Miai counting made easy
Miai counting is a technical go concept, useful for evaluating exchanges. It is not so much a tactical guide as a tool for decision making. It treats go as a series of trade-offs, one could say, rather than a single conflict.
If you know what the ideal local play is in each case, of a number of options, then miai counting may well help. It is very useful in the endgame. Unlike other counting methods, it is mainly 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. Urgency in go is linked to priority; so the first thought is that you should normally play in the largest place.
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. (Now if T = 0 there is an obvious problem, but this as much as anything tells us something in go terms.)
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.
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.
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.
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...
Maybe Miai Counting With Trees will help?
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 gobase article which explains the value of such techniques in the context of a ko fight.