takes a ko, any gain that the koloser makes is not counted if the komaster is able to resolve the ko safely.

Consider bent four in the corner. At some point in the play a ko arises. Only the player who takes the new ko is allowed to be komaster.

I haven't checked everything out, but I think this approach works pretty well.

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"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
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 Post subject: Re: Komaster concept for hypothetical play
Post #3 Posted: Thu Nov 28, 2019 12:26 pm 
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lightvector's reply

lightvector wrote:
Bill Spight wrote:
As for evaluating kos that remain on the board after the main play or arise in an encore, I am considering a variant of Berlekamp's komaster rule. By that rule if the komaster takes a ko (or plays in a superko) she must immediately resolve the ko or superko. My variant is to allow the opponent to reply instead of having the komaster make more than one move at her turn.

How does one computer-implementably define "komaster"?

Also, how does one computer-implementably define "resolve"? It cannot be "fill the ko" because sometimes a player needs to capture a surrounding group rather than filling. And I think "resolving" might also sometimes even involve a non-capture move that leaves the ko mouth to still exist on the board longer. For example, here white should be able to kill everything no matter what, but if black is the first to play and plays "a", then white will need to capture at "b" or "c" to generate a liberty before playing at "d". White must not be forced to fill "b" or "c" thereafter, and neither should we prevent white from being allowed to later capture into "b" or "c" a second time after finishing capturing the black group on the upper side.

Click Here To Show Diagram Code
[go]$$c
$$ ---------------------------------------
$$ | . X c X O O X . X d O . . . . . . . . |
$$ | X X X O . O X X X O O . . . . . . . . |
$$ | b X O O O O X O O O . . . . . . . . . |
$$ | X O O X X X O O . . . . . . . , . . . |
$$ | O O a X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


It seems to me also if the opponent's "reply" is an arbitrary move elsewhere on the board that is threatening in some way, and the opponent keeps playing such moves, one must allow a potentially arbitrary number of responses by the komaster to those moves before "resolving" the ko - is there a way to handle this?

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— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
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 Post subject: Re: Komaster concept for hypothetical play
Post #4 Posted: Thu Nov 28, 2019 12:30 pm 
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My reply to lightvector, which deals pretty clearly with temperature -1 double kos, I hope.

Bill Spight wrote:
lightvector wrote:
Bill Spight wrote:
As for evaluating kos that remain on the board after the main play or arise in an encore, I am considering a variant of Berlekamp's komaster rule. By that rule if the komaster takes a ko (or plays in a superko) she must immediately resolve the ko or superko. My variant is to allow the opponent to reply instead of having the komaster make more than one move at her turn.

How does one computer-implementably define "komaster"?


I have not gotten that far. :) But first, you have to have identified a ko or superko. In Berlekamp's original formulation, the komaster is the player who is permitted to break the ban for that ko but then must continue, at the same turn, to make one or more plays to win the ko. It may not be obvious, but that is a cost to the komaster.

In the case of end of game resolution of kos, "winning" the ko may actually not be desirable. And giving the komaster two or more moves in a row may be a benefit to the komaster. So we give the koloser the option of responding to the komaster. But the komaster still has to resolve the ko.

So for these cases we allow either player to claim the right to be komaster, i.e., to resolve the ko by playing first. The koloser has no right to break the ko ban. If and only if neither player claims the right to be komaster for a ko does that ko remain unresolved.

Since we are talking about hypothetical play, the komaster of a ko is the player who, for that period of play, has the right to resolve that ko.


Quote:
Also, how does one computer-implementably define "resolve"?


A ko is resolved when it no longer exists.

Quote:
It cannot be "fill the ko" because sometimes a player needs to capture a surrounding group rather than filling. And I think "resolving" might also sometimes even involve a non-capture move that leaves the ko mouth to still exist on the board longer. For example, here white should be able to kill everything no matter what, but if black is the first to play and plays "a", then white will need to capture at "b" or "c" to generate a liberty before playing at "d". White must not be forced to fill "b" or "c" thereafter, and neither should we prevent white from being allowed to later capture into "b" or "c" a second time after finishing capturing the black group on the upper side.

Click Here To Show Diagram Code
[go]$$c
$$ ---------------------------------------
$$ | . X c X O O X . X d O . . . . . . . . |
$$ | X X X O . O X X X O O . . . . . . . . |
$$ | b X O O O O X O O O . . . . . . . . . |
$$ | X O O X X X O O . . . . . . . , . . . |
$$ | O O a X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


An interesting position, which I will discuss below. :)

Quote:
It seems to me also if the opponent's "reply" is an arbitrary move elsewhere on the board that is threatening in some way, and the opponent keeps playing such moves, one must allow a potentially arbitrary number of responses by the komaster to those moves before "resolving" the ko - is there a way to handle this?


