Yes. An important point, thanks.



The text amends the AGA text to show how simple changes to the AGA rules would produce button go. The AGA superko rule, along with the two pass rule and preserving the ko ban with resumption, is vulnerable to one known case of the 1-eye flaw.

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

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On ending play without passes

Before recently games normally ended without passes. Japanese and Korean players agreed to end play, usually while there were still dame left, and then filled the dame informally and then scored the game. But how do you end a no pass game before the bitter end without resigning?

Click Here To Show Diagram Code

[go]$$ Capture game
$$ ----------
$$ | . O X X . |
$$ | . O O X . |
$$ | . O X X . |
$$ | . O O X . |
$$ | . O X X . |
$$ -----------[/go]

We have seen that this is a place where the players could agree to end play and score the game. That is because they have learned the concept of territory and realize that playing inside territory loses at least 1 point. They have learned how to count territory and agree that each player has 3 points of territory, so the overall score is 0. The player with the move loses. This is a natural place to end play and score.

Now let's back the game up one move.

Click Here To Show Diagram Code

[go]$$ Capture game
$$ ----------
$$ | . O X X . |
$$ | . O O X . |
$$ | . O a X . |
$$ | . O O X . |
$$ | . O X X . |
$$ -----------[/go]

Now there is a neutral point at a. Neither player wants to play inside territory, and will play at a instead. We have seen the position after Black plays there. What about the position after White plays?

Click Here To Show Diagram Code

[go]$$ Capture game
$$ ----------
$$ | . O X X . |
$$ | . O O X . |
$$ | . O O X . |
$$ | . O O X . |
$$ | . O X X . |
$$ -----------[/go]

Obviously, this position also has a score of 0. The score is the same, but there is a big difference. It is Black's turn and she loses the game. In the other diagram where Black took the neutral point it is White's turn and he loses the game.

Click Here To Show Diagram Code

[go]$$ Capture game
$$ ----------
$$ | . O X X . |
$$ | . O O X . |
$$ | . O . X . |
$$ | . O O X . |
$$ | . O X X . |
$$ -----------[/go]

So this position with a neutral point, despite the fact that we can predict a score of 0, no matter who plays first, is not a natural place for the players to stop play and score the game. In the no pass capture game the player with the move has a move that does not lose any points and should simply play it. Then let the opponent suggest ending play.

Edit: Suppose, however, that the players can pass without cost. Then the player to move could pass without changing the score. However, that pass would not be necessary. The question of whether a pass is necessary may arise, for instance, if unnecessary passes are not allowed. No pass baduk supplies the answer.

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

Visualize whirled peas.

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Here is my conjecture how "no territory in seki" rule naturally(?) emerged a few hundred years ago. What would a hypothetical rule theoretician with decent strength and experience in territory scoring feel about seki? (Assuming one knows nothing about area scoring, which is probably a wrong assumption.)



First, one sees shapes like upper left corner and upper side. It looks natural(!) to say that A, B, and C are not territory while D and E are territory. Well, it does not really make a difference here, but for the shape at the upper right corner, Black can gain two points (H and I), and it looks like a fair ending, until now.

Then, one meets the shape at the right side. Is J a territory? The rule theoretician starts to feel uncomfortable. To the person, J really looks like a false eye, but the person also realizes that there is no way White can force Black to play at J, unlike most other false eyes. J is a point Black can freely fill in at any time one wants. Well... that sounds like a real territory! Some may give up territory in seki now, or some may proceed, reluctantly accepting J as a territory. (It is weird to say that D cannot be played by White but people are much more generous to D than J just because it looks prettier as an eye.)

Now let's check the shape at the left side. Any play of White will kill one's whole group, but Black can freely play at R and Q. Are they Black territory? Now we are crossing the boarder between the territory and area scoring rules, and this claim is likely to be rejected on the ground that Q and R are not surrounded by Black stones. OK, it still sounds fair.

The final challenge is at the lower left corner. Is K and L White territory? Both look like false eyes, but White can freely fill in K or L any time one wants. Accepting the logic developed for J, they will be White's territory. But wait, White can fill in any of them, but White shouldn't fill in both. Does it mean White has only one point here or is it still two points? If we recall two-eyed life with, let's say, 15 points. We can only fill in 13 of them. So "impossibility of filling" is not a definite evidence that something cannot be a territory unless we are reviving the group tax rule.

