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 Post subject: Re: Komaster concept for hypothetical play
Post #21 Posted: Fri Dec 06, 2019 12:45 am 
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moha wrote:
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?


Ah, OK. Nice point. :)

Let me refer you to post #8 https://lifein19x19.com/viewtopic.php?p=251206#p251206 on the "triple ko with eye". Per my original idea, it is fine for the komaster to answer a finite number of ko threats before resolving the ko, because the koloser cannot take the ko back, anyway. lightvector rightly points out that, for purposes of programming, that is inefficient.

My attempt at answering the programming problem is to allow the komaster to ignore an arbitrary ko threat, one which does not prohibit resolving the ko. But she can still answer a ko threat that does so, as in this case. :)

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


Per Berlekamp's original formulation, Black gets two moves in a row and wins the ko. White is dead.

Click Here To Show Diagram Code
[go]$$B White plays ko threat
$$ -----------------------------
$$ | O . X O . O . O 1 3 X 4 O |
$$ | O . X X O O O O O X X 2 O |
$$ | O O O X X X O X X X O O O |
$$ -----------------------------[/go]


:w2: is allowed. It prevents Black from winning the ko, since Black is captured if she does.

Click Here To Show Diagram Code
[go]$$B Black answers the threat
$$ -----------------------------
$$ | O . X O . O . O 1 5 X 3 O |
$$ | O . X X O O O O O X X 2 O |
$$ | O O O X X X O X X X O O O |
$$ -----------------------------[/go]


:b3: is allowed, because :w2: is not an arbitrary threat. Then :b5: cannot be prevented.

One more variation, to be clear.

Click Here To Show Diagram Code
[go]$$B double ko elsewhere
$$ -----------------------------
$$ | O . X O . O . O 1 3 X . O |
$$ | O 2 X X O O O O O X X . O |
$$ | O O O X X X O X X X O O O |
$$ -----------------------------[/go]


:w2: threatens to save White. However, :b3: stops play because Black has successfully resolved the ko, thus verifying her komaster claim. For subsequent play, which is necessary to show that White dies, we cancel :w2: and revert to the original diagram. I think that this answers the inefficiency objection. :)

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Last edited by Bill Spight on Sat Dec 07, 2019 7:08 am, edited 1 time in total.
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 Post subject: Re: Komaster concept for hypothetical play
Post #22 Posted: Fri Dec 06, 2019 10:47 pm 
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Ok, so resolving the ko can wait. But I still don't see all conditions of this approach - have you written them somewhere?

For example, the last diagram of the post you refer to ("white komaster, variation") seems unclear. If W only aim to resolve the ko, the previous diagram seems better for him. If not, I don't see how he could capture (or achieve anything) in the last diagram if B insist on the cycle. What rules are in place there?

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 Post subject: Re: Komaster concept for hypothetical play
Post #23 Posted: Sat Dec 07, 2019 12:33 am 
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moha wrote:
Ok, so resolving the ko can wait. But I still don't see all conditions of this approach - have you written them somewhere?


This is an idea I have had in the back of my mind for some time, but I had not written anything down yet. I decided to bring it up in response to lightvector's topic about his version of the Japanese rules. It is based upon Berlekamp's original komaster rule, where the komaster gets two moves in a row (unless only one is needed to win the ko). I have adapted it for play at temperature -1 and for multiple kos, and I allow each player to attempt to claim komaster status.

Originally I allowed the koloser to make a ko threat that the komaster might answer, because the koloser cannot take the ko back, anyway. She may capture the komaster's stones, however, which would invalidate the komaster's claim.

There are four possible outcomes. 1) Only Black can successfully claim komaster status, and gets to win the ko. 2) Only White can do so. 3) Neither player can do so, in which case the ko remains unfilled, normally as seki. Sometimes during the play at temperature -1 conditiions will change and one player or other will be able to make a successful claim. 4) Both players can do so, in which case the ko position is not scorable. The rules will have to deal with that problem. The anti-seki of the J89 rules is not allowed at the end of play, for example.

Also, for kos that arise during the play at temperature -1, such as in Bent Four, if the player whose turn it is can successfully claim komaster status, then the other player cannot attempt to do so. And I suppose that there can be only one komaster claim at a time.