The komaster does not have to answer any arbitrary play. Her job is to resolve the ko. As long as she can do so safely, all hypothetical plays by the koloser are ignored. Details may need to be worked out. :)

Click Here To Show Diagram Code
[go]$$c Ambiguous temperature
$$ ---------------------------------------
$$ | . X c X O O X . X d O . . . . . . . . |
$$ | X X X O . O X X X O O . . . . . . . . |
$$ | b X O O O O X O O O . . . . . . . . . |
$$ | X O O X X X O O . . . . . . . , . . . |
$$ | O O a X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


While this is a scorable corner, it has an ambiguous temperature.

Click Here To Show Diagram Code
[go]$$Bc Black first
$$ ---------------------------------------
$$ | . X . X O O X . X . O . . . . . . . . |
$$ | X X X O . O X X X O O . . . . . . . . |
$$ | 2 X O O O O X O O O . . . . . . . . . |
$$ | X O O X X X O O . . . . . . . , . . . |
$$ | O O 1 X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


:b1: raises the temperature quite high, as it threatens to recolor many White intersections. :lol:

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


After :w1: the local temperature is 0, as either player can play at 2. What these two sequences show is that we can regard the local temperature as lying between 0 and -1, inclusive. At or below temperature zero, either player can make a play, but neither player has to make a play.

For scoring purposes what we want is a position unambiguously with temperature -1. Such as the following position.

Click Here To Show Diagram Code
[go]$$Wc Temperature -1
$$ ---------------------------------------
$$ | . X . X O O X . X . O . . . . . . . . |
$$ | X X X O . O X X X O O . . . . . . . . |
$$ | O X O O O O X O O O . . . . . . . . . |
$$ | . O O X X X O O . . . . . . . , . . . |
$$ | O O X X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Assuming that White wishes to show that Black is dead, we presumably will reach this position via the White first diagram above. ;) By human rules White may have to reopen play in order to do so.

Now, in this position neither player will claim to be komaster for either of the double kos.

Click Here To Show Diagram Code
[go]$$Wc White claims to be komaster for ko :bc:
$$ ---------------------------------------
$$ | . X 1 B O O X . X . O . . . . . . . . |
$$ | X X X O 4 O X X X O O . . . . . . . . |
$$ | O X O O O O X O O O . . . . . . . . . |
$$ | 2 O O X X X O O . . . . . . . , . . . |
$$ | O O X X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

:w3: at :bc:

After :b2: White is forced to resolve the ko by filling at :bc:, losing a large group. OC, it does no good for Black to claim komaster status, either.

So in the encore White will recolor the Black points on the right before tackling the very corner. :) In fact, White could start off that way, as in the following diagram.

Click Here To Show Diagram Code
[go]$$Wc Variation
$$ ---------------------------------------
$$ | . X . X O O X 3 X 1 O . . . . . . . . |
$$ | X X X O . O X X X O O . . . . . . . . |
$$ | . X O O O O X O O O . . . . . . . . . |
$$ | B O O X X X O O . . . . . . . , . . . |
$$ | O O 2 X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Now let White claim komaster status for the :bc: ko. Black could do so, as well, and fill the ko safely — for the moment, anyway. But why bother? ;)

Click Here To Show Diagram Code
[go]$$Wcm5 Variation, continued
$$ ---------------------------------------
$$ | 7 X 5 X O O . O . O O . . . . . . . . |
$$ | X X X O . O . . . O O . . . . . . . . |
$$ | 1 X O O O O . O O O . . . . . . . . . |
$$ | B O O X X X O O . . . . . . . , . . . |
$$ | O O X X . . . . . . . . . . . . . . . |
$$ | X X X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

:w7: at :bc:

As komaster White takes the ko and, without objection, resolves it by filling it. Then White claims komaster status for the remaining corner ko and takes and resolves it. OC, Black could claim komaster status for the last ko, as well, but to no avail. She would just have to fill it and let White capture. :)

_________________
The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Komaster concept for hypothetical play
Post #5 Posted: Thu Nov 28, 2019 12:49 pm 
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Approach ko

This is Diagram 10 from the Nihon Kiin commentary on the J89 rules.

Click Here To Show Diagram Code
[go]$$W Approach ko
$$ +--------------
$$ | X O . . X O .
$$ | . X X X X O .
$$ | X X O O O O .
$$ | O O O . . . .
$$ | . . . . . . .[/go]


First, let Black claim komaster rights.

