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Miai counting question: game example [#366]

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erislover: Miai counting question: game example (2006-03-24 00:27) [#1336]

Saw this in a dan game on KGS. There was some discussion about the value of a play. I thought I had a grasp on miai counting until this came up.

Black to play?  

White has just played the marked stone. I am trying to figure out the size of the play at a for black, or the value of b for white.

I am completely stumped. Well, not completely. I have an answer, but I do not know if I am right.

White b is just gote: it captures three stones directly for 6 points and the other three in a snapback for 7 points, so this is 13 points gote for white. That's easy enough.

How to approach the situation for black?

If black plays a that is one point for capture. White then plays b, making 6 points, and placing black's group in atari. So black connects. This makes a local count of 5 (right?) with a tally of 1 (black played one more than white), so its miai value is 5.

Since both are gote, does this mean that the play at b by white is more urgent than the play at a by black? Or have I totally botched the counting? If only gote remained, and if black had a 6 point gote move elsewhere, should he take that instead?

Bildstein: Re: Miai counting question: game example (2006-03-24 00:53) [#1338]

Bildstein: Here's my analysis. The first important thing to realise is that the three black stones on the left are dead, and so will not effect the miai value (just like the three living White stones in the middle which will not die). So if Black plays, he saves three stones, captures one white one that could otherwise live, and gains no territory. If White plays, he captures three black stones that could otherwise live, saves one white stone, and makes four points of territory (under the three captured black stones, and the point a.

For miai counting, we need to consider some starting point we can call 0, so I will consider that the black stones on the left are dead, but everything else is alive (because everything else can live. So if Black plays, locally he has gained 1 point, because he has killed the white stone, but gained no territory. If White plays, locally he gains 3 points for prisoners and 4 points for territory. I.e. the value of a play is the value of the three black stones that can be captures plus the one white stones that can be captured plus the four points of territory White can make. So by my calculation, play locally is worth 8 points.

Like you said, it is gote, so the miai value is 4. But take this with a grain of salt, because I'm no expert.

Also, if Black has a 6 point gote move elsewhere, remember that such a move would have a miai value of 3, so would be less urgent. Black would only want to play elsewhere to play a reverse sente play worth 4 or more points, or a gote play worth 8 or more points (like this one).

And what the heck, I may as well add some diagrams, too:

Black plays  
White plays  
Bill: Re: Miai counting question: game example (2006-03-24 00:59) [#1339]
Region of interest  

The region of interest is marked with circle s. Other points are unaffected by local play.

White plays first  

W1 captures 3 stones and kills the rest with a snapback. The local result is -13 (13 points for White).

Black plays first  

B3 connects at white+circle.

B1 - B3 saves 3 stones and captures 1. The local result is -5.

This is gote, with 2 net plays separating the results. Each play gains, on average, (-5 - (-13))/2 = 8/2 = 4 points, which is the miai value of a play in the original position. The local count for the original position is -9. A Black play gains 4 points to bring the local score to -5; a White play gains 4 points to bring the local score to -13.

Es claro?

Bill: Re: Miai counting question: game example (2006-03-24 01:24) [#1341]

Some positions are easier to evaluate by area scoring, and this is one of them.

Black plays first  

For counting purposes, with area scoring we can just fill the territory in, so let's do so.

White plays first  

5 points are Black or White, depending on who plays first. So the miai value by area scoring is 5. To get the miai value by territory scoring, we just subtract 1 point, for a miai value of 4.

erislover: Re: Miai counting question: game example (2006-03-24 01:54) [#1342]

Very clear! Thank you so much.

erislover: Re: Miai counting question: game example (2006-03-24 02:13) [#1343]

(later) Yes for some reason what seems to have messed me up was not understanding exactly where the tally came from. It should have been clear since double-sente moves have no miai value (division by zero is undefined) but such are the mental blocks we must break from time to time.

The area counting explanation is also very interesting. Thanks again.

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