All I want to say here is that some territory in seki may have made the ancient rule theoretician feel uncomfortable, and one may have ended up declaring that "No territory is recognized in seki". How about Haneseki shape? There are many stones under atari situation, but none can really be captured. How many points are there for each player? How about double ko seki? How many points does each player have? One wants to scream "None!" to stop all the debates.

Having said all of these, I am not a fan of that conclusion. I think there is no logical problem in saying that D, E, H, I, J, K and L are territory. (Though not R and Q, unless you want to initiate an area scoring revolution.) For the shape at the lower right corner, give Black 6 points and White one point. The current Korean/Japanese rule says playing M is an important Go skill(!), but I bet the ancient rule theoretician might have felt that it is also a weird conclusion against one's own intuition.

[Edited] In order to reject territory in seki, a fair amount of the rule text must be spent to distinguish "perfect(?) life" and "life due to seki", and we know it initiates so many problems. Well, its elimination does not clear all the problems of the current territory scoring rules, but it certainly helps a lot.

_________________
Jaeup Kim
Professor in Physics, Ulsan National Institute of Science and Technology, Korea
Author of the Book "Understanding the Rules of Baduk", available at https://home.unist.ac.kr/professor/jukim/bbs/board.php?bo_table=notice&wr_id=5

I think that it is quite likely that modern territory baduk evolved from territory baduk with the group tax. We already know that by the time of the most ancient surviving scored game records, the rationale for the group tax had largely disappeared, because they stopped play with neutral points still on the board. Beginners who asked why there is a group tax could be told, because you don't count the points of territory needed for life. The implication, OC, is that you count the number of points of territory that you can play on without dying, plus dead stones. But by that time nobody did that to score the game. Instead, you counted the obvious points of territory and subtracted two. The group tax was ready to be eliminated as an unnecessary complication.

As you point out, the rationale for scoring seki by the number of points you can play on without dying, plus dead stones, is even more complicated and non-intuitive. Take the seki in the top right corner. Having been taught that there are no points there, because you don't count the points needed for life, when you drop the group tax as an unnecessary complication, giving Black two points of territory introduces a new complication. Easier just to say, as you always had, that Black has no territory there. Giving up the group tax simplifies the concept of territory. Now territory is not based upon play, but on life and death and surrounding points. What about the false eye at J on the right side. If we are not going to count the points in the real eyes in that seki, why count points in the false eyes? Unnecessary complications! Just say no points in seki.

Edit: This new concept of territory as empty points surrounded by independently living stones explains why the rules theorists of the 20th century focused on questions of life and death instead of scoring per se. For instance, if a game ends because one player has taken a simple ko and the opponent cannot make a play without filling territory, why count the open point in the ko as territory? It's a false eye, and the stone in the ko mouth is not independently alive, even if we grant that it cannot be captured. Go Seigen and Shusai may have disagreed, but they, despite their eminence, were in the minority.

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

Visualize whirled peas.

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Thank you, very interesting. That territory in seki is (more?) often formed by false eyes and weak shapes sounds like a convincing argument how the idea emerged historically - but this is still less than a real theoretical necessity like no suicide (and to today's ears remain an unnecessary rule complication).

Although this surely had no historical relevance, a similar logic manifests if one tries to define territory as areas that can be occupied by pass-alive formations. Something like this would give imperfect ruling in a few rare shapes, but as J89 and three points without capturing shows, such could still be accepted by the community (if the rule is simple and convincing enough - but then you are already in the "imperfect approximation" domain!). In any case the bigger problem is ko in hypothetical play.

What about dead stones?

A frequent question by beginners has to do with dead stones. It doesn't make sense to them that dead stones can be removed without capture, and they realize that filling territory to capture dead stones costs points. So why shouldn't that happen?

This is actually quite a good question. Notice that they are making the natural assumption that scoring should be settled by play, which is reasonable. They are also making the assumption that the person sacrificing the stone gets to pass (for free) while their opponent captures the dead stone. That is not an unreasonable assumption, but perhaps not quite as reasonable as the first assumption.

Our first surprise about no pass baduk is that the concept of territory naturally emerges from no pass baduk. Our second surprise is that so does the concept of dead stones. Now, different versions of no pass baduk have different concepts of territory and dead stones (when they have them; the no pass capture game does not). Let me illustrate with straight no pass baduk.