Click Here To Show Diagram Code
[go]$$B Black komaster
$$ +--------------
$$ | X W 1 . X O .
$$ | . X X X X O .
$$ | X X O O O O .
$$ | O O O . . . .
$$ | . . . . . . .[/go]


:b1: resolves the ko by capturing the :wc: stone.

Now let White claim komaster rights.

Click Here To Show Diagram Code
[go]$$W White komaster
$$ +--------------
$$ | B O 4 . X O .
$$ | 1 X X X X O .
$$ | X X O O O O .
$$ | O O O . . . .
$$ | . . . . . . .[/go]

:w3: at :bc:

Without objection, White resolves the ko by filling it. It does White no good to be komaster of this ko.

----

Note: For evaluation of the ko during regular play, Berlekamp allows White to utilize komaster rights in this manner.

Click Here To Show Diagram Code
[go]$$W White komaster of both kos
$$ +--------------
$$ | B O 3 5 X O .
$$ | 1 X X X X O .
$$ | X X O O O O .
$$ | O O O . . . .
$$ | . . . . . . .[/go]


For evaluation purposes we may consider that White is not only the komaster of the initial approach ko, but of the direct ko formed by :w3:. In such a case the temperature is plainly greater than 0, not to mention -1. If White had the ko threats to be komaster of both kos, she should have fought the ko during regular play.

_________________
The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Komaster concept for hypothetical play
Post #6 Posted: Sun Dec 01, 2019 12:57 pm 
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Bent Four in the Corner

Click Here To Show Diagram Code
[go]$$B Bent four in the corner
$$ +--------------
$$ | X X X . O X .
$$ | . O O O O X .
$$ | O O X X X X .
$$ | X X X . . . .
$$ | . . . . . . .[/go]


OC, if White approaches the three Black stones, Black can capture the White group. Black doesn't even need to capture, as Black can kill White if White captures the Black stones. If Black plays first:

Click Here To Show Diagram Code
[go]$$B Bent four in the corner
$$ +--------------
$$ | X X X 2 O X .
$$ | 1 O O O O X .
$$ | O O X X X X .
$$ | X X X . . . .
$$ | . . . . . . .[/go]


:b1: makes the bent four shape, then :w2: captures the four Black stones.

Click Here To Show Diagram Code
[go]$$B Bent four, continued
$$ +--------------
$$ | 4 3 7 O O X .
$$ | 5 O O O O X .
$$ | O O X X X X .
$$ | X X X . . . .
$$ | . . . . . . .[/go]


:b3: threatens to play at 4, which would obviously kill without ko. :w4: throws in to make ko.

When a ko arises in the encore, the player who takes the ko is its komaster. Without objection, :b7: wins the ko.

With this approach there is no pass for ko rule. The koloser cannot prevent the komaster from resolving the ko.

_________________
The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Komaster concept for hypothetical play
Post #7 Posted: Sun Dec 01, 2019 1:48 pm 
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Three Points without Capturing

Click Here To Show Diagram Code
[go]$$ 3 points without capturing
$$ +----------
$$ | . X X O .
$$ | O X X O .
$$ | X O O O .
$$ | X X X . .
$$ | . . . . .[/go]


We assume that the outside stones are alive, and that all of the corner stones might score nothing. It behooves White to try to make points by capturing the four stones.

Click Here To Show Diagram Code
[go]$$W 3 points without capturing
$$ +----------
$$ | 1 X X O .
$$ | O X X O .
$$ | X O O O .
$$ | X X X . .
$$ | . . . . .[/go]


Click Here To Show Diagram Code
[go]$$W 3 points, II
$$ +----------
$$ | O 3 4 O .
$$ | O 2 . O .
$$ | X O O O .
$$ | X X X . .
$$ | . . . . .[/go]


:w3: is a sacrifice tesuji.

Click Here To Show Diagram Code
[go]$$W 3 points, III
$$ +----------
$$ | 8 7 B O .
$$ | 6 X 5 O .
$$ | X O O O .
$$ | X X X . .
$$ | . . . . .[/go]

:w9: fills at :bc:

White has captured 5 Black stones and lost 3 White stones, for 2 points, net. If White is allowed to make this play in the encore at temperature -1, he will get one point for the extra stone, for a net local score of 3 points for White. As advertised.

Click Here To Show Diagram Code
[go]$$W Variation, :b6: makes ko
$$ +----------
$$ | 6 7 B O .
$$ | 9 X 5 O .
$$ | X O O O .
$$ | X X X . .
$$ | . . . . .[/go]


Black can make a ko with :b6:, but White takes it and is komaster. Without objection, White captures the corner with :w9:. This, OC, would be very good for White.

