Miai counting
Table of contents | Table of diagrams Example diagram (gote) Black's play White's play Example diagram (sente) White moves Black moves |
Introduction
Miai Counting is a method to assess the value of a move.^{[1]} 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 M 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).
- 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.
Example 1 - gote
In this example^{[2]}, the count is 2 (Black has 2 points more than White). We will calculate the miai value:
White's hane-connect shifts the count to 1 point: 7 for Black minus 6 for White.
Each play gains 1 point. Otherwise stated: the miai value of those plays is 1.
Example 2 - sente
Here the count is 0. Each side has 5 points. (It will become clear why the two white stones are counted as captured already).
is sente, threatening to connect to the two white stones. (The move is sente, because the follow-up of it is bigger than the move itself. We don't bring in the possibility that White saves the stones, because this will only occur in ko situations. Otherwise, Black would have a play elsewhere that is bigger than capturing the stones, but then White would not have played here to start with. This reasoning is called temperature.)
Each player has made one play, for a net tally of 0 plays, and the count remains the same. (This is meant with sente gains nothing.)
is reverse sente, gaining 1 point. So the miai value is the count (1), divided by the local tally (1), and equals 1/1 = 1.
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.
Comparison
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.
Thus a 1 point sente, like the above example 2, and a 1 point gote by miai counting have the same urgency.
History
The Japanese amateur Sakauchi Jun'ei is credited with some of the development of miai counting. Otherwise, most of the ideas explained here are due to the work of Berlekamp and Wolfe in their treatise Mathematical go.
More examples
See also
[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).
[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.