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Miai values list
Path: Endgame   · Prev: YoseFromGames   · Next: CountingProblem1
  Difficulty: Advanced   Keywords: EndGame

Charles: I suggest that we compile a reference list of miai values. These are rational numbers, but I propose we round to two decimal places to keep things relatively clear: 0.005 of a point is really a matter for the experts.

Bill: In practice, 0.5 +/- is good enough precision. E. g., 1.0- is better than 0.5+. There will be times when a tiny fraction of a point will make a difference, but figuring that fraction is not usually easier than reading it out, anyway. ;-)

In fact, as I add plays, I'm starting to feel that 2 decimal points is tedious. Yes, there is a difference between 1.73 and 1.75. But really!

Charles: It gives an ordering. When this list gets spread out over many pages I think this level of detail will look appropriate.

Bill: Bueno, Carlos! :-)

See /Discussion for questions and discussion about material on these pages.

Important footnotes: [1][2]

Conventions:

  • All examples are framed by empty spaces. There are no alternative plays in the frame, and all stones that are connected to the frame are alive.
  • Black scores are positive, White scores are negative.

Bill: For posters: Please show territory unambiguously. E. g., close it off. Also, give the initial count.

Suggestion 2: If your diagram leaves more play, say how much the next play is worth. That will help the reader look it up. Also indicate the value of any sente followup.

You can also link to the relevant followers, if they exist. And create them, if necessary.


0.00

[Diagram]
Fill neutral point

There are other types of neutral (dame) points including: protective moves (teire) against the cut when outside liberties are filled; capturing stones in seki, etc.



[Diagram]
Miai

Either player can play first, with the same result.

[Diagram]
Ko threat (teire)

B1 may be a ko threat. At the dame stage, an immediate W2 is a protective play.



0.33 (1/3)

[Diagram]
Connect ko

Initial count: -0.33

White has 1/3 point equity in the BC stone. We may think of it as 1/3 captured.


[Diagram]
Take ko

HolIgor: This move together with the one above should give a point, shouldn't it?

Bill: Yes, but Black started with 1/3 point net equity WC, so each move gains 1/3 point, on average. :-)

See half-point ko.


[Diagram]
Hidden ko

B3 fills.

Initial count: 0.67

1 and 2 are miai points.[3]



[Diagram]
Make ko

Initial count: 8.67



[Diagram]
Take ko in sente

Initial count: 5.67

[Diagram]
Make ko



0.5

[Diagram]
Take away potential point

Initial count: -0.5

[Diagram]
Defend potential point



[Diagram]
Take stone

Initial count: 1.5

[Diagram]
Take away territory

B3 at 1.

[Diagram]
Jump to take potential point

Initial count: -3.5

[Diagram]
Defend potential point

Initial count: 2.5

[Diagram]
Take away potential point



[Diagram]
Take away potential point

Initial count: -0.5

[Diagram]
Defend potential point



[Diagram]
Under the stones sacrifice

Initial count: -2.5

After B3 the corner is worth -2. White has captured 3 Black stones, but Black can claim the W2 stone.

(Note: If White is komaster she can make ko to protect W2, but Black gets 3 moves elsewhere.)

[Diagram]
Prevent sacrifice

After W1 White gets 2 Black stones plus 1 point of territory.

[Diagram]
Real half-point ko, W komaster



0.58 (7/12)

[Diagram]
Real half-point ko, B komaster

If B were komonster, it would be 0.75.



0.67 (2/3)

[Diagram]
Take away potential point, set up ko capture

[Diagram]
Defend potential point, set up ko capture

[Diagram]
Take stone to set up ko

Ambiguous.


[Diagram]
Make ko

[Diagram]
Take two stones

[Diagram]
Take away territory (i)

[Diagram]
Take away territory (ii)

[Diagram]
Take three stones



0.75

[Diagram]
Take away potential point (corridor)



0.83

[Diagram]
Defend potential point, set up 0.67 position

[Diagram]
Take away potential point

[Diagram]
Sente

Take stone in sente, leaving 0.67 point play.


[Diagram]
Reverse Sente

Save stone, leaving 0.5 point play.


[Diagram]
Protect, threaten 0.67 play



0.88

[Diagram]
Take away potential point (corridor)

[Diagram]
One more number

[Diagram]
Take away potential point



0.94

[Diagram]
Take away potential point (corridor)



0.97

[Diagram]
Take away potential point (corridor)



For higher values see miai values list - 1.00 to 1.99, miai values list - 2.00 and more.


[1] Territory scoring, naturally; add one for area scoring (see Miai counting - ratio explanation, 'pedantic note about scoring method' for why, and note that points in seki may make a difference as well). Explanations can be added to this page, and annotations (links to other pages, too). The point would be to consolidate a list.

[2] Black to play first (AFAICS we aren't adhering to this Charles): the sequence shown will naturally be Black's sente or ambiguous exactly when White is shown as the last to play. The default for values involving ko is the 'divide by three' miai counting convention. Some values, though, depend on the komaster concept.

Bill: Mea culpa, Charles. If I have just copied a diagram I haven't bothered to change the colors of the stones. Also, when showing both sides of a play, I think it's better to keep the stable stones the same and change who plays first.

[3] Bill, now I'm confused - I think. Black's sente - I've switched the colours for B1, W2. OK, so using miai values means sequences don't need to be flagged as such (sente, or gote). Ah, I get it: White connecting on either side leaves

[Diagram]
Hidden ko (2)



where Black has in effect 0.33.

Leaving this comment for others' benefit. Charles

Bill: This is an ambiguous position. Its miai value is 1/3, but Black can take one stone and threaten to connect with sente. Then, OC, the position still has a miai value of 1/3, and Black's sente has gained nothing locally. (It may have been a ko threat.) In thermographic terms, it has a blue mast up to temperature 1 2/3.



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This is a copy of the living page "Miai values list" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.