Miai counting

  Difficulty: Intermediate   Keywords: EndGame, Theory

Miai Counting is a method to assess the value of a move.[1] [3] It 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 significance, importance, or priority of a play.[1]

In a position whose value does not depend upon ko threats, the miai value of a play is given by:

M = C/T

C and T are found by comparing the count and LocalTally when (1) Black plays first and when (2) White plays first

The net count C is given by subtracting the count in situation (2) from that in situation (1). For non-kos C is the same as the Deiri Value of the play. The net Local Tally T is found by subtracting the Local Tally in situation (2) from the Local Tally in situation (1). Here the Local Tally is (the number of stones Black played) - (the number of stones White played) in the position.

In a gote play, the first player plays an extra stone, while in a sente play, the players play the same number of stones. Hence, T=2 if a the position is gote and T=1 if a play is sente.

[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

Bass: If I compare miai values directly, and add and subtract like ordinary numbers, will I not go wrong in the situation where the three remaining endgame plays are A: a two point reverse sente, B: a 6 point gote, and C: a 5 point gote? The respective miai values are 2, 3 and 2.5, and yet, A (with the lowest miai value) is the only move.

tapir: Most probably that is because this example involves tedomari considerations with an unnaturally big size of the last given move. Deiri counting would mislead in the same way (giving 4,6,5 points as size respectively.)

Bass: I am not yet quite convinced that miai counting is as useless as deiri, it is entirely possible that I am just missing something. I wonder if Bill could enlighten me?

Bill: Neither deiri counting nor miai counting involve tedomari. Quite the opposite. They assume a rich environment of many plays ranging from the size of the play in question down to zero, in the sense that in such an environment the biggest play is best. When you have tedomari, you do not have a rich environment, but a drop in temperature, and the biggest play may not be best.

Bass: Ok, I see. Might it be possible to add some counting rules to take tedomari into account, along the lines of gote move addition having every even-numbered term negated, so that 6+5 -> 6-5 = 1, and 5+5+4+3+2 -> 5-5+4-3+2 =3 or something like that? I have not thought this out at all, but if it were possible, then the system would be much better applicable to real life go situations. It would work in this situation, at least.

Bill: Well, just use the miai values and plain arithmetic. If you make the largest play first, then the result will be 3 - 2.5 = 0.5 (The opponent gets the sente, but sente gains nothing.) If you take the reverse sente instead, the result will be 2 - 3 + 2.5 = 1.5 , which is 1 point better. :)

Note: It is conceivable that the threat of the 2 point sente is worth less than 2.5 points, and that it will not be answered. But I am assuming that the sente is currently sente (in a different sense, of course). :)

Bass: Ok, I think I get it now. The disappearing two seems to defy the rules of plain arithmetics, but I think I am just trying to put too much weight on this thing, which is not even supposed to work because of the big tedomari.

Bill: About them missing 2: 3 - Big + Big - 2.5 = 0.5 . Big = the size of the sente threat. :)


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.


RobertJasiek: What about positions in that passing is best for both players? Is the miai value 0 then? If it is undefined for those positions, then I would like to define: The miai value is 0 then. Or should we rather leave miai value undefined then and refer to the temperature being 0 instead?

Bill: If correct, and not dictated by a ko or superko prohibition, a pass is worth 0 or less (down to -1 by territory scoring). See pass stones, AGA rules, and Spight rules for when a pass is worth -1.

The miai value of a gote is how much it gains, on average. If there is no penalty for an unconstrained pass, it simply leaves the board position unchanged. The value of the position is unchanged, and the gain is zero.


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 Practical Endgame Test 8 and the solution is at Practical Endgame Test 8 / Analysis.


[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.

[3] aLegendWai: The author doesn't explain how to calculate a lot of figures. Beginners who don't know how the figures are calculated should read this one first:



This is a copy of the living page "Miai counting" at Sensei's Library.
(OC) 2011 the Authors, published under the OpenContent License V1.0.
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