Click Here To Show Diagram Code

[go]$$Wcm16 No Pass Baduk
$$ ----------
$$ | . O X X . |
$$ | 4 O O X 2 |
$$ | 5 O X X 1 |
$$ | 6 O O X 3 |
$$ | . O X X . |
$$ -----------[/go]

We can count the score in this game. In regular baduk each player has 6 points, with 2 points of territory plus 2 dead stones worth 2 points each. But in no pass baduk White has 2 points in each eye, for 4 points of territory minus 2 points for the group tax, for a score of 2 points; Black has 1 point in one eye plus 2 points in the other, for 3 points of territory minus 2 points for the group tax, for a score of only 1 point. White is 1 point ahead, which means that White wins, even if White goes first.

Click Here To Show Diagram Code

[go]$$Wcm22 No pass baduk
$$ ----------
$$ | 1 O X X . |
$$ | X O O X X |
$$ | O O X X W |
$$ | X O O X O |
$$ | 5 O X X 2 |
$$ -----------[/go]

at captures

After the overall score is 0, and Black to play loses.

Note that dead stones in straight no pass baduk, unlike dead stones in regular baduk, do not have an independent value. An eye with one empty point and one dead stone is worth the same as an eye with one empty point and two dead stones. The concept of dead stones in no pass baduk cannot be separated from the concept of territory.

In regular baduk each dead stone is worth two points of territory. That being the case, we can count one point for the stone and one point for the point which it occupies. A dead stone is worth the same as a captured stone. We can regard the concept of territory separately from the concept of a dead or captured stone. That simplifies things.

To make his version of no pass baduk almost identical to regular baduk, Professor Berlekamp said that a move could be a board play, or it could be returning a captured stone (prisoner) to the opponent. OC, returning a prisoner to the opponent costs one point, and is therefore like passing and giving the opponent a pass stone, except that to return a prisoner you alread have to have captured one. If you eliminate the group tax, No Pass Baduk with Prisoner Return and without a Group Tax is a form of modern territory scoring. While not the same as Japanese or Korean rules, it can provide a model for handling the problems of modern territory scoring.

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

Visualize whirled peas.

Everything with love. Stay safe.

Basic seki and basic evaluation

Click Here To Show Diagram Code

[go]$$ Basic seki
$$ -------------
$$ . O X . O X .
$$ . O X . O X .
$$ . O X X O X .
$$ . O O O X X .
$$ . . . . . . .[/go]

This is a basic seki, a standoff between two eyeless groups with two shared neutral points between them. (We assume, per convention, that the outer stones are alive.) Neither player wants to put the opponent's stones in atari, because that would put their own stones in atari, and the opponent would capture them. Baduk players intuitively regard this seki as worth 0. We can show that for no pass baduk with prisoner return and without a group tax. (From now on I'll just call that prisoner return baduk. )

Click Here To Show Diagram Code

[go]$$ Black first
$$ -------------
$$ . O X 2 O X .
$$ . O X 1 O X .
$$ . O X X O X .
$$ . O O O X X .
$$ . . . . . . .[/go]

If Black plays , White takes with , for a score of -10. (I.e., 10 points for White. By convention we take Black's point of view.)

Click Here To Show Diagram Code

[go]$$W White first
$$ -------------
$$ . O X 2 O X .
$$ . O X 1 O X .
$$ . O X X O X .
$$ . O O O X X .
$$ . . . . . . .[/go]

If White plays , Black takes with , for a score of +8.

There is a basic principle of evaluation by play. If a player makes a play that gains a certain amount, and the opponent replies with a play that gains the same amount, the new position has the same value as the original position. In this case it is obvious that either White's reply gained more than Black's play, or Black's reply gained more than White's play, or both. The true value of the seki could lie anywhere between -10 and +8. You could argue that the true value of the seki is the average of -10 and +8, or -1. However, by the rules of no pass baduk the seki is worth 0, because whoever plays first loses. No pass baduk verifies the players' intuitions.

Now, there are other standoff positions in baduk where the score after the opponent's reply is worse for the player than the score if the opponent plays first and the player replies, but the position is not seki. In that case the score of the position in no pass baduk is the one closer to 0. Edit: That result may not be intuitively obvious.

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

Visualize whirled peas.