Click Here To Show Diagram Code
[go]$$W Variation II, :b8: connects
$$ +----------
$$ | X O 9 O .
$$ | 8 X O O .
$$ | X O O O .
$$ | X X X . .
$$ | . . . . .[/go]


After :b8: connects and White, as komaster, is required to fill the ko with :w9:. The result is the same as in the main line.

Any conditions on plays made by the koloser need to be clarified, because the koloser should ideally not be allowed to make and carry out an arbitrary ko threat. Here, :b8: could be considered as a ko threat. In this case, :b8: may be justified as saving the stones that were threatened by White's capture of the ko. The same justification may be made for replying to taking one of the kos in a double ko seki.

_________________
The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller


Last edited by Bill Spight on Tue Dec 03, 2019 6:53 am, edited 2 times in total.
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 Post subject: Re: Komaster concept for hypothetical play
Post #8 Posted: Sun Dec 01, 2019 2:31 pm 
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Triple ko with eye

This is Life and Death example 8 in the Official Commentary of the J89 rules. Black is dead.

Click Here To Show Diagram Code
[go]$$B Triple ko with eye
$$ | . . . . . .
$$ | O O . . . .
$$ | X O . . . .
$$ | a X O O O .
$$ | X X X X O .
$$ | O X . X O .
$$ | . O X O X .
$$ | O O O O X .
$$ | . O X X X .
$$ | O O X . . .
$$ | X X X . . .
$$ | . . . . . .[/go]


As we know from previous examples of double kos, neither play can afford to claim komaster status for either of the double kos. And Black cannot afford to claim komaster status for the ko at a.

Click Here To Show Diagram Code
[go]$$B Black komaster
$$ | . . . . . .
$$ | O O . . . .
$$ | X O . . . .
$$ | 1 X O O O .
$$ | X X X X O .
$$ | O X 2 X O .
$$ | . O X O X .
$$ | O O O O X .
$$ | . O X X X .
$$ | O O X . . .
$$ | X X X . . .
$$ | . . . . . .[/go]


If Black is komaster for that ko she is required to fill at :b1: immediately, and then White can capture all the Black stones.

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

:w3: fills at :bc:

If White, as komaster, is required to resolve the ko immediately, then we could get this result.

We could allow :w4: to reply to :b3:, since doing so will not allow Black to take the ko back at :bc:.

Click Here To Show Diagram Code
[go]$$W White komaster, variation
$$ | . . . . . .
$$ | O O . . . .
$$ | B O . . . .
$$ | 1 X O O O .
$$ | X X X X O .
$$ | W X 3 X O .
$$ | 2 O X O X .
$$ | O O O O X .
$$ | , O X X X .
$$ | O O X . . .
$$ | X X X . . .
$$ | . . . . . .[/go]

:w5: at :wc:

:w3: replies to :b2:. Then, without objection, :w5: wins the ko by capturing all the Black stones.

IIUC, lightvector's possible objection is that Black may be able to keep White, as komaster, from winning the ko indefinitely, perhaps interminably, by making ko threats.

I was going to suggest a different way to handle this, but I can see possible problems with it, so I'll pass for now.

_________________
The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Komaster concept for hypothetical play
Post #9 Posted: Mon Dec 02, 2019 3:57 am 
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Moonshine Life

Diagram from Sensei's Library (https://senseis.xmp.net/?MoonshineLife )

Click Here To Show Diagram Code
[go]$$B Moonshine Life
$$ ---------------------------------------
$$ | O 1 W X . . . . . . . . . O X 2 X O . |
$$ | . O X X . . . . . . . . . O X X O O O |
$$ | O O X . . . . . . . . . . O X . X O 3 |
$$ | X X X , . . . . . , . . . O X X X X O |
$$ | . . . . . . . . . . . . . O O O O X X |
$$ | . . . . . . . . . . . . . . . . O O O |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

:w4: at :wc:

The argument that the White group in the top left corner is alive is that, because White has an infinite supply of sufficiently large ko threats in the double ko seki on the right, Black can never capture the White group on the left, and it is therefore alive. Opinions have differed about Moonshine Life over the centuries. Modern professional rules deem it to be dead.

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


White as komaster cannot live. When White fills the ko at :w1:, :b2: captures the whole group

Click Here To Show Diagram Code
[go]$$B Black komaster
$$ ---------------------------------------
$$ | O 1 O X . . . . . . . . . O X . X O . |
$$ | 3 O X X . . . . . . . . . O X X O O O |
$$ | O O X . . . . . . . . . . O X . X O . |
$$ | X X X , . . . . . , . . . O X X X X O |
$$ | . . . . . . . . . . . . . O O O O X X |
$$ | . . . . . . . . . . . . . . . . O O O |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]


As komaster Black takes and wins the ko, capturing the White group.

