I don't want to waste any of the original author's effort on this page, but I think that miai counting has not been described in a simple enough manner on Sensei's Library yet. I propose that the following material eventually replaces the stuff on the main page (miai counting made easy). I will just edit the most important stuff from the main page into here. Please give your opinion as to what material is relevant, and even add some if you've got something to say.
The main problem with the page as it currently is is that a method of working out the miai value is given but no proper explanation of where it comes from so that people can understand what it really means and how to use it. As there was a "coming soon..." bit on the page which hasn't been edited since 2005, I hope the author won't be upset if the page gets butchered too much.
Lastly, I'm the beginner here really, so correct my silly mistakes. For instance, is it always wrong to play a smaller miai value play? Or does tedomari only come into it if the plays are equal sized?
-- The Count
Bill: It is not always wrong to make a smaller play. And tedomari does not depend upon the plays having the same size.
And thanks for adding to this topic. Every good explanation helps.
A local position can be given a count. This represents what the final score of the position will be on average. If a play is made in a local position, the resulting position could then also be given a count, representing what the final score would then be on average. Therefore, the difference between the two counts represents by how much the play increased the final score in the local position. This is the essence of what the miai value is – how much a move gains on average.
Of course, a player wants to make the play that results in the best overall score for that player, and so in general the best play is the one with the biggest miai value. The main exception is sente plays. The miai value only really reprents what the reverse sente would gain if it is played, and usually the player whose sente it is gets to make the play before it is worthwhile for his opponent to play there. Also, note that the miai value is just an average value.
Here is a simple example to get started.
A local position? can be given a count, which represents what the final score in that position is likely to be on average. Of course, score usually refers to the whole board, and so we really mean local score?. Also note, score here means score difference, or Black's score minus White's score. Determining the count is the crucial part of miai counting, and it is discussed in detail later. For now, just remember that the count represents what the final score in a local position is likely to be on average.
In the simplest of positions, when either player makes a play, there is no urgent need for the opponent to reply in the same local position. This is known as a gote position. In this case, a miai value can be assigned to a play in that position. The miai value is the difference in the count before and after the play. Therefore, the miai value represents the amount that a player gained by making a play. We can think of this as a player giving up his turn in exchange for some points. Of course, a player wants to gain as many points as he can on their turn, and so often the play with the highest miai value is the best.
Not all positions are gote, and sometimes if a player makes a play, there is an urgent need for the opponent to reply. This is known as a sente position. If Black plays and White has to reply, it is known as a sente for Black, or Black's sente. Because it's still Black's turn after he makes a sente play, he doesn't give up his turn in exchange for some points, and so a miai value cannot really be assigned to the move. White can play in this position before Black does, but White has to give up her turn in order to stop Black playing the sente at some point in the future. We say that White plays the reverse sente. Therefore, White's play does have a miai value. It's the difference in the count between the position after White plays the reverse sente and the position after Black plays the sente (and White replies). However, because it is free for Black to force this exchange, we assume that he will play it at some point. White may gain only a relatively small amount by playing the reverse sente, so Black can play the sente first, before these small moves become worthwhile. Because of this, the count of the original position is determined to be the same as the count after Black plays the sente (and White replies).
This last paragraph should highlight the fact that to understand miai counting, we must understand sente and gote relationships. They are really part of the same concept. Now, here is a simple example to get started.
| The Count: Why am I wasting my time redoing the intro? I started by trying to separate out count and miai value and take non-gote plays as they come along, but you can't do that. There is no simple definition for either count or miai value which doesn't get tangled up in all the other things.
There are some unplayed points in the corner of this board. First, a count must be assigned to this position. Remember, this represents what the score is likely to be in this local position. For this simple case where there is only one move left, we just work out what the score would be if Black played first, then what it would be if White played first, and then we take the count as the average of these two values.
If Black plays first, his best move is as shown in the diagram. Black has 6 points of territory and White has 4. Black has 2 more points than White. We can say the local score is +2. Of course, only a small part of the board is shown in the diagram, and it doesn't matter where you start counting from as long as you do it from the same place each time.
If White plays first, she would play on the same point. The corner point is just a neutral point now, and so there are no more plays left in the position. Black has 5 points of territory and White again has 4. The local score is +1. (Note that we are using territory scoring here. The vast majority of information about miai values on Sensei's Library uses territory scoring, but area scoring could just as easily be used. The miai value using area scoring is almost always 1 more than that for territory scoring because the stone that just got played counts towards the score.)
The average of +2 and +1 is +1.5, so we say the count for the original local position is +1.5.
So, now that we know what the count of the original position is, to work out the miai value of a move, we have to work out the count of the position after a play is made there. In fact, we've just done this! When Black makes a play in this position, the count of the resulting position was +2. So when Black makes a play, he increases the count from +1.5 to +2. The miai value of the move is 0.5. Similarly, the miai value of a move for White in this position is also 0.5, because the count would decrease from +1.5 to +1.
This example shows that we could instead just calculate the count after Black plays and after White plays and divide the difference by 2 in order to determine the miai value of a play. It is important to remember the original concept though, that the miai value is the change in the expected final local score that a single move makes.
For the example we just had, it was easy to calculate the count, but if you want to become a pro with miai values, make sure you read the count page. The main thing to realise here is that taking turns is not assumed. The reason is that a player may always play in a different part of the board, and so Black, for instance, may end up taking three moves in a row in the local position. When moves are not sente, this is a fair assumption.
In this example, we consider what might happen if Black were to play first in this area and what would happen if White were to play first.
If Black were to play first, the best move would be . There are no more useful moves left in this area of the board. Black has 3 points of territory and White has 6. Black has 3 less points than White. We say the local score is -3.
If White were to play first, the best move would be at . If Black does not respond immediately in this area, White could play at , killing Black's group. Because this would be very bad for Black, Black will usually respond immediately after with . Black has 2 points of territory to White's 6. The score after this sequence is -4, one point better for White.