Semedori example 2

In the initial position, if Black plays a White will lose two stones. Something has to be done.

The obvious play at is not very good. Black will draw back to .

Comment: is sente? Not by a long shot. Saving the two white stones is plainly larger than saving the two black stones. --Bill Spight

By doing this the hane remains (or becomes?) Black's sente, and Black will probably get to play it, so that eventually the situation will look like the next diagram:

If we just count the points along the sides (the area around White's finger is assumed to be dame) Black has 6 (circled) points, and White has 7 (squared) points, i.e. one point for White locally.

However, White can do better:

White throws in a stone at . The moves up to are more or less forced (although what happens after Black at instead of wasn't clear immediately^[1]).

Comment: Less forced. is not sente. --Bill

However Black's hane at a no longer works because of shortage of liberties - a connection one point to the left of a would be an auto-atari, so Black would have to play something like the next diagram if he were hell-bent on that hane (playing one point to the right leads to a picnic ko for White):

Which seems like gote to me. However because of a snapback, White can descend to in sente, and so probably will.

Charles No snapback, I think.

Jan: You're completely right. But then I'm at a loss to give a short reason why is sente. Ideas?

GoranSiska Do you need one? is sente () and the playing order of and is not that important.

Bill: Two things about W 1 below: First, it's not sente, it's an ambiguous move (assuming that Black is not komaster). Second, it's dominated by the atari at . Discussion below.^[2]

Jan: That goes a long way to explain why I couldn't argue for 's being sente :-) I've thought about some of the diagrams in the footnote, but it wasn't clear where they fitted in. Does the rest of the analysis still stand?

Bill: Well, as I have said, saving the two white stones is not sente.

Jan: (Sorry Bill, I didn't read the diffs properly so I missed your first comment; but I didn't say that the first play by White was sente...)

Aaargh! Is nothing in the endgame ever simple? Anyway, I was paraphrasing The Endgame without really thinking things through. It made sense to me that this was an example of semedori, I wasn't considering whether and when White would want to play here in the first place.

Maybe my comment at the 'Too simple' diagram should read 'When the time comes, the obvious play at is not very good. Black will eventually draw back to .'?

Also I'm not 100% sure if we're referring to the same ... Maybe I'll do penance - Karate Kid style ;-) - by renumbering all the diagrams. That would make it clearer when Black plays tenuki.

If we now count the score, Black has 5 points (three circled points plus two for the circled White prisoner), however White has 9. Local count is therefore 4 points for White, 3 points better than the first way of playing! One point of this can be attributed to the fact that Black had to capture the single White throw-in stone using two stones (that's the semedori bit), and the other two points come from the fact Black's hane is no longer sente.

[2]:

(Here we are assuming that Black cannot afford to make ko.)
Then Black plays - , picking up 1 point (circled), by comparison with White's sente.

As a 1 point White sente, this is a tiny in chilled go.

The descent, , is dominated. Obviously, it carries a smaller threat for White than the atari. It also allows a reply to a position that is at least as good for Black. After , Black at is a possibility. Even assuming - , Black is still at least as well off.

is an ambiguous move because it does not change the local temperature. After , Black a and White b are miai. That may not be obvious, because either player can play at c, but the exchange of Black a and White b still leaves the play at c, with the same effect for each player. (Skeptics may verify that the position in the next diagram is equal to the one in this diagram after , by playing a difference game.)

This position is a 0|tiny in chilled go, with an atomic weight of 1. It is positive, which means that it gives Black an advantage in the fight for tedomari at temperature 1. Black has three chances to get the last play at that temperature. First, he can fill at 1. Second, he can fill at 2 if White plays at 1. And third, he can take back if White captures at 2.

See infinitesimals and playing infinitesimals.