Click Here To Show Diagram Code
[go]$$B Black komaster, White takes double ko
$$ ---------------------------------------
$$ | O 1 O X . . . . . . . . . O X 2 X O . |
$$ | 3 O X X . . . . . . . . . O X X O O O |
$$ | O O X . . . . . . . . . . O X 4 X O . |
$$ | X X X , . . . . . , . . . O X X X X O |
$$ | . . . . . . . . . . . . . O O O O X X |
$$ | . . . . . . . . . . . . . . . . O O O |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]


In this variation White takes and wins the double ko. However, doing so does not allow White to capture the Black group in the top left corner, so Black's claim of komaster status is valid.

That means that Black can be komaster of the ko in the top left, while White cannot, so those stones are dead.

----

The procedure of letting the komaster make two moves in a row to resolve the ko, and only allowing the koloser to reply to prevent the komaster from doing so safely avoids having to answer arbitrary ko threats. Let's revisit a couple of ko positions to illustrate that.

Double Ko Seki

Click Here To Show Diagram Code
[go]$$B Double ko seki
$$ --------------
$$ . O X . X O . |
$$ . O X X O O O |
$$ . O X . X O . |
$$ . O X X X X O |
$$ . O O O O X X |
$$ . . . . O O O |
$$ . . . . . . . |[/go]


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


Black's claim to komaster status is originally supported when she resolves the ko with :b1: and :b3:. Now White gets the chance to refute Black's claim.

Click Here To Show Diagram Code
[go]$$B Black komaster, II
$$ --------------
$$ . O X 2 X O . |
$$ . O X X O O O |
$$ . O X 4 X O 1 |
$$ . O X X X X W |
$$ . O O O O X X |
$$ . . . . O O O |
$$ . . . . . . . |[/go]

:b3: at :wc:

Now White is allowed to reply with :w2:. As komaster Black is forced to resolve the ko by filling it. :w4: captures the Black group, thus refuting Black's claim.

Neither player can successfully claim komaster status for the double ko seki, so it remains on the board with the kos unresolved.

Now let's take another look at the triple ko with eye position.

Click Here To Show Diagram Code
[go]$$W White komaster
$$ | . . . . . .
$$ | O O . . . .
$$ | B O . . . .
$$ | 1 X O O O .
$$ | X X X X O .
$$ | O X . X O .
$$ | . O X O X .
$$ | O O O O X .
$$ | . O X X X .
$$ | O O X . . .
$$ | X X X . . .
$$ | . . . . . .[/go]

:w3: at :bc:

:w1: takes the ko and :w3: resolves it by filling it.

Black has no reply that makes the capture and fill unsafe, so White's claim of komaster status is sustained. Obviously, Black cannot sustain a claim of komaster status. What remains is a double ko death, so all of the Black stones in the original position are dead.

_________________
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"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
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 Post subject: Re: Komaster concept for hypothetical play
Post #10 Posted: Tue Dec 03, 2019 2:43 am 
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Molasses ko

Diagram from Sensei's Library at https://senseis.xmp.net/?MolassesKo

Click Here To Show Diagram Code
[go]$$ Molasses ko
$$ | . . . . . . . . . .
$$ | . . . X X X O O O .
$$ | . . . X O O X X O .
$$ | . . . X O . O X O .
$$ | . . X X O . O X O .
$$ | . . X O O O X X O .
$$ | . . X O O X . X O .
$$ | . . X O X a X X O .
$$ ----------------------[/go]


Molasses ko is very rare and unusual, only once known to have occurred in actual play. See the Sensei's Library page for a discussion of it.

If this position remains on the board at the end of play, it is plain that Black will not claim komaster status for the ko at a, as if she fills there White will capture all the Black stones.

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

:w3: at :bc:

Given two moves in a row White as komaster can take and win the ko, leaving the Black group dead. Now let's give Black the right to reply.

Click Here To Show Diagram Code
[go]$$W White komaster, II
$$ | . . . . . . . . . .
$$ | . . . X X X O O O .
$$ | . . . X O O X X O .
$$ | . . . X O 2 O X O .
$$ | . . X X O . O X O .
$$ | . . X O O O X X O .
$$ | . . X O O X 3 X O .
$$ | . . X O X 1 X X O .
$$ ----------------------[/go]


But :b2: does not prevent White from winning the ko. So White's claim to be komaster of the ko at :w1: is sustained. White can take the ko and capture the Black stones.

We have not considered repetitions arising from taking two stones intead of just one. But what happens if we consider being komaster for the two stone capture? Obviously White cannot be komaster of it. What about Black?

