Miai values

[daal]

As a tangent to the midsummer's endgame problem, Kirby showed a much simpler example from SL. While I think I can assess the miai values of a and b, c is a bit more tricky, and I wonder if someone could offer a detailed explanation of how one arrives at the correct miai value of it.

$$B
$$ +-----------+
$$ | . O X X X |
$$ | O O c O X |
$$ | . X . X X |
$$ +-----------+

Click Here To Show Diagram Code

[go]$$B
$$ +-----------+
$$ | . O X X X |
$$ | O O c O X |
$$ | . X . X X |
$$ +-----------+[/go]

Edit: put in the correct link for the "simpler example" of Endgame Problem 24

[Bill Spight]

Code: Select all

                           A
                     | . O X X X 
                     | O O . O X 
                     | . X . X X 
                     +-----------
                   / Count = -0.75 \ 
                  /                 \
             B   /                   \      C
       | . O X X X                    | . O X X X 
       | O O B O X                    | O O W O X 
       | . X . X X                    | . X . X X
       +-----------                   +-----------
        B captures                    W connects
        Local score = 1             / Count = -2.5 \
                                   /                \                                                                               
                             D    /                  \      E                        
                       | . O X X X                    | . O X X X
                       | O O O O X                    | O O O O X 
                       | . X B X X                    | . X W X X
                       +-----------                   +-----------
                        B connects                    W captures
                        Local score = -1              Local score == -4

The miai value (or absolute value, as O Meien puts it) is simply the difference between the counts of a position and one of its stable followers. In the case of sente, it is the difference between the count of the original position and its stable reverse sente follower.

[daal]

For the more visually minded among us:

[EdLee]

Hi daal, the photo is a nice touch. But if I saw those stones as pictured,
I would compulsively adjust the stray ones so that each is more centered on its intersection.

[mitsun]

$$B
$$ +-----------+
$$ | . O X X X |
$$ | O O c O X |
$$ | . X . X X |
$$ +-----------+

Click Here To Show Diagram Code

[go]$$B
$$ +-----------+
$$ | . O X X X |
$$ | O O c O X |
$$ | . X . X X |
$$ +-----------+[/go]

If you are interested in the value of a play at (c), rather than the value of the position as it stands, the calculation is similar. Instead of drawing the full tree, this position is probably simple enough to visualize mentally as:

immediate (2 point gain for B) +
opportunity to later get or prevent (3 point gain for W)

Generally we simplify this to 2+1/2(3) = 3.5 points double gote.

However, if the follow-on play is large enough (depending on the rest of the board when this position arises), it might really be 2 points sente for W and hence 2 points reverse-sente for B.

(Gratuitous side comment -- for kyu players, when W plays (c), it is important to curb your instinct to immediately defend the stone below. If you do that, you have given W two points in sente, which perhaps he did not deserve. Before responding, look around the board and see if there is anything bigger than three points in gote.)

[Splatted]

Why is black's capture worth only 1 point? Doesn't he get 1 for the capture + 2 for the territory at a and b?

$$B
$$ +-----------+
$$ | . O X X X |
$$ | O O B a X |
$$ | . X b X X |
$$ +-----------+

Click Here To Show Diagram Code

[go]$$B
$$ +-----------+
$$ | . O X X X |
$$ | O O B a X |
$$ | . X b X X |
$$ +-----------+[/go]

[Bill Spight]

Why is black's capture worth only 1 point? Doesn't he get 1 for the capture + 2 for the territory at a and b?

$$B
$$ +-----------+
$$ | . O X X X |
$$ | O O B a X |
$$ | . X b X X |
$$ +-----------+

Click Here To Show Diagram Code

[go]$$B
$$ +-----------+
$$ | . O X X X |
$$ | O O B a X |
$$ | . X b X X |
$$ +-----------+[/go]

If you look at the original problem, this position is in the bottom left corner. So it should really look like this.

$$B
$$ | c O X X X
$$ | O O B a X
$$ | . X b X X
$$ +-----------

Click Here To Show Diagram Code

[go]$$B
$$ | c O X X X
$$ | O O B a X
$$ | . X b X X
$$ +-----------[/go]

That means that "c" is a point for White, and "b" is not a point for Black. "a" is one point for Black. Add one point for the captured stone, and you get a local score of 1 + 1 - 1 = 1 for Black.

[Splatted]

Hmm... but why is "c" included in the valuation of if none of the local moves affect it in any way?

[Kirby]

I thought the miai value was 1.75 per the SL page: http://senseis.xmp.net/?EndgameProblem24%2FSolution

[snorri]

Hmm... but why is "c" included in the valuation of if none of the local moves affect it in any way?

It doesn't matter, since in this case we are only interested in the difference (swing) and the local tally. You have to draw the boundary somewhere in calculating the local count. Since the rectangle shown from a larger position includes that point, one might as well add it, but it is not required.

[snorri]

I thought the miai value was 1.75 per the SL page: http://senseis.xmp.net/?EndgameProblem24%2FSolution

Yes, that's the miai value of the move, because the net local tally is 2 (typical of double gote), so we need to divide the swing of 3.5 by that. If white could play the connection in sente, as mitsun suggests might be the case depending on the board position, the net local tally would be 1 (difference between white moves and black moves), but then the swing would be 2, and then the miai would be 2 (swing) / 1 (net local tally) = 2.

[Kirby]

I thought the miai value was 1.75 per the SL page: http://senseis.xmp.net/?EndgameProblem24%2FSolution

Yes, that's the miai value of the move, because the net local tally is 2 (typical of double gote), so we need to divide the swing of 3.5 by that. If white could play the connection in sente, as mitsun suggests might be the case depending on the board position, the net local tally would be 1 (difference between white moves and black moves), but then the swing would be 2, and then the miai would be 2 (swing) / 1 (net local tally) = 2.

I don't get it. Is the miai value for the local position 1.75, 2, -0.75 or something else? I thought the miai value was for the move, anyway. If I look at the position, I would think that it's 0.25, because you have average of (2+0)/2 = 1 point for first position, if white responds white has follow up of 3 points for w or 0 net points for -1.5. Since it happens with 50% chance, that's -0.75 to give 1-0.75 = 0.25...

So I thought SL was talking about the move and that was the 1.75. But now there's this tree on this thread that says the value is -0.75. And it wounds like you are talking about a local tally, which is 2...

This gets back to what I was trying to ask in the other thread: WTH do we want to measure and how do we use it to play optimally?

[John Fairbairn]

Now more hippopotami began to convene
On the banks of that river so wide
I wonder now what am I to say of the scene
That ensued by the Shalimar side
They dived all at once with an ear-splitting sposh
Then rose to the surface again
A regular army of hippopotami
All singing this haunting refrain:

Mud, mud, glorious mud
Nothing quite like it for cooling the blood
So follow me follow, down to the hollow
And there let me wallow in glorious mud

[daal]

It's not the feet that cause the mud. Flattery will get you nowhere.

[Shinkenjoe]

I don't get it.

The value of the starting position is -0,75 points, a move is worth 1,75 ponts, if there is something gote on the globe that is worth more than 3 points.

If there is not, the move is worth two points.

Thats how i understood it.