For the more visually minded among us:
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| Miai values http://www.lifein19x19.com/viewtopic.php?f=15&t=8824 |
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| Author: | daal [ Mon Jul 29, 2013 3:26 pm ] |
| Post subject: | Miai values |
As a tangent to the midsummer's endgame problem, Kirby showed a much simpler example from SL. While I think I can assess the miai values of a and b, c is a bit more tricky, and I wonder if someone could offer a detailed explanation of how one arrives at the correct miai value of it. Edit: put in the correct link for the "simpler example" of Endgame Problem 24 |
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| Author: | Bill Spight [ Mon Jul 29, 2013 4:15 pm ] |
| Post subject: | Re: Miai values |
Code: 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. |
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| Author: | daal [ Mon Jul 29, 2013 5:08 pm ] | ||
| Post subject: | Re: Miai values | ||
For the more visually minded among us:
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| Author: | EdLee [ Mon Jul 29, 2013 5:37 pm ] |
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| Author: | mitsun [ Mon Jul 29, 2013 5:43 pm ] |
| Post subject: | Re: Miai values |
If you are interested in the value of a play at (c), rather than the value of the position as it stands, the calculation is similar. Instead of drawing the full tree, this position is probably simple enough to visualize mentally as: immediate (2 point gain for B) + opportunity to later get or prevent (3 point gain for W) Generally we simplify this to 2+1/2(3) = 3.5 points double gote. However, if the follow-on play is large enough (depending on the rest of the board when this position arises), it might really be 2 points sente for W and hence 2 points reverse-sente for B. (Gratuitous side comment -- for kyu players, when W plays (c), it is important to curb your instinct to immediately defend the stone below. If you do that, you have given W two points in sente, which perhaps he did not deserve. Before responding, look around the board and see if there is anything bigger than three points in gote.) |
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| Author: | Splatted [ Mon Jul 29, 2013 6:02 pm ] |
| Post subject: | Re: Miai values |
Why is black's capture worth only 1 point? Doesn't he get 1 for the capture + 2 for the territory at a and b? |
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| Author: | Bill Spight [ Mon Jul 29, 2013 6:17 pm ] |
| Post subject: | Re: Miai values |
Splatted wrote: Why is black's capture worth only 1 point? Doesn't he get 1 for the capture + 2 for the territory at a and b? If you look at the original problem, this position is in the bottom left corner. So it should really look like this. That means that "c" is a point for White, and "b" is not a point for Black. "a" is one point for Black. Add one point for the captured stone, and you get a local score of 1 + 1 - 1 = 1 for Black. 
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| Author: | Splatted [ Mon Jul 29, 2013 6:43 pm ] |
| Post subject: | Re: Miai values |
Hmm... but why is "c" included in the valuation of  if none of the local moves affect it in any way?
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| Author: | Kirby [ Mon Jul 29, 2013 8:44 pm ] |
| Post subject: | Re: Miai values |
I thought the miai value was 1.75 per the SL page: http://senseis.xmp.net/?EndgameProblem24%2FSolution |
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| Author: | snorri [ Mon Jul 29, 2013 8:54 pm ] |
| Post subject: | Re: Miai values |
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. |
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| Author: | snorri [ Mon Jul 29, 2013 9:07 pm ] |
| Post subject: | Re: Miai values |
Kirby wrote: I thought the miai value was 1.75 per the SL page: http://senseis.xmp.net/?EndgameProblem24%2FSolution Yes, that's the miai value of the move, because the net local tally is 2 (typical of double gote), so we need to divide the swing of 3.5 by that. If white could play the connection in sente, as mitsun suggests might be the case depending on the board position, the net local tally would be 1 (difference between white moves and black moves), but then the swing would be 2, and then the miai would be 2 (swing) / 1 (net local tally) = 2. |
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| Author: | Kirby [ Mon Jul 29, 2013 10:09 pm ] |
| Post subject: | Re: Miai values |
snorri wrote: Kirby wrote: I thought the miai value was 1.75 per the SL page: http://senseis.xmp.net/?EndgameProblem24%2FSolution Yes, that's the miai value of the move, because the net local tally is 2 (typical of double gote), so we need to divide the swing of 3.5 by that. If white could play the connection in sente, as mitsun suggests might be the case depending on the board position, the net local tally would be 1 (difference between white moves and black moves), but then the swing would be 2, and then the miai would be 2 (swing) / 1 (net local tally) = 2. 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? |
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| Author: | John Fairbairn [ Tue Jul 30, 2013 12:48 am ] |
| Post subject: | Re: Miai values |
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 |
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| Author: | daal [ Tue Jul 30, 2013 2:34 am ] |
| Post subject: | Re: Miai values |
It's not the feet that cause the mud. Flattery will get you nowhere. |
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| Author: | Shinkenjoe [ Tue Jul 30, 2013 3:10 am ] |
| Post subject: | Re: Miai values |
Kirby wrote: I don't get it. The value of the starting position is -0,75 points, a move is worth 1,75 ponts, if there is something gote on the globe that is worth more than 3 points. If there is not, the move is worth two points. Thats how i understood it. |
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| Author: | Bill Spight [ Tue Jul 30, 2013 4:20 am ] |
| Post subject: | Re: Miai values |
Bill Spight wrote: Code: 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.
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| Author: | daal [ Tue Jul 30, 2013 4:55 am ] |
| Post subject: | Re: Miai values |
snorri wrote: Yes, that's the miai value of the move, because the net local tally is 2 (typical of double gote) Why is the net local tally of double gote 2 and not 0? Ain't zero minus zero zero? |
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| Author: | HermanHiddema [ Tue Jul 30, 2013 5:17 am ] |
| Post subject: | Re: Miai values |
@daal: Your examples are sente, as the opponent responds and then there is no further play. Double gote is this: |
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| Author: | daal [ Tue Jul 30, 2013 5:55 am ] |
| Post subject: | Re: Miai values |
HermanHiddema wrote: @daal: Your examples are sente, as the opponent responds and then there is no further play. Double gote is this:  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 |
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| Author: | daal [ Tue Jul 30, 2013 7:26 am ] |
| Post subject: | Re: Miai values |
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. |
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