Quote:
For example, the last diagram of the post you refer to ("white komaster, variation") seems unclear. If W only aim to resolve the ko, the previous diagram seems better for him. If not, I don't see how he could capture (or achieve anything) in the last diagram if B insist on the cycle. What rules are in place there?


Since White is claiming komaster status for the top ko, Black cannot take it back. And by ordinary ko rules Black cannot take the double ko back, either. That allows White's komaster claim to succeed. Then there is still the double ko to resolve, but it is fairly obvious that Black is dead.

Here is the diagram again.

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:

After :w3: Black has no local play. White can then win the ko by capturing the Black stones, assuring life. If Black plays elsewhere White ignores the play, since he can make a successful claim. Presumably White could make a successful claim by filling the ko with :w3:, but this way there is no question.

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 Post subject: Re: Komaster concept for hypothetical play
Post #24 Posted: Sat Dec 07, 2019 2:47 am 
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Bill Spight wrote:
Since White is claiming komaster status for the top ko, Black cannot take it back.

Ok, this is what I missed earlier.

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

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 Post subject: Re: Komaster concept for hypothetical play
Post #25 Posted: Sat Dec 07, 2019 5:12 am 
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moha wrote:
Bill Spight wrote:
Since White is claiming komaster status for the top ko, Black cannot take it back.

Ok, this is what I missed earlier.

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


Initially, neither player can claim komaster status of either ko on the right. For example,

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


:w2: is allowed as a response to :b1:. Then :b3: must resolve the ko, and :w4: captures. I guess your point is that, since Black can reply to :w2: instead of filling, that would lift the ban on taking :w2: back, and Black can capture White in the corner.

Click Here To Show Diagram Code
[go]$$B Black komaster?
$$ -----------------------------
$$ | O O O O O O O O X X X X 2 |
$$ | X O X O . O . O O O X O B |
$$ | . X 4 X O X O X O X X O O |
$$ | X X X X X X X X O X 7 O 1 |
$$ | . . X . . X . 3 O X X X . |
$$ -----------------------------[/go]

:b5: at :bc:

Keeping all ko bans in effect, which is what the J89 rules do, until the komaster resolves the ko, if she can, is possible, but smacks of ad hockery. What is consistent is to allow the komaster to delay resolving the ko if that is necessary to allow her to do so safely. But we still want the ko ban against taking :w2: to remain in effect during the process. So I guess we should keep all ko bans in effect, to keep other ko fights from interfering with the process.

So in this case:

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

:w3: at :bc:

We do not allow White to do anything but fill the ko. As this is hypothetical play, we will roll back :b4: unless it allows Black to capture :w1:, thus denying White's komaster claim. If it does so, then we will allow :w3: to reply at a, which does save :w1:.

Let me continue in the next post.

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 Post subject: Re: Komaster concept for hypothetical play
Post #26 Posted: Sat Dec 07, 2019 6:01 am 
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The komaster claim for a ko is that the komaster can win that ko by resolving it safely, taking it first if necessary. The komaster may make two moves in a row if the second move resolves the ko. Otherwise, all plays are made in alternation. Other plays are allowed only in order to refute or defend the komaster claim. In particular, the koloser may make a play just before the komaster wins the ko in order to refute the claim. All ko bans remain in effect during the hypothetical play.

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


:w2: captures :b1:, so Black's claim fails. Maybe Black can succeed if she becomes komaster for the :wc: ko.

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


:b1: and :b3: safely win the ko. But White has a reply to prevent the capture with :b3:.

Click Here To Show Diagram Code
[go]$$B White refutes Black's claim
$$ | . . . . . .
$$ | O O . . . .
$$ | X O . . . .
$$ | 4 X O O O .
$$ | X X X X O .
$$ | W X 2 X O .
$$ | 1 O X O X .
$$ | O O O O X .
$$ | , O X X X .
$$ | O O X . . .
$$ | X X X . . .
$$ | . . . . . .[/go]

:b3: at :wc:

:w2: is allowed in order to refute Black's claim. :b3: fills the ko, but not safely, as :w4: captures :b1:.

Now let's look at a White komaster claim in this position.