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Three points without capturing

I suppose that most readers are familiar with the three points without capturing position. How to evaluate it is not obvious, but the story is that Honinbo Shuwa ruled around 1850 that Black had three points without having to capture the four White stones. The reason that a ruling had to be made was that the position is, or appears to be, a standoff. Black to play can only guarantee one or two points, but if White plays first Black can get three points. This position even bumfuzzled Shimada, a rules theorist of the mid-20th century ( http://harryfearnley.com/go/shimada/chap6.html ). Under the J89 rules Black has to capture before the end of play. As was typically the case with such rulings, Shuwa did not explain his reasoning, but we can justify his ruling with prisoner return baduk.

Click Here To Show Diagram Code

[go]$$Bc Three points without capturing
$$ ----------
$$ | . B O O .
$$ | W W X O .
$$ | W W X O .
$$ | X X X . .
$$ | . . . . .[/go]

In all cases this corner is advantageous for Black, but it does not fit the concept of territory as empty points or dead stones surrounded by independently living stones. (It does fit the concept of territory that emerges from no pass baduk with prisoner return. But that is not the question. Evaluation is the question.)

Shuwa did not explain his thinking, but we can make some educated guesses. Further play leads to possible kos, but the long standing tradition of evaluating Bent Four in the Corner as dead, in both Chinese and Japanese texts, relies upon there being no (external) ko threats. So Shuwa probably made that assumption. In that case, if White plays first the result is 3 points for Black, while if Black plays first the result is 2 points for Black. That is why it is a standoff.

With prisoner return baduk we can check whether the corner is worth 3 points to Black. All we have to do is to give White 3 prisoners, with Black having none. Then if the corner is worth 3 points to Black the combination is worth 0, which means that the player to move loses. White to play yields 3 points to Black after an even number of moves, and with 3 prisoners White also has 3 points, so we have a 0 position with White to play. White first loses. Black to play from the original position gets 2 points after an odd number of plays, but White has 3 points, so Black loses. Whoever plays first loses, as advertised.

This way of scoring was not available to Shimada, or anyone else, before the 1970s, with the development of combinatorial game theory, a mathematical theory that was inspired by baduk. The J89 rules get the value of this position "wrong", by this theory. How did Shuwa get it right?

The Japanese 1949 rules have the Three Points without Capturing position as one of its special cases, along with two standoff positions that the rules evaluate as Five Points without Capturing. If White plays first that is the result for Black, but I doubt if that was Shuwa's reasoning. Surely Black is forced to play first. If neither player plays that indicates that the position is a seki, worth 0. Besides, prisoner return baduk supports the value of 5 points in only one of the cases.

Here is my guess about Shuwa's reasoning. Since the result after White plays first is better for Black than the result after Black plays first, we must be in a situation where plays are costly, as a rule. That being the case, when Black plays first and gets only 2 points she makes one more play than White does. And that indicates that the value of the corner for Black is greater than 2 points. Nobody had yet thought of fractional points as a possibility*, and the value had to lie between 2 and 3, so 3 points it is. (Besides we know that plays can lose one point.) The "mistake" of the J89 rules is to force Black to play first when plays in theory lose nothing. The theoretically correct result could be found by having White reply with a move that also loses 1 point. The J89 rules force Black to play too early because their hypothetical play focuses on life and death instead of evaluation.

*Bill Fraser discovered the first known position with a fractional territory value. I evaluated it.

Anyway, here is an sgf file that illustrates the evaluation by play of those positions.

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

Visualize whirled peas.

Everything with love. Stay safe.

Komaster

Around 1990 or perhaps earlier, Professor Berlekamp came up with the idea of komaster to provide a method for evaluating kos, including difficult to understand kos such as approach kos and 10,000 year kos. Here is a simple example of komaster, which, I think, sheds light on the rules.

Click Here To Show Diagram Code

[go]$$Bc Black komaster
$$ -----------------
$$ | O 9 O 1 O O . .
$$ | X X X W X O . .
$$ | O O X X X O O .
$$ | . O O X X 8 O .
$$ | 6 5 O X . X O .
$$ | . O X X X X O .
$$ | O O O X . X O .
$$ | . O X X X 3 O .
$$ | O O X O 2 O . O
$$ | X X X X X O O .
$$ | . . . . . . . .[/go]

, take ko

The rest of the board is settled, with no ko threats, but several dame.

Is there anything remarkable about this line of play? Let's compare it with another possibility.

