This is almost the only move now.... This move has some weakness, but still I need to play here

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[go]$$Bcm101 white : 1 black : 1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . O X . . . . |
$$ | . . X . . O . . . . X O O X X . . . . |
$$ | . . . O O X O . X X O O X O . , X . . |
$$ | . . X . . . . . . O X O X . . . . . . |
$$ | . . X O O . . . . . X O X O O X X . . |
$$ | . . . X . . . . . O . O X X O O O . . |
$$ | . . . . . . . . . . . . X O X X . . . |
$$ | . . . . . . . . . 9 . . . . O X O . . |
$$ | . . X , . . . . 5 8 0 . . . . X O . . |
$$ | . . . . . . . X 4 6 7 . . . X . . . . |
$$ | . O . X . . X O 2 3 . . . . O . X . . |
$$ | . . . . . . O X X . . . . . . O X . . |
$$ | . . O . X . W O . . . . . . X X . X . |
$$ | . . O . . X X O . O . . . . . O X . . |
$$ | . O . O . . O O . X . . . . . X O . . |
$$ | . . O X X X . . . . . O . . O O X . . |
$$ | . X X O . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

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[go]$$Bcm111 white : 1 black : 1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . O X . . . . |
$$ | . . X . . O . . . . X O O X X . . . . |
$$ | . . . O O X O . X X O O X O . , X . . |
$$ | . . X . . . . . . O X O X . . . . . . |
$$ | . . X O O . . . . . X O X O O X X . . |
$$ | . . . X . . . . . O . O X X O O O . . |
$$ | . . . . . . . . . . 3 5 X O X X . . . |
$$ | . . . . . . . . . X 2 4 6 8 O X O . . |
$$ | . . X , . . . . X O O 1 7 9 . X O . . |
$$ | . . . . . . . X O O X . . . X . . . . |
$$ | . O . X . . X O O X . . . . O . X . . |
$$ | . . . . . . O X X . . . . . . O X . . |
$$ | . . O . X . W O . . . . . . X X . X . |
$$ | . . O . . X X O . O . . . . . O X . . |
$$ | . O . O . . O O . X . . . . . X O . . |
$$ | . . O X X X . . . . . O . . O O X . . |
$$ | . X X O . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Ladder works

if you play this game while playing pocker... you lose pocker and misread on go.

His white stones inside can't live but he can profit from the center using the weakness of N16 group

A rather unfortunate misread by Magicwand. I guess he should have interposed 1 for 2 before playing at "a":

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[go]$$Wc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . O X . . . . |
$$ | . . X . . O . . . . X O O X X . . . . |
$$ | . . . O O X O . X X O O X O . , X . . |
$$ | . . X . . . . . . O X O X . . . . . . |
$$ | . . X O O . . . . . X O X O O X X . . |
$$ | . . . X . . . . . O . O X X O O O . . |
$$ | . . . . . . . . . . . . X O X X . . . |
$$ | . . . . . . . . . . . . . . O X O . . |
$$ | . . X , . . . . . , . . . . . X O . . |
$$ | . . . . . . 1 . . . . . . . X . . . . |
$$ | . O . X . 2 B O . . . . . . O . X . . |
$$ | . . . . . . O X X . . . . . . O X . . |
$$ | . . O . X . a O . . . . . . X X . X . |
$$ | . . O . . X X O . O . . . . . O X . . |
$$ | . O . O . . O O . X . . . . . X O . . |
$$ | . . O X X X . . . . . O . . O O X . . |
$$ | . X X O . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Why is he wasting ko threats?

Interesting endgame study, if the fighting is really over. Here is my analysis of the upper left. Maybe someone else wants to try counting some of the other big areas?

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[go]$$
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . O X . . . . |
$$ | . . X . . O . . . . X O O X X . X . . |
$$ | . . . O O X O . X X O O X O . O X . . |
$$ | . . X . . . . . . O X O X . . . . X . |
$$ | . . X O O . . . . . X O X O O X X O . |
$$ | . . . X . . . . . O . O X X O O O . . |
$$ | . . . . . . . . . . . . X O X X . . . |
$$ | . . . . . . . . . . . . . . O X O . . |
$$ | . . X , . . . . . , . . . . . X O . . |
$$ | . . . . . . . X . . . . . . X . . . . |
$$ | . O . X . . X O O X . . . . O . X . . |
$$ | . . . . . . O X X . . . . . . O X . . |
$$ | . . O . X . O O . . . . . . X X . X . |
$$ | . . O . . X X O . O . . . . . O X . . |
$$ | . O . O . . O O . X . . . . . X O . . |
$$ | . . O X X X . . . . . O . . O O X . . |
$$ | . X X O . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

A play in the upper left is worth around 14 points double gote by my count (see diagrams below), but sente considerations make it more interesting than that.

