Miai counting made easy

    Keywords: EndGame, Theory

Miai counting is useful for comparing the urgency of simple miai exchanges (or situations that don't require an answer) when you know what the ideal local play is in each case. It's very useful in the endgame, but unlike other counting methods you may have encountered it isn't related to fighting or life and death, nor is it a simple matter of counting territory, but rather it is concerned with the relationship between points gained or lost and moves spent.

Miai counting produces a number for each exchange: the larger the number, the more urgent (and therefore, if there are only these exchanges left, you should normally play the largest one first).

There are three concepts which you must understand first: miai, deiri counting (a.k.a. swing) and local tally. Please read these entries before proceeding.

To calculate miai value for an exchange, first you need to calculate both the swing and local tally difference that result from the exchange. So you simply divide swing by local tally difference, and there's your answer. So M = S/T where M is miai value, S is swing, and T is local tally difference.

Local tally difference is easy to get from the two local tallies of stones played in the miai exchange depending on who plays first (not stones already in the area), but the name is a little misleading. In math terms, you might call it an absolute difference, because you don't get negative numbers.

Basically, you treat black as positive and white as negative (so BB is 2, and W is -1,and BWBWBWB reduces to B which is 1), subtract the two numbers, and throw away the minus sign if it comes out negative.

Let's look at a simple gote/gote example: whoever plays first will play one more stone, so black plays first = B = 1, and white plays first = W = -1, and so 1 - -1 = 2.

[Diagram]

double gote

[Diagram]

double gote (black plays first)

[Diagram]

double gote (white plays first)

So this yields a 1 point territory reduction for whoever plays first, making a swing of 2 points. We've established that the tally difference is 2, so swing/tally diff. = 2/2 = a miai value of 1.

Now, in a sente/sente (double sente) the tally difference will be nil. Divide by zero doesn't make sense, and neither does miai value for a sente/sente exchange. However, it does hint that these exchanges are very urgent (of course, sente is relative, and you can evaluate a double sente as a gote move to compare).

For sente/gote situations, the tally difference will be 1, so the miai and swing values will be the same.

You get thirds from simple, unthreatening ko situations.

[Diagram]

unthreatening ko

In this case, the swing is 1 point. White can play 2 moves to make one point in a capture, or black can play 1 to prevent a capture. So the tally difference is 3. Miai value is 1/3.

And then it gets tricky...

So far, I've been assuming that there's only one miai point: that after the first play, either no answer is required or the answer becomes more urgent than playing in the first place, so the other player has basically no options. That makes the calculation simple, but it's not always true.

How to factor in branches, coming soon...

Interesting Stuff

Miai Counting main entry

More on the Half-point ko

Various common miai values: Miai Values List

How those fractional points can matter: Numbers

A rather in-depth [ext] gobase article which explains the value of such techniques in the context of a ko fight.


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