Click Here To Show Diagram Code

[go]$$Bc Black komaster
$$ -----------------
$$ | O 3 O 1 O O . .
$$ | X X X W X O . .
$$ | O O X X X O O .
$$ | . O O X X 4 O .
$$ | . . O X . X O .
$$ | . O X X X X O .
$$ | O O O X . X O .
$$ | . O X X X 5 O .
$$ | O O X O 2 O . O
$$ | X X X X X O O .
$$ | . . . . . . . .[/go]

This line of play is simpler, as Black just goes ahead and wins the ko with . There is nothing particularly remarkable about either line of play. The final score is the same.

So what does this have to do with the rules? Well, let's look at an analogous position, where the plays gain one point less.

Click Here To Show Diagram Code

[go]$$Bc W4, B7 take ko
$$ ---------------------------------------
$$ | . . . . . . . . . . . X O O O O O . O |
$$ | X X X X X . 3 X X . X X O X O O O . O |
$$ | O O X O O X X O O X X O O X X O O O . |
$$ | O . O O O O O O O X X O O X X X X O O |
$$ | O O O X 2 X O O X X X X X . . . X X X |
$$ | X . O X X X O X X O X O . . . X O . . |
$$ | . O O X O X X O O O O X X X . . X X X |
$$ | . O X X O O O O . . O X O O X X O O X |
$$ | O O X . X O . . . X O O O X X O O O O |
$$ | O X X X X O . . X O O O O O X X O X . |
$$ | O O X . X O X . X O O X X X X O O 8 . |
$$ | X X . O X O . O O X X X O X X O O X . |
$$ | X X O . X O . O X X 9 O 1 O X X O . . |
$$ | O X X . X O X O O X X X O O O O O . . |
$$ | O O X X . X O O X X . X X X O X O O . |
$$ | O . O X X X X O O O X X O X O X X O O |
$$ | 5 O O O X X O O . O O O O X X . X X O |
$$ | X O O X X X X X O . O X X X . . X . X |
$$ | 6 . O O X . X O O . O O X . . . . X . |
$$ ---------------------------------------[/go]

Obviously, the result is the same as if just won the ko.

Some of you probably recognized this game. It was played between Go Seigen (White) and Iwamoto Kaoru in 1948. (See https://senseis.xmp.net/?RuleDisputesInvolvingGoSeigen ). This was the game that White won by "1 or 2 points". Despite the characterization, it probably was not an actual rules dispute. (See the discussion page on SL.) The question was whether Black needed to actually make a play to win the ko, since he had more ko threats than White. The game was played before the Nihon Kiin had written rules, so the players and referee were unsure. Afterwards, a "by-law" of the Nihon Kiin was discovered that said that Black did not have to make the extra play. The Japanese 1949 rules required Black to make the play to win the ko. Prisoner return baduk supports having Black make the play.

But that does not mean that prisoner return baduk supports the Nihon Kiin rule, either. Consider the following sequence.

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . X O O O O O . O |
$$ | X X X X X . . X X . X X O X O O O . O |
$$ | O O X O O X X O O X X O O X X O O O . |
$$ | O . O O O O O O O X X O O X X X X O O |
$$ | O O O X W X O O X X X X X . . . X X X |
$$ | X . O X X X O X X O X O . . . X O . . |
$$ | . O O X O X X O O O O X X X . . X X X |
$$ | . O X X O O O O . . O X O O X X O O X |
$$ | O O X . X O . . . X O O O X X O O O O |
$$ | O X X X X O . . X O O O O O X X O X . |
$$ | O O X . X O X . X O O X X X X O O 2 . |
$$ | X X . O X O . O O X X X O X X O O X . |
$$ | X X O . X O . O X X 3 O 1 O X X O . . |
$$ | O X X . X O X O O X X X O O O O O . . |
$$ | O O X X . X O O X X . X X X O X O O . |
$$ | O . O X X X X O O O X X O X O X X O O |
$$ | . O O O X X O O . O O O O X X . X X O |
$$ | X O O X X X X X O . O X X X . . X . X |
$$ | . . O O X . X O O . O O X . . . . X . |
$$ ---------------------------------------[/go]

Suppose that the last dame at is already filled when takes the ko. White cannot win the ko fight and so fills a point of territory with . Then wins the ko. The result is the same as if play stopped after and Black did not have to play . There is nothing remarkable about this line of play, either.