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

:w5: at :wc:

This variation telescopes the process. :w1: takes the ko. :b2: is allowed to prevent the capture with :w3:. :w3: is allowed because filling the ko at :bc: is unsafe, and :w3: defends the komaster claim by making it safe to win the ko. Finally, :w5: wins the ko.

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Everything with love. Stay safe.


Last edited by Bill Spight on Sat Dec 07, 2019 6:15 am, edited 2 times in total.
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 Post subject: Re: Komaster concept for hypothetical play
Post #27 Posted: Sat Dec 07, 2019 6:12 am 
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Approach ko, revisited

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


Obviously, :b1: can safely win the ko. What about White?

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

:w3: at :bc:

White takes the ko and resolves it with :w3:, but not safely, as :b4: captures :w1:.

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


This sequence is not allowed, because :w3: does not resolve the ko. The second play in a row must resolve the ko. (At higher temperatures before the end of play it might be allowed, however.)

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At some point, doesn't thinking have to go on?
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 Post subject: Re: Komaster concept for hypothetical play
Post #28 Posted: Sat Dec 07, 2019 6:26 am 
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moha's example 1, revisited

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


:b1: and :b3: win the ko. White is dead.

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


:w2: is allowed to refute Black claim.

Click Here To Show Diagram Code
[go]$$B Black komaster success
$$ -----------------------------
$$ | O . X O . O . O 1 5 X 3 O |
$$ | O . X X O O O O O X X 2 O |
$$ | O O O X X X O X X X O O O |
$$ -----------------------------[/go]


:b3: is allowed to make it safe to resolve the ko. :b5: wins the ko. White is dead.

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 Post subject: Re: Komaster concept for hypothetical play
Post #29 Posted: Sat Dec 07, 2019 6:28 am 
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Bill Spight wrote:
I guess your point is that, since Black can reply to :w2: instead of filling, that would lift the ban on taking :w2: back, and Black can capture White in the corner.

In that last example I wondered about the komaster status of left kos (cannot W claim, fill and avoid capture?). I'm still not sure if I understand everything about this approach yet.

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 Post subject: Re: Komaster concept for hypothetical play
Post #30 Posted: Sat Dec 07, 2019 6:30 am 
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To be deleted. :)

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Everything with love. Stay safe.


Last edited by Bill Spight on Sat Dec 07, 2019 7:19 am, edited 1 time in total.
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 Post subject: Re: Komaster concept for hypothetical play
Post #31 Posted: Sat Dec 07, 2019 6:35 am 
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moha wrote:
Bill Spight wrote:
I guess your point is that, since Black can reply to :w2: instead of filling, that would lift the ban on taking :w2: back, and Black can capture White in the corner.

In that last example I wondered about the komaster status of left kos (cannot W claim, fill and avoid capture?). I'm still not sure if I understand everything about this approach yet.


Me, either. ;) As I said, it is something that has been in the back of my mind for a while. It is based upon the idea that to evaluate a ko you should resolve it. The play must be hypotethical because you want the komaster to lose in some cases at temperature -1. And you want to let each player have a try at being komaster.

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 Post subject: Re: Komaster concept for hypothetical play
Post #32 Posted: Sat Dec 07, 2019 7:02 am 
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moha's example 2, revisited

First, let Black make repeated komaster claims.

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


Since Black has two eyes, :b1: is safe. So we let Black fill it and continue.

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


Ditto.

Click Here To Show Diagram Code
[go]$$B Black komaster success
$$ -----------------------------
$$ | O O O O O O O O X X X X . |
$$ | X O X O 3 O 5 O O O X O X |
$$ | X X X X O X O X O X X O O |
$$ | X X X X X X X X O X . O . |
$$ | . . X . . X . 1 O X X X O |
$$ -----------------------------[/go]


Black approaches with :b1: before making a komaster claim, which succeeds. White is dead

Now let White make komaster claims.

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


Black lets White's claim succeed, since she can roll White up later, anyway.

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


:w1 : fills the ko, but :b2: captures the :w1:.

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

:w3: at :bc:

Again, Black lets White's claim succeed, because she can capture White later.

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

:w3: at :bc:

Again, a telescoping variation. :w1: threatens to capture the Black stones, so :b2: is allowed to prevent that. :w3: cannot then safely resolve the ko.

Black could allow White to win another ko on the left, but then White has nothing left, and dies.