If W plays first, he has a nice clamp:

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[go]$$W
$$ ---------------------
$$ | . . . . . . . . |
$$ | . 4 3 7 . . . . |
$$ | . 6 X 5 . O . . |
$$ | . 2 1 O O X O . |
$$ | . . X . . . . . |
$$ | . . X O O . . . |
$$ | . . . X . . . . |[/go]

W might want to omit the final connection to take sente, having already limited the potential gain for B if he gets the next move. If B later captures, he gains around 6+ points more than shown above.

If B plays first, he can go this far in gote. The difference between this diagram and the previous diagram is around 14 points.

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[go]$$B W4 tenuki
$$ ---------------------
$$ | . . . . 7 5 6 . |
$$ | . . . . 1 2 8 . |
$$ | . . X 3 . O . . |
$$ | . . . O O X O . |
$$ | . . X . . . . . |
$$ | . . X O O . . . |
$$ | . . . X . . . . |[/go]

But it looks better for B to hold back as shown below, for a large partial gain, in an attempt to take sente. B threatens a monkey jump worth another 6+ points if W does not respond.

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[go]$$B
$$ ---------------------
$$ | . . . . . . . . |
$$ | . . . 1 2 . . . |
$$ | . . X . . O . . |
$$ | . . . O O X O . |
$$ | . . X . . . . . |
$$ | . . X O O . . . |
$$ | . . . X . . . . |[/go]

He should have played M12 instead of O11

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[go]$$Bcm101 white : 1 black : 1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . O X . . . . |
$$ | . . X . . O . . . . X O O X X . X . . |
$$ | . . . O O X O . X X O O X O . O X . . |
$$ | . . X . . . . . . O X O X . . . . X . |
$$ | . . X O O . . . . . X O X O O X X O . |
$$ | . . . X . . . . . O . O X X O O O . . |
$$ | . . . . . . . . . . . W X O X X . . . |
$$ | . . . . . . . . . 7 0 . B . O X O . . |
$$ | . . X , . . . . 3 6 8 9 . . . X O . . |
$$ | . . . . . . . X 2 4 5 . . . X . . . . |
$$ | . O . X . . X O O X . . . . O . X . . |
$$ | . . . . . . O X X . . . . . . O X . . |
$$ | . . O . X . W O . . . . . . X X . X . |
$$ | . . O . . X X O . O . . . . . O X . . |
$$ | . O . O . . O O . X . . . . . X O . . |
$$ | . . O X X X . . . . . O . . O O X . . |
$$ | . X X O . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Gladly!

A play at the bottom area is huge. If Black plays there, White not only loses points, but also has to be careful not to get a bunch of his stones disconnected. For example:

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[go]$$Bc The marked stones are one foot in the grave.
$$ | . . . . . . W X X . . . . . . O X . . |
$$ | . . O . X . W W . . . . . . X X . X . |
$$ | . . O . . X X W . W 5 . . . . O X . . |
$$ | . O . O . . W W . X 4 . . . . X O . . |
$$ | . . O X X X . . 3 . . O . . O O X . . |
$$ | . X X O . . . 1 . 2 . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

With this in mind, let's try doing the counting. The branch of mathematics called probability provides the appropriate framework for determining the value of endgame moves. To carry out the calculation, two pieces of data are required--the set of possible outcomes and the respective probabilities of each outcome coming about (those of you who play poker will know this as the "expected value" calculation).

Now, let's focus on the following area, where the task is to evaluate the difference between White playing at "a" and Black playing at "b":

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[go]$$B
$$ . . X X O . O . . . .
$$ O . . O O . X . . . .
$$ X X X a . . . . O . .
$$ O . . . b . . . . . .
$$ . . . . . . . . . . .
$$ ---------------------[/go]

Let's look first at White playing at "a":

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[go]$$W Diagram Da
$$ . . X X O . O . . . .
$$ O . . O O . X . . . .
$$ X X X 1 . . . . O . .
$$ O . c d . . . . . . .
$$ . . . . . . . . . . .
$$ ---------------------[/go]

