A
| . O X X X
| O O . O X
| . X . X X
+-----------
/ Count = -0.75 \
/ \
B / \ C
| . O X X X | . O X X X
| O O B O X | O O W O X
| . X . X X | . X . X X
+----------- +-----------
B captures W connects
Local score = 1 / Count = -2.5 \
/ \
D / \ E
| . O X X X | . O X X X
| O O O O X | O O O O X
| . X B X X | . X W X X
+----------- +-----------
B connects W captures
Local score = -1 Local score == -4
The miai value (or absolute value, as O Meien puts it) is simply the difference between the counts of a position and one of its stable followers. In the case of sente, it is the difference between the count of the original position and its stable reverse sente follower.
A has two stable followers, B and C. C has two stable followers, D and E.
The Adkins Principle: At some point, doesn't thinking have to go on?
— Winona Adkins
[go]$$W one extra move for white
$$ +-------------+
$$ | . 2 1 3 . . |
$$ | . X X O O . |
$$ | . . X O . . |
$$ | . . X O . . |
$$ | . . . . . . |
$$ | . . . . . . |
$$ +-------------+[/go]
Been staring at a screen too long today. So the local tally is calculated from one point of view (black's) by comparing the difference in each scenario thusly?:
top: 2 - 1 = 1
bottom 1 - 2 = -1
Local tally 1 - (-1) = 2
This is a (shall we say muddy) attempt to address Kirby's question of how to play correctly in the endgame, and at the same time to clarify endgame terminology for non-specialists (me).
At the beginning of a go game, neither player has any points. At the end of the game, each player has made moves that have secured points. A game is won by making more points than your opponent. Many moves do not secure points. Instead, they create possibilities to do so. With each move, we attempt to increase our potential to make more points than our opponent.
As the game progresses, opportunities arise for positions to be finalized and points to be secured. In order to decide where to play in this phase, we need to know how much a move gains from what we already have. But if the postion is not finalized, how do we know what we have? For this, endgame specialists have devised a way of calculating the points each player can expect from an incomplete position. This calculation, called the count, depends on whether or not the position is sente for one player. If it is, then the count reflects the fact that we expect the sente move to be played. If the move is gote for both players, the count is an average of the locally available points.The count should be distinguished from the score, which is the points of a finalized position.
As play progresses, the players alternate making moves which can secure points and/or narrow the options for securing points. The point value of these moves can be calculated by adding the secure points made to the average of the remaining potential (as Mitsun demonstrated above). This however is different from what a move gains. This is important because the gain is relative to the expectation (the count), and also comes at a cost, namely the cost of the stones necessary to make that gain. This cost is expressed by endgame specialists using the local tally, which shows whether one side would spend more in a local exchange.
The local tally is the difference between the number of stones each side would play if white went first and the number of stones each side would play if black went first. If an exchange is sente for one side, but not the other, then the cost of the move is greater for the side needing gote, and the local tally expresses that cost numerically. This allows the the cost of the stones can be included in the calculation of the move's value. The local tally will be 2 if the position is equally advantageous for both sides, and 1 if it is sente for one and not the other.
This value is called miai value, and is not to be confused with the miai value of the count. Both are determined by averaging the remaining possibilities, but in the first case we are calculating the value of a move, and in the second case we are calculating what each player can expect on the average from a position. The calculation of a move's miai value is as follows:
M(iai value) = C(ount)/T(ally)
In simpler positions, it is possible (and perhaps even preferable) to calculate what a move gains - its miai value - without the help of the above equation. The simplest such position is one in which the move is the last move to be made in that exchange, thus finalizing both the local position and score. In this case, the miai value is the point difference between a white move and a black move divided by 2. Its divided by 2 because what it gains is not the points made, but rather the difference to the count - which as we recall was the average of what either side could make locally.
The second simplest position is the one explained by Mitsun, in which a move clarifies the score and also leaves two possible further outcomes. In this case we add the score change of the first move to the average of the two outcomes of a follow-up move. This again gives us points, but not miai value, which again is half of the points.
So now that we have a way of determining the value of moves, the question remains, when to play them. Common sense would dictate that larger moves be played first, and in most cases, this is correct. There is however an interesting exception to that rule. As players alternate plays, we can assume that the miai values roughly cancel each other out. The last move however cannot be answered and as such gives the player who can make it an inherent advantage. This fact can sometimes be exploited due to the existence of asymmetrical positions such as the one in the first post. Asymmetric refers to the fact that if one player gets the move, a follow-up move is available, whereas if the other player plays it, no follow-up exists. By calculating the values of the remaining moves, and jockeying to get that last move, a predicted outcome can (at least theoretically) be upended.