Many thanks, moha, for your excellent examples. :)

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 Post subject: Re: Komaster concept for hypothetical play
Post #33 Posted: Sat Dec 07, 2019 7:12 am 
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Bill Spight wrote:
Me, either. ;) As I said, it is something that has been in the back of my mind for a while. It is based upon the idea that to evaluate a ko you should resolve it.
The way I understood so far, is to introduce a new kind of hypothetical play beside/before the normal hypothetical sequences for string L/D, to decide which ko moves are allowed later in those. But this would seem useful if the rules during komaster validation could be kept close to normal rules - to avoid becoming redundant (with altered rules one could also aim direct L/D).

Quote:
Black lets White's claim succeed, since she can roll White up later, anyway.
What are the exact consequences of a successful claim?

BTW I think the last example would be clearer with more kos to make W filling on the left safer:
Click Here To Show Diagram Code
[go]$$B
$$ -------------------------------------
$$ | O O O O O O O O O O O O X X X X . |
$$ | X O X O X O . O . O . O O O X O X |
$$ | . X . X . X O X O X O X O X X O O |
$$ | X X X X X X X X X X X X O X . O . |
$$ | . . . X . . . X . . . . O X X X O |
$$ -------------------------------------[/go]

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 Post subject: Re: Komaster concept for hypothetical play
Post #34 Posted: Sat Dec 07, 2019 8:06 am 
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moha wrote:
Bill Spight wrote:
Me, either. ;) As I said, it is something that has been in the back of my mind for a while. It is based upon the idea that to evaluate a ko you should resolve it.
The way I understood so far, is to introduce a new kind of hypothetical play beside/before the normal hypothetical sequences for string L/D, to decide which ko moves are allowed later in those. But this would seem useful if the rules during komaster validation could be kept close to normal rules - to avoid becoming redundant (with altered rules one could also aim direct L/D).


It is only kos and superkos that cause evaluation problems for territory rules in general. For modern Japanese and Korean rules you have to account for not having a group tax and for not counting points in seki, as well. But it is kos that cause the real problems. My 1998 paper showed how to evaluate kos and superkos, except that it relied upon the rules to evaluate them at temperature -1. The lack of a theoretical way to evaluate them at temperature -1 has bugged me ever since. ;) Some while ago I realized that I could use a modification of Berlekamp's komaster idea to prove that double ko seki is seki. We already knew that the original komaster concept did not apply to double ko seki, but the modified komaster concept meant that neither player would want to be komaster, just as in a seki neither player wants to put the other in atari.

As for later play, once a ko has been evaluated, it can be settled at temperature -1, and then ignored in further hypothetical play. Double ko seki cannot be resolved, but taking one of the kos can be prohibited. :)

If the board really has temperature -1, then it should not matter which player plays first, so we cannot just have an encore with only one player to play, we have to allow both players a shot. Letting each play play first eliminates a number of problematic positions from consideration, because they are actually too hot to score. Play has ended too soon. The J89 anti-seki is a good example. Instead of torturing the rules with a strange definition of seki, just admit than play has ended incorrectly.

Quote:
Quote:
Black lets White's claim succeed, since she can roll White up later, anyway.
What are the exact consequences of a successful claim?

BTW I think the last example would be clearer with more kos to make W filling on the left safer:
Click Here To Show Diagram Code
[go]$$B
$$ -------------------------------------
$$ | O O O O O O O O O O O O X X X X . |
$$ | X O X O X O . O . O . O O O X O X |
$$ | . X . X . X O X O X O X O X X O O |
$$ | X X X X X X X X X X X X O X . O . |
$$ | . . . X . . . X . . . . O X X X O |
$$ -------------------------------------[/go]


I'll deal with it next. :)

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 Post subject: Re: Komaster concept for hypothetical play
Post #35 Posted: Sat Dec 07, 2019 8:48 am 
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moha's example 3, modified

Click Here To Show Diagram Code
[go]$$W White komaster success
$$ -------------------------------------
$$ | O O O O O O O O O O O O O O X X X X . |
$$ | X O X O X O X O 1 O . O . O O O X O X |
$$ | 2 X 4 X 5 X 3 X O X O X O X O X X O O |
$$ | X X X X X X X X X X X X X X O X . O . |
$$ | . . . X . . . X . . . . . . O X X X O |
$$ -------------------------------------[/go]


White plays :w1: as komaster for that ko. Then if Black attempts to capture :w1:, :w3: and :w5: give White two liberties because the ko bans cannot be broken. This defense works for a while.

