Komaster concept for hypothetical play

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Matti
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Re: Komaster concept for hypothetical play

Post by Matti »

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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Re: Komaster concept for hypothetical play

Post by Bill Spight »

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.
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Re: Komaster concept for hypothetical play

Post by moha »

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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Re: Komaster concept for hypothetical play

Post by Bill Spight »

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.
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Re: Komaster concept for hypothetical play

Post by moha »

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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Re: Komaster concept for hypothetical play

Post by Bill Spight »

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 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. :)
Last edited by Bill Spight on Sat Dec 07, 2019 7:08 am, edited 1 time in total.
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Re: Komaster concept for hypothetical play

Post by moha »

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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Re: Komaster concept for hypothetical play

Post by Bill Spight »

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.
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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Re: Komaster concept for hypothetical play

Post by moha »

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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Re: Komaster concept for hypothetical play

Post by Bill Spight »

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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Re: Komaster concept for hypothetical play

Post by Bill Spight »

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.
Last edited by Bill Spight on Sat Dec 07, 2019 6:15 am, edited 2 times in total.
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Re: Komaster concept for hypothetical play

Post by Bill Spight »

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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Re: Komaster concept for hypothetical play

Post by Bill Spight »

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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Re: Komaster concept for hypothetical play

Post by moha »

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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Re: Komaster concept for hypothetical play

Post by Bill Spight »

To be deleted. :)
Last edited by Bill Spight on Sat Dec 07, 2019 7:19 am, edited 1 time in total.
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