I'd like to apologize for this post in advance, because I am sure it contains numerous inaccuracies and could easily be construed as an example of those who can't do trying to teach. Its just the result of a day's struggled thought while digging in SL, and a night's deep glass (which accounts for the disorderly stones above). I'm ready for my test now. Please make it easy.
John Fairbairn wrote:Now more hippopotami began to convene
On the banks of that river so wide
I wonder now what am I to say of the scene
That ensued by the Shalimar side
They dived all at once with an ear-splitting sposh
Then rose to the surface again
A regular army of hippopotami
All singing this haunting refrain:
Mud, mud, glorious mud
Nothing quite like it for cooling the blood
So follow me follow, down to the hollow
And there let me wallow in glorious mud
Yes, because I expressed my confusion about endgame calculations, I'm basically the same as a hippopotamus (maybe one that resembles mickey mouse?) wallowing in mud.
I suppose I should know better than to show that which I don't understand.
Thanks to daal, though, for at least explaining some of the different terms here. I still don't know how this is tied to optimal play, but I guess it'll be more efficient to try to figure out myself than ask questions here.
I don't get it. Is the miai value for the local position 1.75, 2, -0.75 or something else? I thought the miai value was for the move, anyway. If I look at the position, I would think that it's 0.25, because you have average of (2+0)/2 = 1 point for first position, if white responds white has follow up of 3 points for w or 0 net points for -1.5. Since it happens with 50% chance, that's -0.75 to give 1-0.75 = 0.25...
So I thought SL was talking about the move and that was the 1.75. But now there's this tree on this thread that says the value is -0.75. And it wounds like you are talking about a local tally, which is 2...
This gets back to what I was trying to ask in the other thread: WTH do we want to measure and how do we use it to play optimally?
The numbers are the counts or local scores, from Black's point of view. B, D, and E are terminal positions.
The move from C to D by Black gains the difference between the counts of the two positions. The local score at D is -1. The count at C is -2.5. So Black gains -1 - (-2.5) by the move from C to D, or 1.5 pts. Similarly, by the move from C to E White gains -2.5 - (-4) = 1.5 pts. The gain is the same because C is gote.
Similarly, the move from A to B or the move from A to C each gains 1.75 pts. (1 - (-0.75) = -0.75 - (-2.5) = 1.75.) A is also gote.
Using swings and tallies gets you the same answer, but is not as clear about the concept, IMO.
The Adkins Principle: At some point, doesn't thinking have to go on?
— Winona Adkins
Yes, because I expressed my confusion about endgame calculations, I'm basically the same as a hippopotamus (maybe one that resembles mickey mouse?) wallowing in mud.
I suppose I should know better than to show that which I don't understand.
Sorry to disappoint you but the poem was not aimed at you. I see the hippopotami as the cruel mathematicians who, for the numerically challenged like me, turn everything about the endgame into mud. OK, I'm breaking a major rule of life in the wild: don't mess with a hippo. But many readers will know I am not a fan of strict rules either.
To daal: I think your confusion and the need for a stiff one are understandable, but are also built on a bit of a con. In just the same way that our go is plagued by people who can't live without attaching numbers to everything, so Japanese go has suffered. I think it is significant that miai (in the boundary play sense) is really a construct of Japanese amateurs who happened to be mathematicians. This was in two main waves - the 1930s and 1950s. Shimada Takuji was the dominant force in the first wave, but the detail of miai really belongs Sakauchi Junei whose main work on it was published in 1955.
In other words: the likes of Jowa, Shusaku, Shuei and so on apparently got away without it. Furthermore, I have seen many comments on the value of a move in pro commentaries, but I'm pretty certain that these references (like Genan's seminal work) have all been to deiri counting. To rephrase that: I have never seen a pro comment using miai values. Modern books on boundary plays or the endgame often mention miai counting, but these are either definitely (as in the case of the Mokusuu Shoujiten", which has the subtitle "Deiri counting and Miai counting") or probably (in the case of ghost writers) written by amateurs.
Pros memorise large numbers of standard boundary shapes and their deiri counts (as an insei Rob van Zeijst was said to have learnt about 1,000). I have never been able to shake off the suspicion that miai counting was introduced as a snake oil remedy that was supposed to spare you the pain of all that work. That is, you apply a theory and skip the drudge.