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

With two moves in a row Black can win the "ko". Now we let White reply to prevent being captured.

Click Here To Show Diagram Code
[go]$$B Black komaster, II
$$ | . . . . . . . . . .
$$ | . . . X X X O O O .
$$ | . . . X O O X X O .
$$ | . . . X O 1 O X O .
$$ | . . X X O 3 O X O .
$$ | . . X O O O X X O .
$$ | . . X O O X 4 X O .
$$ | . . X O X 2 X X O .
$$ ----------------------[/go]


This is the usual play in the molasses ko. But now as komaster Black must make another play in the ko

Click Here To Show Diagram Code
[go]$$B Black komaster, II, continued
$$ | . . . . . . . . . .
$$ | . . . X X X O O O .
$$ | . . . X O O X X O .
$$ | . . . X O X 5 X O .
$$ | . . X X O X 6 X O .
$$ | . . X O O O X X O .
$$ | . . X O O . O X O .
$$ | . . X O . O X X O .
$$ ----------------------[/go]


But if Black does so White captures the Black stones. So Black's claim to be komaster is not sustained. At the end of play in the original position Black is dead.

_________________
The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Komaster concept for hypothetical play
Post #11 Posted: Tue Dec 03, 2019 6:23 am 
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Round Robin Ko

Click Here To Show Diagram Code
[go]$$B Round Robin Ko
$$ ---------------
$$ . X O . O X O .
$$ . X O O X X O .
$$ . X O . O X O .
$$ . X O . O X O .
$$ . X O O X X O .
$$ . X O X . X O .
$$ . X O X . X O .
$$ . X O O X X O .
$$ . X X X O O O .
$$ . . . . . . . .[/go]


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


:b2: is the only play to save Black from being captured immediately. However, :w3: kills, anyway.

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

:b5: at :wc:, :w6: captures

If Black is komaster for the :wc: "ko", :w2: and :w4: protect the White stones. Then Black has to fill at :wc: or next to it, and White captures the Black group. Black's claim is not sustained.

Click Here To Show Diagram Code
[go]$$B Black komaster, II
$$ ---------------
$$ . X O 1 W X O .
$$ . X O O X X O .
$$ . X O 5 O X O .
$$ . X O . O X O .
$$ . X O O X X O .
$$ . X O X 4 X O .
$$ . X O X 6 X O .
$$ . X O O X X O .
$$ . X X X O O O .
$$ . . . . . . . .[/go]

:b3: at :wc:

If Black claims komaster status for the ko at :wc:, then White allows :b3: to fill the ko, and captures Black with :w4: and :w6:.

If the original position is left on the board at the end, Black is dead.

_________________
The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Komaster concept for hypothetical play
Post #12 Posted: Tue Dec 03, 2019 8:14 am 
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Ten Thousand Year Ko

Click Here To Show Diagram Code
[go]$$W Ten Thousand Year Ko
$$ ----------------
$$ | . W X . O X . .
$$ | O X X . O X . .
$$ | O O O O O X . .
$$ | X X X X X X . .
$$ | . . . . . . . .
$$ | . . . . . . . .[/go]


At the end of play, if White claims komaster status, then White will have to fill the ko, and will die.

Click Here To Show Diagram Code
[go]$$B Black komaster
$$ ----------------
$$ | 1 W X . O X . .
$$ | O X X . O X . .
$$ | O O O O O X . .
$$ | X X X X X X . .
$$ | . . . . . . . .
$$ | . . . . . . . .[/go]

:b3: at :wc:

As komaster Black can take and fill the ko. leaving a seki. Since the result is seki, by the Japanese rule against scoring points in seki Black does not get to keep :wc: as a prisoner nor to get compensation for her two moves, :b1: and :b3:. If possible, then, Black should at least take the ko before the end of play to score the :wc: stone.

----

Note: I did not come up with the idea of komaster at temperature -1 to craft a new set of Japanese rules. I was looking for a theoretical way to evaluate kos and superkos at temperature -1. However, this use of komaster can give rise to a new Japanese style rule set. It has, it seems to me, to have a couple of advantages.

1) It does away with the pass for ko rule. There are no ko threats at all, not even a pass, since the koloser is not allowed to take the ko back. The komaster is not required to resolve a ko to prevent the opponent from taking it back, she has to resolve it anyway, sometimes to his detriment.

2) It does away with questions of locality, at least for kos. The komaster must immediately resolve the ko if she took it. That's as local as it gets.

3) It reveals positions where the temperature is greater than -1, when both players can sustain the claim of komaster for the same ko. Such positions should be played out before scoring.

