Never Mind the Ko, Here’s the Dead Group
In another thread, @le_4TC threw down the proverbial, pedantic gauntlet…
Chinese Rules Analysis
In order to appreciate and understand how peculiar this position is under the Japanese rules, we should first analyze and make sense of it under the Chinese (or similar area-scoring) rules, where complicated life-and-death is settled by the principal of “playing it out” (which is not what is done under Japanese rules, of course).
Let’s first examine the position superficially, by imagining that either the left or right existed in complete isolation from the other. If we pretend that all of the black stones on the right side (on the D column) were alive (say, by imagining that there were no pesky white stones on the right side), then the white group on the left would clearly be dead, since black could almost-fill with the bulky-five shape. On the other hand, if we were to forget about the status of the left-side (imagining something different where the white stones on the C column were unconditionally alive), then the right side could either be converted to a simple seki, or potentially played out (or left as is) as a ten thousand year ko.
However, in this position, both sides simultaneously exist, which leads to some interesting complications.
Let’s consider all of White’s options if it were their turn to play. Of course, A1, A4, and F1 are all self-ataris that would lead to all White stones dying. White could play F4 to convert the right side into a (temporary) seki…
However, from this position, Black would simply proceed to capture the White stones on the left side and then be free to capture remaining White stones on the right side as well. Hence, F4 also clearly leads to all White stones dying.
The final option for White is to start the ko fight, however this is a ten thousand year ko, where Black gets to take first…
and since White does not have any ko threats, all White stones will eventually die. Hence, it does not seem that playing any stone for White is a good idea. To see if passing does any better, we need to see what Black’s options might lead to.
Now, let’s look at Black’s options if it were their turn to play. Of course, if Black were to consider starting the ko fight…
then White gets to take the ko first, and Black does not have any meaningful ko threat (since even an atari on the left side would simply be answered by capturing with F1), which now leads to all Black stones dying.
Another option for Black is to play at E1, but that is bad as well, leading down this path…
where this is a capturing race that Black would lose.
Finally, let’s consider what if Black simply just decided to try to capture the White stones on the left side first…
which requires Black to follow up to kill the bulky five, however this now allows White to start the ko fight and make a ko threat on the left…
It would be futile for Black to respond to the ko threat, since that would merely allow White to retake the ko, and eventually kill all Black stones…
Instead, Black should ignore the ko threat, which leads to this final settled position…
where both Black and White control 12 points of area. However, if we compare to the original position above, Black is worse off, since originally, Black had 10 stones and White only had 9, and neither player had any territory. If this contrived 4x6 game had a 0.5 komi, then playing out the above capture attempt and ko fight, would even cost Black the game!
Thus, it does not make sense for either Black or White to play any move from the original position. Under area-scoring rules (with the play-out disputes principle), neither player should try to assert and capture any of their opponents stones, and hence, all of the stones in the original position would be considered alive in seki, which leads to a outcome of B+1 (if there is no komi).
White is entirely dead under Japanese rules
The above analysis is still valid to consider, from the perspective of deciding that both players should pass. White can only lose everything by playing further another stone (and hence should pass). The best Black can do is split the board (as shown in the last figure above), which turns out to be now much worse than what would result if Black simply passed.
What makes the Japanese rules behave very differently, is that the life/death status of position has to then be evaluated under a very different sort of ko rule (which we also discussed earlier in this thread)…
Article 7. Life and death
…
2. In the confirmation of life and death after the game stops in Article 9, recapturing in the same ko is prohibited. A player whose stone has been captured in a ko may, however, capture in that ko again after passing once for that particular ko capture.
To decide upon life/death after both players have passed, the players consider the best possible hypothetical play outs, while applying a very different sort of ko rule that essentially nullifies ko threats. Thus, even though a group might not be killable during the normal course of the game (before passing) since the cost of the ko fight would be too great to make it worthwhile, that group could possibly be considered dead (after both players have passed) during the life/death confirmation phase since this special ko rule nullifies the potential cost of actually fighting the ko!
In our example, Black could demonstrate that all of the White stones are dead with this hypothetical play out that begins similarly to as discussed above…
However, now, White starting the ko threat with move 4 is futile, since the ko threat at 6, won’t let White take back the ko…
Black should now respond to the ko threat with 7 (keeping the left side White stones dead), and it would actually be illegal for White to play at 8 (taking back the ko)…
In order to take back the ko, White first needs to instead pass, which would allow Black to then win the ko with move 9 at F1, and thus lead to all White stones dying.
Thus, under Japanese rules, from the original position, both players should pass, and all White stones should be ruled as dead.