(Edited for clarity.)

Note that trying to have it one way because other way seems illogical or anomalous may be a mistake. Prisoner return baduk allows us to evaluate the position with natural, unremarkable play.

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

Visualize whirled peas.

Everything with love. Stay safe.

Double ko seki

Click Here To Show Diagram Code

[go]$$Bc Double ko seki
$$ --------------
$$ . O X . X O . |
$$ . 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]

Everybody knows that this is a double ko seki, and that its value is 0. But how to prove that? Can we evaluate this position with play?

Click Here To Show Diagram Code

[go]$$Bc Black first
$$ --------------
$$ . O X 2 X O . |
$$ . 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]

take one ko of the double ko, and takes the other. We are not exactly back to where we started, but with the other form of this double ko seki. How now?

Frustrating. We start with a position whose value we know, but we don't know how to evaluate, and end up in a similar position.

The thing is, the information we need to evaluate kos and superkos lies outside them. Just going around taking and retaking kos does not tell us what we need to know. The Go Seigen-Iwamoto ko is a good example. Leaving the ko unsettled left us in a position we could not evaluate. The answer for the double ko seki is to keep going.

Click Here To Show Diagram Code

[go]$$Bc Black first, continued
$$ --------------
$$ . O X W . O . |
$$ . O X X O O O |
$$ . O X 4 X O B |
$$ . O X X X X 3 |
$$ . O O O O X X |
$$ . . . . O O O |
$$ . . . . . . . |[/go]

After the local score is -28.

Click Here To Show Diagram Code

[go]$$Wc White first
$$ --------------
$$ . O X . X O 2 |
$$ . 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]

Since taking the ko is futile, White simply fills at and captures the White stones. Then the local score is +16.

This indicates that this double ko is a 0 game. Now, kos are not actually combinatorial games. The double ko being a 0 game does not mean that whoever plays first loses, it means that whoever exits the ko first loses.

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

Visualize whirled peas.

Everything with love. Stay safe.

Ko evaluation

Since kos are the main cause of rules confusion, it helps to know how to evaluate kos by play. The basic principle is the same as with evaluation of other games. If a player makes a play from a position that gains a certain amount and the opponent replies with a play that gains the same amount, the resulting value is the same as that of the original value.

Let's apply that principle to this simple ko.

Click Here To Show Diagram Code

[go]$$Bc Simple ko
$$ --------------
$$ . O X . X O . |
$$ . O X X O O O |
$$ . O X . X O O |
$$ . O X X X X O |
$$ . O O O O X X |
$$ . . . . O O O |
$$ . . . . . . . |[/go]

To evaluate the ko we have to exit the ko. Let Black play first.

Click Here To Show Diagram Code

[go]$$Bc Black first
$$ --------------
$$ . O X . X O 1 |
$$ . O X X O O O |
$$ . O X . X O O |
$$ . O X X X X O |
$$ . O O O O X X |
$$ . . . . O O O |
$$ . . . . . . . |[/go]

After the local score is +16.

Now let White exit the ko.

Click Here To Show Diagram Code

[go]$$Wc White first
$$ --------------
$$ . O X 1 X O . |
$$ . O X X O O O |
$$ . O X 3 X O O |
$$ . O X X X X O |
$$ . O O O O X X |
$$ . . . . O O O |
$$ . . . . . . . |[/go]

In two moves White captures the Black stones, for a local score of -25. On average each ko move gains (16 + 25)/3 = 13⅔ pts. And the mean territorial value of the ko position is 2⅓ pts.

Let's check our figures. From the original position Black can play to a score of +16, and then if White replies with a play that gains 13⅔ pts. we get a position with a value of 2⅓ pts. (OC, in real life White is unlikely to be able to reply with a play that gains exactly 13⅔ pts. This is an idealization. Now let White play first and let Black reply with a play that gains 13⅔ pts. Do that again and the ko position has a local score of -25. Add 27⅓ pts. for the two Black plays and the result is 2⅓ pts. As advertised.

These plays that the opponent plays are assumed to be the best plays elsewhere on the board, and if they exist, the players are indifferent between playing in the ko or playing somewhere else. When these plays gain less than 13⅔ pt., normally playing in the ko is best.

