Seki with Eyes Question 2

    Keywords: Question, Rules

Here's an interesting seki that showed up in a game one night. I've simplified the shapes of the territories somewhat, but Black's false eye position and the corner are exact.

This is a zero score under Japanese rules. Note that under area scoring rules, however, Black has at least one more eye than White. (If White can win a ko, I think, then Black's false eye in the corner can be filled.)

I would welcome scoring analysis from some of the experts. -- Thomas Bushnell, BSG

(Copied from Seki): I think it's interesting enough to have its own page. See also Seki with Eyes Question 1. Shall we organize a seki path?
An interesting seki  

It seems to me that Black has to fill the ko in order to keep the seki. If not, White takes the ko, ignores the threat (it would have to be enormous!) and lives in the corner, killing Black.

Am I right?

-- dougm?

TakeNGive: Yes, when White makes atari at a, Black will have to fill the ko at b to preserve the seki. But, White can't really start the attack without a killer ko threat:

jfc: There are 3 scoring rules to consider the position under:

  1. Territory scoring with no points in seki (Japanese)
  2. Territory with points in seki (nobody anywhere uses this, right?)
  3. Area scoring.

Under Japanese (1) and area scoring (3) black plays b as this simplifies the position and has no negative impact on his score. Under territory with points in seki (2) black should omit b unless there is the large unremovable ko threat.

Pledger: Under area scoring, White gains a point for playing a and forces Black to waste a move on b (assuming White would win the possible ko). Under territory scoring with points in seki (e.g. IGS rules), White a gains nothing directly, while Black b loses a point. Only under Japanese scoring does White a Black b have no effect.

Black 2 and 4 are tenuki  

TnG: Now the board looks as below, and it's Black's turn; and Black is free to retake the ko at b. So, White shouldn't play this without a large un-removable ko threat or some kind of double ko situation to use as a threat; and when White does initiate this, Black should just fill the ko instead of tenuki.

Black is safe unless White has a terrific ko threat  

Ah, yes, I had overlooked that White must fill an own liberty to start the ko. Your explanation makes perfect sense. -- dougm?

Dave: Note that White does not need such a terrific threat. If Black ignores a White ko threat in this position, he gains about 18 points. So all White needs is a twenty-point ko threat to make a net profit here should Black not connect the original atari. On the other hand if White captures here, she gains nearly sixty points. The difference in the size of the ko threats required puts quite a burden on Black. It is quite likely that White would be able to succesfully fight this ko. Black most likely needs to connect.

erislover: Let's take a look at the miai value. White fills, white takes the ko, black plays elsewhere, white approaches. Let's just begin the analysis here.

If black plays elsewhere again, white takes the black group and kills everything. This is -57 points. The local tally here is -1.

Black fights the ko. One move to capture the ko , white plays elsewhere, and one more to capture white's whole group. This will result in 15 points from the capture plus two eye points for black, plus the ko capture, yielding 18. The local tally here is 2.

This makes the swing 18-(-57) =75, the tally is 2-(-1)=3, and the miai value then seems to be 25 points.

Hope I did this right. You are right that this will be tough for white to fight the ko: there are not many 50+ point threats lying around your average game (50+ points / 2 plays = 25+). But white and black don't need to make different sized threats... the value of the ko is what it is for both players, right?

blubb: Once the big ko is started, there is no difference between the sizes of threats needed by either side. But as long as that ko can still be avoided, the situation is hyperactive (see Bill`s account below).

In terms of Normal Values, you are asking for the value of the node labelled as pos2 in the following graph:

                     /         /              \         \
                    /  (19/2, 0)              (15/2, 0)  \
                   /                                      \
        (80/3, 40/3)..................__..................(40/3, 40/3)
        /                                                            \
  (40, 0)                                                            (0, 0)

  • The position labelled as pos1 is reached by W1 from start or from pos2 by bT17, whilst pos2 is reached by wT16 from pos1.
  • For the sake of simplicity, scores are referring to the entire area being black as zero.

Whatever values you try to assign to pos1, pos2 and start, they won`t be consistent with both the huge and the small ko at the same time (note that 19/2 < 40/3). They can be correct for a particular choice of play only, which in turn depends on the ko threats available.

10,000 year ko  

Bill: I am going to start from this position, after W1 makes a 10,000 year ko, and use Japanese scoring. Either player may make a direct ko with a play at a.

Bill: Black can make seki by filling the ko, for a local count of 0. If White makes and wins the ko, the local count will be -60. (White kills or captures 29 stones and has 2 points of territory besides.) If White loses the ko, the local count will be +17. (Black captures 7 stones and has 3 points of territory besides.)

Bill: How big a threat does White need to make and play the ko? Say that White's threat is { || 0 | -2w}. I. e., it is an unremovable threat; if Black answers it the local result (to the threat) will be 0, but if Black ignores it and White completes it the local result will be -2w.

Bill: We compare two lines of play:

1) White plays a gote elsewhere, Black fills the ko.

Result: -t, where t is the miai value of White's play.

2) White takes the ko, Black plays elsewhere,
White plays at a, Black takes the ko,
White plays his threat, Black wins the ko,
White completes the threat, and Black plays elsewhere.

Result: 2t - 2w + 17. (We assume that both of Black's plays elsewhere are worth t.)

White should make the ko when w > 8.5 + 1.5 t.

When Black is the one with the threat, {2b | 0 || }, we make a similar comparison.

Then Black should make the ko when b > 30.5 + 1.5 t.

It is much easier for White to make the direct ko.

Karl Knechtel: See also mannenko.

See also Seki with Eyes Question 1 and the pages in the Eyes Collection.

Seki with Eyes Question 2 last edited by Pledger on August 1, 2010 - 01:21
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