Click Here To Show Diagram Code
[go]$$W White komaster success
$$ -------------------------------------
$$ | O O O O O O O O O O O O O O X X X X . |
$$ | X O X O X O X O W O 1 O . O O O X O X |
$$ | 2 X 4 X 5 X 3 X O X O X O X O X X O O |
$$ | X X X X X X X X X X X X X X O X . O . |
$$ | . . . X . . . X . . . . . . O X X X O |
$$ -------------------------------------[/go]


Since White won his komaster claim, he fills the ko. Now he makes another komaster claim, which succeeds.

Click Here To Show Diagram Code
[go]$$W White komaster fail
$$ -------------------------------------
$$ | O O O O O O O O O O O O O O X X X X . |
$$ | X O X O X O B O O O O O a O O O X O X |
$$ | 2 X 4 X 5 X 1 X O X O X O X O X X O O |
$$ | X X X X X X X X X X X X X X O X . O . |
$$ | . . . X . . . X . . . . . 6 O X X X O |
$$ -------------------------------------[/go]

:w3: at :bc:

Now, obviously White cannot safely resolve the ko at a. So let him take and resolve a different ko. He can take another ko with :w5:, but he cannot get another ko ban, and Black can capture the large group, including :w1:. So White's komaster claim fails.

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


Because Black has two eyes, Black can win each ko on the left and finally capture the large White group, leaving White dead on the right. Black can also do so in the original position, so White is dead from the start.

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 Post subject: Re: Komaster concept for hypothetical play
Post #36 Posted: Sat Dec 07, 2019 9:23 am 
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Bill Spight wrote:
Then if Black attempts to capture :w1:, :w3: and :w5: give White two liberties because the ko bans cannot be broken.
My first idea as W would be to verify komaster for any of the left kos by filling it, then (whatever B does) proceed to have 3 open kos, after which the group (and the filled ko) is safe because of the double ko on the right (unless there are altered rules about ko bans - are there?)

Quote:
Since White won his komaster claim, he fills the ko. Now he makes another komaster claim, which succeeds.
Does he need another claim? And are claims verified together - your diagrams seems to show this - or individually?

What are the consequences of a successful claim? And what if W has an eye instead of the shared lib at bottom?

IIRC you mentioned that cases where both can verify as komaster for a ko are not scorable (and W would be happy if that would mean B must add stones before stop).

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 Post subject: Re: Komaster concept for hypothetical play
Post #37 Posted: Sat Dec 07, 2019 9:29 am 
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Matti's seki

In this position, being discussed by Matti and lightvector in another thread, neither player can sustain a komaster claim, so it is seki.

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


Obviously, Black cannot safely fill either of the kos, so let him make a komaster claim for the :wc: ko. :b1: and :b3: win that ko safely, so far so good. Now we let White defend against :b3:.

Click Here To Show Diagram Code
[go]$$Bc Black komaster fail
$$ ----------------------
$$ | X X X X X X X O . . .
$$ | X W X 4 X 2 X O O . .
$$ | 6 1 O X O X O X O . .
$$ | 3 O O O O O O X O . .
$$ | O O X X X X X X . . .
$$ | X X X . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

:b5: at :wc:

After :w2: Black cannot fill the ko safely, so she is allowed to take again with :b3:. As this threatens to take the White stones, White is allowed to take the other ko with :w4:. Now Black cannot fill at :wc: safely, or at :w6:, either. So Black's komaste claim fails.

Now for White's komaster claim.

Click Here To Show Diagram Code
[go]$$Wc White komaster claim fail
$$ ----------------------
$$ | X X X X X X X O . . .
$$ | X O X 3 X 1 X O O . .
$$ | O 2 O X O B O X O . .
$$ | 4 O O O O O O X O . .
$$ | O O X X X X X X . . .
$$ | X X X . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

:w5: at :bc:, :b6: captures

This diagram telescopes the process. Obviously, White cannot fill at :b2: safely, so White makes a komaster claim for one of the other kos. Again, for safety Black is allowed to capture at :b2:. And for safety White cannot fill at :bc: and is allowed to capture the other ko with :w3:. Again, Black is allowed to capture with :b4:. Now WHite has no safe play. After :w6: resolves the ko Black captures the White group.