Suppose that these plays gain 10 pts. Let Black play first. She plays to a local score of 16, and then White returns to a value of 6 pts. In this exchange Black has gained 3⅔ pts. So far, so good.


Komaster, again

Now suppose that Black is komaster (as in the Go Seigen-Iwamoto game). If Black plays first she can win the ko and White returns to the value of 6 pts. Now let White play first.

Click Here To Show Diagram Code

[go]$$Wc White first
$$ --------------
$$ . O X 1 X O 6 |
$$ . O X X O O O |
$$ . O X . X O O |
$$ . O X X X X O |
$$ . O O O O X X |
$$ . . . . O O O |
$$ . . . . . . . |[/go]

= ko threat, = reply:, takes ko, elsewhere,

The result of this exchange is 16 - 10 = 6 pts. This is the result regardless of who plays first, and is therefore the value of the ko under these conditions. When Black is komaster and White's reply elsewhere gains 10 pts. the value of the ko is 6 pts. If White's reply gains 4 pts. the value of the ko is 12 pts. If White's reply gains 0 pts. (White fills a dame) the value of the ko is 16 pts. If White's reply loses 1 pt. (White fills in territory) the value of the ko is 17 pts. How the value of the ko changes with the value of plays elsewhere when one player is komaster explains the phenomenon observed with the Go Seigen-Iwamoto game.

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

Visualize whirled peas.

Everything with love. Stay safe.

Moonshine Life

We are not going to approach Moonshine Life with the question of whether it is alive or not, but what it's value is.

Click Here To Show Diagram Code

[go]$$Bc Ko
$$ ----------
$$ | O . O X .
$$ | . O X X .
$$ | O O X . .
$$ | X X X , .
$$ | . . . . .[/go]

This is not Moonshine Life, but is a ko position that could be part of a Moonshine Life. OC, by itself this ko is dead, but let's evaluate it, anyway.

Click Here To Show Diagram Code

[go]$$Wc White first
$$ ----------
$$ | O 1 O X .
$$ | . O X X .
$$ | O O X . .
$$ | X X X , .
$$ | . . . . .[/go]

White exits the ko for a local score of +13.

Click Here To Show Diagram Code

[go]$$Bc Black first
$$ ----------
$$ | O 1 O X .
$$ | 3 O X X .
$$ | O O X . .
$$ | X X X , .
$$ | . . . . .[/go]

Black takes and exits the ko for a local score of +10.

Each play in the ko gains on average (10 - 13)/3 = -1 pt. The original ko position is worth 12 pts. OC, this is what we would expect from a dead ko.

Now let's see a Moonshine Life position. The following diagram comes from https://senseis.xmp.net/?MoonshineLife . You may recognize the double ko seki in the top right corner. The two ko positions are not independent; we cannot simply evaluate each one separately and add them together.

Click Here To Show Diagram Code

[go]$$Bc Moonshine Life
$$ ---------------------------------------
$$ | O . O X . . . . . . . . . O X . X O . |
$$ | . 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]

At the end of the game Black claims that the White stones in the top left corner are dead. (The surrounding Black stones are assumed to be alive, per convention. For convenience we assume that the empty points in between are settled with no dame.) White denies the claim and says, Kill them. That leads to the following exchange.

Click Here To Show Diagram Code

[go]$$Bc Moonshine Life
$$ ---------------------------------------
$$ | O 1 O X . . . . . . . . . O X 2 X O . |
$$ | . 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]

takes the ko back. Plainly White is komaster of the ko, and we are left with an unfinished ko position and possible confusion. (Moonshine Life has been regarded differently at different times in baduk history.) To evaluate the ko we continue play. plays elsewhere inside territory, losing 1 pt. exits the ko by filling at 1. The top left corner is indisputably dead, with a local score of +13. Subtract 1 pt. for and the value of the Moonshine Life is +12. That's the same as if the stones in the top left corner were dead, so we might as well treat them as such.

----

Well, I have written quite a lot, eh? But I think this gives a good idea of the approach of prisoner return baduk and evaluation by play to the problems and puzzles of the rules.

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

Visualize whirled peas.

Everything with love. Stay safe.

Hi Bill,
I've had a look at area button go. I've tried to see what would be the outcome of normal even games.

I've found that for games ending normally with Black or White making the last board move, and also for games ending with Black or White filling a ko playing twice in a row (the opponent then takes the button), the result of area button go was the same as territory scoring with 6.5 points komi.