4) It reveals sekis where neither player can sustain the claim of komaster for the kos involved. Note that this restores the idea of seki as a kind of standoff, not as a condition of "stones which are alive but possess dame", whatever it means to possess dame.

5) It is consistent with a hypothetical encore to determine the score at temperature -1, rather than to determine the life and death status of stones. OC, determining the score normally does determine life and death status, but it can do more.

Note that hypothetical play at temperature -1 yields the traditional result for Three Points without Capturing. That position is a kind of standoff, but should not be considered seki. It should be the play at temperature -1 that determines life and death status, not the other way around.

BTW, this approach can be used with other territory scoring rules, such as those that allow scoring points in seki, or those that have a group tax, or those that do not allow a player to become komaster for a ko if she made the next to last pass after her opponent took that ko.

_________________
The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Komaster concept for hypothetical play
Post #13 Posted: Tue Dec 03, 2019 9:19 am 
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Ko that arises in the encore

Click Here To Show Diagram Code
[go]$$B White can die
$$ ---------------------------
$$ . X O . O . O . X . . X O .
$$ . X O O O O X X X X X X O .
$$ . X X X X X O O O O O O O .
$$ . . . , . . . . . , . . . .[/go]


This is example 14 in the official commentary on the J89 rules. To me it is an example of the folly of determining the status of life and death before determining best play at temperature -1. Anyway, White is dead for the following reason. The example does not give the hypothetical play, but it could go this way.

Click Here To Show Diagram Code
[go]$$B White dies
$$ ---------------------------
$$ . X O 5 O 3 O 1 X 2 . X O .
$$ . X O O O O X X X X X X O .
$$ . X X X X X O O O O O O O .
$$ . . . , . . . . . , . . . .[/go]

:w4: passes for the ko

:b1: makes an approach ko. :w2: makes it a direct ko. After :w4: passes as a ko threat, :b5: wins the ko.

The problem, as I see it, is this.

Click Here To Show Diagram Code
[go]$$W Seki
$$ ---------------------------
$$ . X O . O . O . X 1 . X O .
$$ . X O O O O X X X X X X O .
$$ . X X X X X O O O O O O O .
$$ . . . , . . . . . , . . . .[/go]


White to play can play :w1:, preventing Black from making the ko. The commentary points this play out. But the J89 rules do not allow White to play it at temperature -1. White needs to play :w1: before the end of play. It can be played in hypothetical play, but only to show that the Black stones are alive.

What it really shows is that the local temperature is greater than -1. It is actually quite high, so this is not a scorable position.

Let's make it scorable. :)

Click Here To Show Diagram Code
[go]$$B White dies
$$ -------------------------------
$$ . X O . O . O 3 X O W O 1 X O .
$$ . X O O O O X X X X X X X X O .
$$ . X X X X X O O O O O O O O O .
$$ . . . , . . . . . , . . . . . .[/go]

:w2: at :wc:

:b3: makes a ko. Now, before I said that when a ko arises in the encore, the player who takes it is komaster. A clearer way to say it, perhaps, is that the player whose turn it is is komaster, if that claim is sustainable. Here White's claim is not sustainable, because filling the ko does not save the White stones. So Black gets to make a komaster claim.

Click Here To Show Diagram Code
[go]$$B White dies, continued
$$ -------------------------------
$$ . X O 7 O 5 O X X 4 O . X X O .
$$ . X O O O O X X X X X X X X O .
$$ . X X X X X O O O O O O O O O .
$$ . . . , . . . . . , . . . . . .[/go]


Black's claim is sustainable, as :b5: and :b7: win the ko.

Edit: Actually, :w4: changes the nature of the ko, doesn't it? Each player's claim would now succeed. But it is Black's turn, and her claim succeeds, so we do not let White make a claim.

_________________
The Adkins Principle:

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— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Komaster concept for hypothetical play
Post #14 Posted: Tue Dec 03, 2019 3:45 pm 
Lives in gote

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Bill Spight wrote:
4) It reveals sekis where neither player can sustain the claim of komaster for the kos involved. Note that this restores the idea of seki as a kind of standoff, not as a condition of "stones which are alive but possess dame"


For the formalization of Japanese rules that I came up with, my original idea for what determines that a group is not in seki is that it can be made to be pass-alive (not that it must be made so, but that if necessary, it could).

I think that idea is very easy to understand even for casual go players, who have not studied thermography or ko evaluation or any other such thing. It's pretty much what you often see taught to beginners verbally in practice. If it can independently live (i.e. get two eyes i.e. if necessary, reach a position where it is completely invulnerable to any opponent moves) then it's not seki, but if it's not practically killable yet without being able to reach such a state, then it's seki.

