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Miai counting
  Difficulty: Intermediate   Keywords: EndGame, Theory

Miai Counting is a method to assess the value of a move.[1] (novices might try: miai counting made easy)

Miai counting assigns a count to the position, and a value to a play in the position. The value of the play is how much it gains, on average, if it is a gote or reverse sente, or how much the reverse sente would have gained, if it is a sente. It indicates the importance or urgency of a play.[1]

[Diagram]
Example diagram (gote)



In this example[2], the count is 2 (Black has 2 points more than White) and the miai value is 1.

[Diagram]
Black's play

Black's hane-connect shifts the count to 3 points.

Reuven - Why is it 3 points? Did you mean that white'll play to get 2 eyes after it? But the group seems to be free - Not surrounded - Or should we assume that it is, since it's the endgame?

Eratos - I think it's 3 points because now Black has 8 points of territory, but White has 5. 8-5=3. The confusion probably lies in the use of the word count. From lower down the page, count refers to the game score, where value refers to the miai value, the subject of this page.

Bill: By convention[2] the White stones are alive as is. As Eratos says, the score difference is three points. Count is a more general term than score, however. You can count a non-terminal position that does not yet have a score.


[Diagram]
White's play

White's hane-connect shifts it to 1 point.

Each play gains 1 point.

[Diagram]
Example diagram (sente)

Here the local count is 0. Each side has 5 points.


[Diagram]
Example diagram (sente)

W1 is sente, threatening to connect to the two white stones.
Each player has made one play, for a net tally of 0 plays, and the count remains the same.


[Diagram]
Example diagram (sente)

B1 is reverse sente, gaining 1 point.

We call the sente a 1 point play, too, because it becomes urgent for White to play it when the size of other plays (ambient temperature) nears 1 point, and Black threatens to play the reverse sente.
Note that a 1 point sente and a 1 point gote by miai counting have the same urgency.

Another example of miai counting is given in Value of a Monkey Jump.

Comment: You can compare miai values directly. In general, you make the play with the largest miai value. Also, miai values add and subtract like ordinary numbers. Neither is true of deiri values. -- Bill Spight


Question: Do miai values take sente/gote into account?

Answer Bill Spight: Yes. You do not have to make any alterations to compare the sizes of sente and gote plays using miai values.

Harpreet: I tried to understand this from the Value of a Monkey Jump page but couldn't. Are there any books that teach miai counting? Am I correct in thinking that The Endgame book teaches deiri counting? From what is written above it sounds to me like I should learn this miai counting stuff for purposes of taking into account sente and gote. Is deiri counting more normal? Perhaps that is why it is taught in the The Endgame. I'm trying to make less sloppy endgame plays and I would just like to learn how to count values better and order moves better but between miai, deiri modified by sente, gote I'm not really sure I know what I'm doing.

Charles Matthews Since a number of people seem to require further explanation, I'm adapting and moving here part of an article from Gobase:

Miai counting - ratio explanation.


See Counting Crawls.


The Japanese amateur Sakauchi Jun'ei is credited with some of the development of miai counting.


I just read most of the miai-counting pages and it is really confusing: there seem to be no clear definition of 'value' and 'count', or people use 'value' instead of 'count'. I need a clear formula for both. Also, suppose you have the miai value and the miai count, which one is most important? What is the relation between the two?

Bill: We do not say miai count, we say miai value. The count is either the local score or a score-like value. The miai value is the difference in count between two positions divided by the net number of plays between those positions. These positions are the stable followers of the original position. A stable follower has a smaller miai value than the original position. There is an apparent circularity there, but you do end up with scorable positions, where the process stops.

See miai values list for the beginnings of a list to support endgame calculations.


An application with all the calculations would be very helpful, and I suggest this problem (problem 365 of [ext] http://www.goproblems.com Is this allowed?). I tried to solve it with miai counting but even if I know the solution, I can't figure it out. Thanks!

[Diagram]
Black to play and win!


- For the same question see EndgameHowToFindTheMove and the solution is at EndgameAnalysis1.


[1] Charles I think the development and discussion of the miai values list indicates clearly that miai values are attached first to positions, by means of pairs of sequences (best play for Black/best play for White).

Karl Knechtel See also the Miai values list / Discussion.

[2] The example is not a full board, but part of a board. The stones framing the example are alive. That is a convention started in Mathematical Go, by Berlekamp and Wolfe.



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