Is it correct so far ?

Right. One effect of the button is that it normally does not matter who takes the last dame, as normally the next play is to take the button. In general, territory go before the button, area go afterwards.

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

Visualize whirled peas.

Everything with love. Stay safe.

I think the answer is No. Isn't Pio2001 asking the situation that a player is holding a half-point ko while filling in all the shared liberties?

If one successfully forces the opponent to make a pass before one connects the last ko, it does make a difference from the traditional(Korean/Japanese) territory scoring, even under the button go rule. (The last two passes cancel each other, and the pass stone for the first pass makes the difference.)

I agree that for most situations, the traditional territory scoring is reproduced.

_________________
Jaeup Kim
Professor in Physics, Ulsan National Institute of Science and Technology, Korea
Author of the Book "Understanding the Rules of Baduk", available at https://home.unist.ac.kr/professor/jukim/bbs/board.php?bo_table=notice&wr_id=5

Well, he said, "ending with Black or White filling a ko playing twice in a row (the opponent then takes the button" To me that means that the button is taken after the ko is filled (won). I don't know what he means by playing twice in a row, though. OC, he can explain what he meant.

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

Visualize whirled peas.

Everything with love. Stay safe.

Here are 4 standard situations, with the score in territory counting (komi 6.5), area counting (komi 7.5) and button go counting (komi 7) :
-Black and White alternate plays on the board and Black plays the last move on the board
-Black and White alternate plays on the board and White plays the last move on the board
-Black plays the two last moves on the board
-White plays the two last moves on the board



In the two cases with perfect alternation, the button go gives the same score as territory counting with komi 6.5.
In the case White plays last, the winner may depend on the style (area vs territory), because the komi is different.
In the two cases with the same player making the two last moves on the board, the score is different between button go (komi 7) and territory scoring (komi 6.5), but the winner is the same thanks to the parity.

It follows that if there is an odd number of neutral intersections in seki (parity is reversed) and if the same player plays the two last moves on the board, the winner may be different under territory scoring with komi 6.5 and button go with komi 7.

I have added the results for territory button go. They are the same as area button go.



So, if I summarize button go :

It is an area + button rule set
The best strategy is most of the times to play as if the score was japanese territory without button (common exceptions : if the last two moves consist in capturing in a ko and filling the ko and ((the handicap is even and different from zero, and the number of neutral intersection is even) or (the handicap is zero or odd, and the number of neutral intersections is odd))),
Pass stones may be used, under condition that a button stone is given in addition to the pass stones, and that if the players who took the button is the second one to pass when both players pass in a row, he or she doesn't hand a pass stone.

If I understand properly, we use nearly-pass stones (plus a button stone) and add them to the "apparent" territory in order to get the area, then we add the button to that area, which in turn tells us who's got the most "true" territory.



Unless a straightforward equivalence with territory or area can be clearly explained, I'm afraid that it doesn't meet my second requirement :

The Korean 2016 Rules are also available as an HTML page:

http://home.snafu.de/jasiek/k2016.html

I think your summary that the winner usually doesn't change at 6.5 komi is correct. I was mentioning that the score changes if you successfully perform "holding half-point ko until the end" strategy. Also, the komi of button go can be anything, and there is no reason to only assume even+0.5 komi for the analysis. (though adopting 6.5 komi for area scoring is one major motivation of it)

In addition, if something like two-stage half-point ko occurs, still the strategy can change the winner even at 6.5 komi. It is probably more likely to happen than the case of half-point ko plus a seki with odd shared liberties. Of course, one should not forget that territory in seki makes additional inevitable changes.



Why? Once we decide to adopt it. It is quite easy to apply. Actually, I don't think we need to use the physical button. All we need to do is to introduce the pass stone, and make sure the opponent of the first passer to make the last pass. All the processes are easy and automatic, and after a few practices, you won't even need the referee to help you. Well, understanding the meaning of it takes more time, but the fact that they are counting the territory in the end, and 95% of the case it reproduces the traditional territory scoring will lower the psychological barrier for players to accept it.

_________________
Jaeup Kim
Professor in Physics, Ulsan National Institute of Science and Technology, Korea
Author of the Book "Understanding the Rules of Baduk", available at https://home.unist.ac.kr/professor/jukim/bbs/board.php?bo_table=notice&wr_id=5