Life In 19x19

moha wrote:

Bill Spight wrote:I guess your point is that, since Black can reply to instead of filling, that would lift the ban on taking 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.

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, 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 before making a komaster claim, which succeeds. White is dead

Now let White make komaster claims.

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[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 captures the .

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]

at

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]

at

Again, a telescoping variation. threatens to capture the Black stones, so is allowed to prevent that. 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.

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).

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]

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.

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:

$$B
$$ -------------------------------------
$$ | O O O O O O O O O O O O X X X X . |
$$ | 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 . |
$$ | . . . X . . . X . . . . O X X X O |
$$ -------------------------------------

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.

moha's example 3, modified

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[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 as komaster for that ko. Then if Black attempts to capture , and 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]

at

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 , but he cannot get another ko ban, and Black can capture the large group, including . 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.

Bill Spight wrote:Then if Black attempts to capture , and 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?)

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).

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 ko. and win that ko safely, so far so good. Now we let White defend against .

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]

at

After Black cannot fill the ko safely, so she is allowed to take again with . As this threatens to take the White stones, White is allowed to take the other ko with . Now Black cannot fill at safely, or at , 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]

at , captures

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

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

moha wrote:

Bill Spight wrote:Then if Black attempts to capture , and 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.

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.

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.

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

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

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.

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.

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.

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.

Bill Spight wrote:

moha wrote: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.

I'm pretty sure I have seen less than you about them, but from the bits of information here and there my vague understanding was that they follow different principles: Korean is about spatial localization (a la Pauli), Japanese is more about ko behaviour. For example, see dia 19 from the version linked on this forum. That may not be about L/D, but the idea of a draw because B repeating would not make sense if he could kill in analysis.

moha wrote: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.

That depends on the exact interpretation of komaster. In a double ko seki, neither player can or intend to win/resolve a ko (with normal play, regardless of threats), so would you really call either komaster?

Although not the same concept, in similar positions there is often a difference: only one side can potentially win a ko, the other only tries to avoid losing it (and/or "only one side can repeat"). I think this behavioral approach is a bit more robust than its alternative.