No doubt the hippo chorus telling me I'm wrong will ensure that "Like thunder the forest re-echoed the sound", but I'll still feel that miai counting is rather like the bit left over after you have, with apparent success, self-assembled a bookshelf. You feel it should have some use, but for the life of you you can't see where.
John Fairbairn wrote:I have never been able to shake off the suspicion that miai counting was introduced as a snake oil remedy that was supposed to spare you the pain of all that work. That is, you apply a theory and skip the drudge.
I don't know anyone claiming that. There's still a lot of brute force either way.
As I understand it, the purpose of miai counting is to put plays into sequence. So whether you remember the value or calculate it on the spot, figuring out the values is still drudgery. It's getting tedomari that's cool. (Or I guess, as a hippopotamus, I should say that tedomari is cooling? chilling, even?)
John Fairbairn wrote:
Sorry to disappoint you but the poem was not aimed at you. I see the hippopotami as the cruel mathematicians who, for the numerically challenged like me, turn everything about the endgame into mud.
Mathematicians can be so cruel!
In other words: the likes of Jowa, Shusaku, Shuei and so on apparently got away without it {miai counting}. Furthermore, I have seen many comments on the value of a move in pro commentaries, but I'm pretty certain that these references (like Genan's seminal work) have all been to deiri counting. To rephrase that: I have never seen a pro comment using miai values.
I got the impression that you liked O Meien's recent yose book. His absolute counting is miai counting under a different name.
The Adkins Principle: At some point, doesn't thinking have to go on?
— Winona Adkins
$$B Original problem:
$$ -------------------
$$ | . . X X a X O . . |
$$ | X X . X O . O . . |
$$ | X O X X O O O O O |
$$ | X O O O . O X X b |
$$ | O O . O O O O O X |
$$ | . O O X O X O X X |
$$ | . O X X X X X . X |
$$ | O O c O X . . X . |
$$ | . X . X X . . . . |
$$ -------------------
[go]$$B Original problem:
$$ -------------------
$$ | . . X X a X O . . |
$$ | X X . X O . O . . |
$$ | X O X X O O O O O |
$$ | X O O O . O X X b |
$$ | O O . O O O O O X |
$$ | . O O X O X O X X |
$$ | . O X X X X X . X |
$$ | O O c O X . . X . |
$$ | . X . X X . . . . |
$$ -------------------[/go]
$$B Area in question:
$$ -------------------
$$ | z O X X X |
$$ | O O c O X |
$$ | . X . X X |
$$ -------------------
[go]$$B Area in question:
$$ -------------------
$$ | z O X X X |
$$ | O O c O X |
$$ | . X . X X |
$$ -------------------[/go]
The reason Bill and Kirby get different answer for the local count is because Bill is including "z", but Kirby is not. But the definition of local is arbitrary. You simply need to remain consistent in your tree and count the same area. For the purpose of determining correct play it does not matter how much of the surrounding area you include in your local count.
Note the only difference is that every node in Kirby's tree has 1 point added to it. In both cases, you will find the value of a move from position A is the same because you are doing B-A = C-A = 1.75 in both cases.
John Fairbairn wrote:
In other words: the likes of Jowa, Shusaku, Shuei and so on apparently got away without it {miai counting}. Furthermore, I have seen many comments on the value of a move in pro commentaries, but I'm pretty certain that these references (like Genan's seminal work) have all been to deiri counting. To rephrase that: I have never seen a pro comment using miai values.
Bill Spight wrote:I got the impression that you liked O Meien's recent yose book. His absolute counting is miai counting under a different name.
There is a conceptual difference between counting to assess the present value of an unsettled position and counting to assess the value of the best move(s) in that position. (A mathematician would probably dispute this distinction; once you know how to perform one count, you can derive the other.) Knowing how to calculate the value of a move is arguably more important to a Go player than knowing how to calculate the value of a position. For position evaluation, miai counting is necessary. But for move selection, I believe deiri counting is more widely (exclusively?) used by professionals.
Splatted wrote:Hmm... but why is "c" included in the valuation of if none of the local moves affect it in any way?
It doesn't matter, since in this case we are only interested in the difference (swing) and the local tally. You have to draw the boundary somewhere in calculating the local count. Since the rectangle shown from a larger position includes that point, one might as well add it, but it is not required.
Been staring at a screen too long today. So the local tally is calculated from one point of view (black's) by comparing the difference in each scenario thusly?:
if none of the local moves affect it in any way?