Since neither player can sustain a komaster claim, the original position is seki.

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 Post subject: Re: Komaster concept for hypothetical play
Post #38 Posted: Sat Dec 07, 2019 10:15 am 
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moha wrote:
Bill Spight wrote:
Then if Black attempts to capture :w1:, :w3: and :w5: give White two liberties because the ko bans cannot be broken.
My first idea as W would be to verify komaster for any of the left kos by filling it, then (whatever B does) proceed to have 3 open kos, after which the group (and the filled ko) is safe because of the double ko on the right (unless there are altered rules about ko bans - are there?)


Your second example showed me that we need to follow the Japanese lead and forbid breaking any ko ban. The double ko cannot provide any ko threat.

Quote:
Quote:
Since White won his komaster claim, he fills the ko. Now he makes another komaster claim, which succeeds.
Does he need another claim? And are claims verified together - your diagrams seems to show this - or individually?


Komaster claims for multiple kos are made one at a time. They are not verified together. If one claim is sustained, that ko is won before making the next claim. It seems like good practice to let a player continue making claims as long as they are verified, although the order should not matter unless the position is not scorable, in which case it may.

Quote:
What are the consequences of a successful claim?

The komaster wins the ko. As your second and third examples illustrate, that may not mean that the komaster's stones are ultimately alive.

Quote:
And what if W has an eye instead of the shared lib at bottom?

Well, one eye is not enough for independent life, right? :)

Quote:
IIRC you mentioned that cases where both can verify as komaster for a ko are not scorable (and W would be happy if that would mean B must add stones before stop).


Yes, but I was wrong, because winning a ko does not guarantee life. Only if both sides survive and both win the same ko can the two results have a different score. But never say never in go. It may be that you can have a case where each player can become komaster and win the same ko and the resulting score is still the same. In that case the position is scorable. :)

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 Post subject: Re: Komaster concept for hypothetical play
Post #39 Posted: Sat Dec 07, 2019 10:38 pm 
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Bill Spight wrote:
Your second example showed me that we need to follow the Japanese lead and forbid breaking any ko ban. The double ko cannot provide any ko threat.
Ok, this changes everything.

However, as I wrote this feels like losing part of the potential advantages of the approach. It would be most attractive if having verified as "komaster" would be the very condition of altered ko rules in later hypothetical play. Having both special ko rules AND komaster concept seems a bit redundant in practice (however significant it may be theoretically).

BTW, I think the ruling of these connected moonshine positions is not completely clear, in particular, Japanese and Korean may differ here.

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 Post subject: Re: Komaster concept for hypothetical play
Post #40 Posted: Sun Dec 08, 2019 1:36 am 
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moha wrote:
Bill Spight wrote:
Your second example showed me that we need to follow the Japanese lead and forbid breaking any ko ban. The double ko cannot provide any ko threat.
Ok, this changes everything.

However, as I wrote this feels like losing part of the potential advantages of the approach. It would be most attractive if having verified as "komaster" would be the very condition of altered ko rules in later hypothetical play. Having both special ko rules AND komaster concept seems a bit redundant in practice (however significant it may be theoretically).


The idea of komaster is to abstract away the ko threat situation. If you apply it to multiple kos at the same time, the komaster is too strong, unrealistically so. That would allow the komaster to win a double ko seki, for instance. So if you are applying the komaster concept to one of the kos in a double ko, you have to let the koloser take the other ko and ban the komaster from taking it back. And that ban must last, or else if other plays are made, the komaster could lift that ko ban and win the double ko. So we need to have unbreakable ko bans to make the komaster concept work without being too strong, and it is simplest, and, I think, fairest, to apply it to both players.

Quote:
BTW, I think the ruling of these connected moonshine positions is not completely clear, in particular, Japanese and Korean may differ here.


Can you say more about that? I saw an English translation online of the Korean rules of several years ago, which I could not understand. The Korean rules have changed since then, but in working on applying the komaster concept, what I recalled of those rules started to make sense. :)

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