And for computers, what simpler way to prove that an area could be made pass-alive than to just actually make it pass-alive during the cleanup phase?

For me, I was focused on computer play and in particular, rules that would not require introducing new protocols or kinds of moves or actions - where the set of legal actions always corresponds to some subset of locations on the board or "pass", and everything the players do is to alternate turns and do things encodable in that space. Just having the players play out of self-interest to pass-alive-ify things during cleanup so that they would count for score easily satisfied this. And sekis would be precisely whatever groups that the players failed to make pass-alive during cleanup despite having every incentive to do so if they could.

So for a while, this was my implementation, and it worked quite well!

The reason I ultimately rejected it in favor of the Japanese-style formulation of "dame" was to reduce computation costs - making everything pass-alive is quite a lot of additional cleanup moves in a game, whereas filling the dame is barely any additional moves beyond what you would make anyways. So it was a practical choice, but I definitely still think "can be made (pass-)alive" is truer to the spirit of when something isn't or is a seki.


This post by lightvector was liked by: Bill Spight
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 Post subject: Re: Komaster concept for hypothetical play
Post #15 Posted: Tue Dec 03, 2019 4:30 pm 
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Thanks, lightvector. Interesting. :)

As you may have noticed one thing that bugs me about the Japanese rules examples is how many they determine life and death for when the play should not be over. Like the last example. Black to play should make the approach ko, White to play should make seki. This position should not even remain on the board at the end of play. That's one reason I go on about temperature -1. If the game is really over, a play should cost one point (at least) by territory scoring. Plain and simple.

And if there are playable dame, that is not the case. So fill all the dame you can. :)

_________________
The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Komaster concept for hypothetical play
Post #16 Posted: Wed Dec 04, 2019 2:15 pm 
Lives with ko

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Click Here To Show Diagram Code
[go]$$W
$$ -------------------------------
$$ . X O . O a O 1 X O W O b X O .
$$ . X O O O O X X X X X X X X O .
$$ . X X X X X O O O O O O O O O .
$$ . . . , . . . . . , . . . . . .[/go]


If white claims komaster and plays at :w1: is black allowed to capture at a or does he need to play at b?

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 Post subject: Re: Komaster concept for hypothetical play
Post #17 Posted: Wed Dec 04, 2019 2:25 pm 
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Matti wrote:
Click Here To Show Diagram Code
[go]$$W
$$ -------------------------------
$$ . X O . O a O 1 X O W O b X O .
$$ . X O O O O X X X X X X X X O .
$$ . X X X X X O O O O O O O O O .
$$ . . . , . . . . . , . . . . . .[/go]


If white claims komaster and plays at :w1: is black allowed to capture at a or does he need to play at b?


:w1: does not take or fill the ko. If White claims komaster status for a, White must fill it. Then Black can capture White, so White's claim fails.

Edit: Actually, the ko does not exist yet, so neither player can claim komaster status now.

_________________
The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Komaster concept for hypothetical play
Post #18 Posted: Thu Dec 05, 2019 11:35 am 
Lives with ko

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It's not clear to me what are the exact consequences of a "komaster claim" regarding move legality.
(mandatory moves? immediate ko resolution? is it enough to resolve the ko some time after taking it?)

Click Here To Show Diagram Code
[go]$$B double ko elsewhere
$$ -----------------------------
$$ | O . X O . O . O . O X . O |
$$ | O . X X O O O O O X X . O |
$$ | O O O X X X O X X X O O O |
$$ -----------------------------[/go]

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 Post subject: Re: Komaster concept for hypothetical play
Post #19 Posted: Thu Dec 05, 2019 12:29 pm 
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moha wrote:
It's not clear to me what are the exact consequences of a "komaster claim" regarding move legality.
(mandatory moves? immediate ko resolution? is it enough to resolve the ko some time after taking it?)

Click Here To Show Diagram Code
[go]$$B double ko elsewhere
$$ -----------------------------
$$ | O . X O . O . O . O X . O |
$$ | O . X X O O O O O X X . O |
$$ | O O O X X X O X X X O O O |
$$ -----------------------------[/go]


Assuming this is the whole board. White as komaster must fill the ko, then Black will take the other ko and capture White. Black as komaster must take and then fill the ko. Since White cannot atari Black, White is a goner.

_________________
The Adkins Principle:

At some point, doesn't thinking have to go on?

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Komaster concept for hypothetical play
Post #20 Posted: Thu Dec 05, 2019 12:37 pm 
Lives with ko

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Bill Spight wrote:
Black as komaster must take and then fill the ko.
But he cannot fill immediately (if W resists). Is it enough if he fills a few moves later? Or B gets two moves in a row? What are the exact conditions?

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