Here, let's make the assumption that Black must remain locally alive in the bottom left corner (a pretty good assumption, considering the aji in the full board position). In that case, Black should not let White play "c." Hence, Black has the choice of "c" and "d." However, "c" lets Black keep sente while "d" is less likely to do so. Therefore, let's assume Black will play "c" with probability 1. This leads to:

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[go]$$B Diagram Dc
$$ . . X X O . O . . . .
$$ O . . O O . X . . . .
$$ X X X O . . . . O . .
$$ O . 1 2 6 . . . . . .
$$ . . 5 3 4 . . . . . .
$$ ---------------------[/go]

Here, Black has 5 points (including the capture) and White has 30 points. Note that I assume the lone Black stone will be captured and that the entire area on the right will be White's. The first assumption is reasonable, but may introduce a slight error to the calculation. This is so because Black can benefit from the aji this stone offers. The second assumption is not correct, but it is irrelevant because these additional points will by canceled by similar points coming from the calculation of Black playing "b"--that is, what we seek is not the absolute value of points in the position but the difference in the values of two moves, meaning that any points not affected by the moves will cancel out.

Hence, adopting the chess convention that White is + and Black is -, the value of White playing "a" is Da = Dc = 30 + (-5) = 25. The probability of this outcome happening is P(Da) = 1.

Next, let's look at Black playing "b":

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[go]$$B Diagram Db
$$ . . X X O . O . . . .
$$ O . . O O . X . . . .
$$ X X X . . . . . O . .
$$ O . . . 1 . . . . . .
$$ . . . . . . . . . . .
$$ ---------------------[/go]

With White needing to worry about getting cut, perhaps the best White can do is the following:

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[go]$$W Diagram Db continued
$$ . . X X O . O 3 . . .
$$ O . . O O . X 1 . 7 .
$$ X X X 9 . . 2 6 O . .
$$ O . . . X . . 8 4 5 .
$$ . . . . . . . . . . .
$$ ---------------------[/go]

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[go]$$B Diagram Db continued (2)
$$ . . X X O . O O . . .
$$ O . . O O 3 X O . O .
$$ X X X O 4 2 X X O . .
$$ O . . 1 X 5 . X X O .
$$ . . . . . . . . e f .
$$ ---------------------[/go]

Next, "e" is gote for White while "f" is sente for Black. Therefore, White is likely to continue playing in the area. Given this, let's take the probability of White "e" to be 2/3 and the probability of Black getting to play "f" to be 1/3. White "e" leads to:

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[go]$$W Diagram De
$$ . . X X O . O O . . .
$$ O . . O O X X O . O .
$$ X X X O O O X X O . .
$$ O . . X X X . X X O .
$$ . . . . . . . 2 1 3 .
$$ ---------------------[/go]

The value of this diagram is De = 9 +(-12) = (-3). The probability of this outcome is P(De) = 2/3. As for Black "f":

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[go]$$B Diagram Df
$$ . . X X O . O O . . .
$$ O . . O O X X O . O .
$$ X X X O O O X X O . .
$$ O . . X X X . X X O 4
$$ . . . . . . . . 3 1 2
$$ ---------------------[/go]

Df = 7 + (-13) = (-6), P(Df) = 1/3.

Therefore, the value of Black playing "b" is Db = (2/3)*(-3) + (1/3)*(-6) = (-4).

From this, it follows that the difference between White playing on the bottom and Black playing there is D(a - b) = D(a) - D(b) = 25 - (-4) = 29. This value might be somewhat inaccurate given the various assumptions made. However, the biggest problem that could plague this result is if I failed to play the best moves from either side throughout the analysis (I am especially worried regarding White's response to Black "b"). Nevertheless, notwithstanding the exact numerical value of the move on the bottom, the conclusion stands. Playing on that part of the board is huge.

Would anyone care to analyze the bottom right corner?

He can make the center stones live, but that is not a big gain. He can also be gote.

ZOMG, if this is what’s needed to become a good Go player, then I better give up—I need to take off my shoes when I want to count to twenty.

Math to the rescue!

In all seriousness, though, once the position becomes simple enough (endgame, especially late endgame), it is mathematically possible--even if tedious and time-consuming--to calculate exactly the value of each move. The problem is, however, that usually the player only has a limited amount of time per move (unlike during these Malkovich games). Therefore, I find it amazing how Lee Changho and other professionals can do all these calculations (or estimates thereof) with great precision in a matter of minutes.

hum.....getting warmer...

He doesn't have to do this now, just waste of ko threats.

I will accept trade if he wants