I have seen them constructed in the past (so I know at least one exists)...I can try to work on either finding that or making a new one when I get the time.

Ok, I did some digging and it looks like this has actually come up on L19 before!

A position for your consideration:

Click Here To Show Diagram Code

[go]$$c Unfillable Dame? \n(Japanese Rules, No prisoners, 5.5 Komi).
$$ ---------------------
$$ | . . O . . O X . X |
$$ | O O O O O O X X O |
$$ | X X X X X O O X . |
$$ | . . . . X O T X . |
$$ | . X . . X O O X X |
$$ | X . X X X X O O T |
$$ | X X O O O X X O O |
$$ | O O . . O X . X O |
$$ | . . O O O X X X O |
$$ ---------------------[/go]

It behaves differently under different Japanese rulesets (at least J2003 (dame create in-seki), WAGC (dame filling is required) and verbal J (dame filling is not required) have three different behaviours). The position is interesting, but, for each ruleset, I need time to do a proper analysis of variations and scoring after each. Under J1989, there is also the ambiguity of the black ko stone's status if the dame are filled and the position is scored then; under J2003, there is no ambiguity.

Sakai's Anomaly. Under J89 rules White to play passes and Black cannot afford to fill a dame. White wins by 0.5, because of the weird seki, which exists only under J89 rules.

Play goes smoothly under Double Button Go, where the players hand over pass stones, except when the same player makes the last pass and the first pass. Here is an SGF file for Double Button Go with two consecutive passes to end play.

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

Visualize whirled peas.

Everything with love. Stay safe.

There's never a case where some set of eyes in seki would count as points? In practice, or theory?

Not in Jap. style rules, no.

Btw, I have to date not seen a satisfactory formal definition of "eye". Currently browsing http://senseis.xmp.net/?FormalDefinitionsOfEye.

From what I've seen I'm lead to believe that there cannot be such a definition. However, if there ever were such a definition, I would prefer that it complies with the rule "two eyes alive" in the sense that a group with 2 "real eyes" (however that's defined in the end) cannot be captured even if the owner passes continuously.

Note that this is clearly not the case in the OP.

It depends on your purpose of application.
- My definition works for all scoring positions for the purpose of scoring, and works (by imagining successive passes) for all positions considered as if they were scoring positions and for the purpose of scoring.
- My semeai-eye definion works for all basic semeais with strong eyes.
- If your purpose is not scoring, but is strategy, a formal definition has not be stated yet. However, it is possible along the idea of considering an intersection, or a connected set of intersections, and verifying whether the opponent can prevent the player's creation of a scoring-eye on at least one of the intersections.



For some purposes, there already is such a definition, see above. For other purposes, such a definition can be found, see above.



Needless to say, such makes sense only for non-seki eyes!

Presuming non-seki scoring eyes, your wish is fulfilled due to the proof of Chris Dams, which relates capturability-life to two-eye-alive:
http://home.snafu.de/jasiek/wagcmod.html
(Google for the actual proof.)

Formal definitions are not always satisfactory. Here is one.

An eye is a connected region of empty points adjacent to two or more stones of one color and no stones of the other color. Now, that definition is unsatisfactory in at least two ways. First, two such eyes do not necessarily confer life. Second, there are regions that are considered eyes that do not fit the definition. Still, it could be perfectly serviceable in a theory of eyes.



IMO you are asking for too much. For instance, there are sekis in which a false eye is necessary for life. We need definitions for different kinds of eyes and, if we define eyes by morphology, we may never be sure that we have discovered all the different types of eyes.

You may be interested in Landman's paper, in which he defines topological eyes and fractional eyes. http://library.msri.org/books/Book29/files/landman.pdf

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

Visualize whirled peas.

Everything with love. Stay safe.

Did you leave out the simplest variation? If W starts by passing, can B respond by passing, ending the game instantly with a 1/2 point victory?

If the game goes pass-pass, the yose ko in the top right corner is not settled. Double Button Go allows it to be played out without stopping play first.

Under Japanese '89 rules, Black does pass, but she then loses the game. Seki is defined by having dame, so that Black gets only 9 pts. and White gets only 4. Then White wins by 0.5. The White stone in the yose ko is dead, but cannot be removed because of the seki. (The Japanese '89 rules are so bad!)

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

Visualize whirled peas.

Everything with love. Stay safe.

i would not count that as seki personally.

Click Here To Show Diagram Code

[go]$$c Unfillable Dame? \n(Japanese Rules, No prisoners, 5.5 Komi).
$$ ---------------------
$$ | . . O . . O X . X |
$$ | O O O O O O X X O |
$$ | X X X X X O O X . |
$$ | . . . . X O T X . |
$$ | . X . . X O O X X |
$$ | X . X X X X O O T |
$$ | X X O O O X X O O |
$$ | O O . . O X . X O |
$$ | . . O O O X X X O |
$$ ---------------------[/go]

if it white to play, white threatens a capture by playing either of the triangle points.
black must capture in response, leaving him with 1 fewer point.
if its black to play, he either needs to capture or pass.
either way i don't see how this could possibly be considered seki.

Yeah, that diagram is "Black owes a move" not seki.

Except that black doesn't owe a move! If white fills the two triangled points, then J8 is dead as it stands and white loses.

Why does it matter who fills the dame? If the dame are left unfilled, one side will win. Therefore the other side will fill the dame. After that a ko may be played, and the result may depend on the rule set (in particular whether passing costs a point). But the position will not end up seki under any rule set.

If black fills the dame, the size of the ko is larger and black does not have a big enough threat to win it. Black loses by a larger margin if he fills the dame. If white fills the dame, black has a ko threat and can win the ko (also winning the game). This means that either player filing the dame will cause themselves to lose points...they thus remain unplayed. Under Japanese 1989 rules living stones with dame are seki, and score no points. This is a seki under J89 rules.

Ah, finally I get it. W is content to let the position remain seki, since the "no points in seki" rule then gives him a win. But B does not want to fill the dame to prevent seki, since those stones would end up as extra captures for W if he wins the eventual ko.

but...
black can capture the 1 white stone first and make it not seki!
white may win, but if so then white will definitely win with it being seki.
if j89 rules really state that, then its to blacks advantage to capture.

If black plays an extra move to capture the white stone, he will be playing in his own territory and will lose a point.

but he would have to play it anyway, if white filled the dame, and capturing the stone and losing 1 point is better than letting the postion be seki and losing more.

No, if white fills the dame then the white stone is dead without black making a move to capture. Black wins the game.