#183 - Magicwand vs Lovelove

lovelove · Post by **lovelove** » Fri Nov 09, 2012 12:44 pm

Click Here To Show Diagram Code: [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 . | $$ | . . . X . . . . . O . O X X O O O . . | $$ | . . . . . . . . . . . . X O X X . . . | $$ | . . . . . . . . . . . . 9 8 O X O . . | $$ | . . X , . . . . . , . . . . . X 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]

Magicwand · Post by **Magicwand** » Fri Nov 09, 2012 1:02 pm

O10

Click Here To Show Diagram Code: [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 . | $$ | . . . X . . . . . O . O X X O O O . . | $$ | . . . . . . . . . . . . X O X X . . . | $$ | . . . . . . . . . . . . X O O X O . . | $$ | . . X , . . . . . , . . . 0 . 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]

use

$$Bcm111 white : 1 black : 1

and start from 1

The Intrepid · Post by **The Intrepid** » Fri Nov 09, 2012 4:16 pm

mitsun wrote:Maybe someone else wants to try counting some of the other big areas?

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:

Click Here To Show Diagram Code: [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":

Click Here To Show Diagram Code: [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":

Click Here To Show Diagram Code: [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:

Click Here To Show Diagram Code: [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":

Click Here To Show Diagram Code: [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:

Click Here To Show Diagram Code: [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]

Click Here To Show Diagram Code: [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:

Click Here To Show Diagram Code: [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":

Click Here To Show Diagram Code: [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?

lovelove · Post by **lovelove** » Fri Nov 09, 2012 4:23 pm

Click Here To Show Diagram Code: [go]$$Bcm111 white : 1 black : 1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 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 . | $$ | . . . X . . . . . O . O X X O O O . . | $$ | . . . . . . . . . . . . X O X X 3 . . | $$ | . . . . . . . . . . . . X O O X O . . | $$ | . . X , . . . . . , . . 1 O . X O . . | $$ | . . . . . . . X . . . . . 2 X . . . . | $$ | . 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]

Bonobo · Post by **Bonobo** » Fri Nov 09, 2012 5:41 pm

The Intrepid wrote:
[..] the value of White playing "a" is Da = Dc = 30 + (-5) = 25. The probability of this outcome happening is P(Da) = 1.

[..] 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 [..]

[..] The value of this diagram is De = 9 +(-12) = (-3). The probability of this outcome is P(De) = 2/3 [..]

[..] 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 [..]

The Intrepid · Post by **The Intrepid** » Fri Nov 09, 2012 6:04 pm

Bonobo wrote:
The Intrepid wrote:
[..] the value of White playing "a" is Da = Dc = 30 + (-5) = 25. The probability of this outcome happening is P(Da) = 1.

[..] 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 [..]

[..] The value of this diagram is De = 9 +(-12) = (-3). The probability of this outcome is P(De) = 2/3 [..]

[..] 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 [..]

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.

Magicwand · Post by **Magicwand** » Fri Nov 09, 2012 6:09 pm

Click Here To Show Diagram Code: [go]$$Bcm111 white : 1 black : 1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 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 . | $$ | . . . X . . . . . O . O X X O O O . . | $$ | . . . . . . . . . . . . X O X X X 4 . | $$ | . . . . . . . . . . . . X O O X O . . | $$ | . . X , . . . . . , . . X O . X O . . | $$ | . . . . . . . X . . . . . O X . . . . | $$ | . 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]

lovelove · Post by **lovelove** » Fri Nov 09, 2012 6:13 pm

Click Here To Show Diagram Code: [go]$$Bcm111 white : 1 black : 1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 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 . | $$ | . . . X . . . . . O . O X X O O O . . | $$ | . . . . . . . . . . . . X O X X X O . | $$ | . . . . . . . . . . . . X O O X O . . | $$ | . . X , . . . . . , . . X O . X O . . | $$ | . . . . . . . X . . . . . O X . 5 . . | $$ | . 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]

Magicwand · Post by **Magicwand** » Fri Nov 09, 2012 6:19 pm

Click Here To Show Diagram Code: [go]$$Bcm111 white : 1 black : 1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 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 . | $$ | . . . X . . . . . O . O X X O O O . . | $$ | . . . . . . . . . . . . X O X X X O . | $$ | . . . . . . . . . . . . X O O X O . . | $$ | . . X , . . . . . , . . X O . X O . . | $$ | . . . . . . . X . . . . . O X . X 6 . | $$ | . 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]

lovelove · Post by **lovelove** » Fri Nov 09, 2012 6:34 pm

Click Here To Show Diagram Code: [go]$$Bcm111 white : 1 black : 1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 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 . | $$ | . . . X . . . . . O 8 O X X O O O . . | $$ | . . . . . . . . . . 7 . X O X X X O . | $$ | . . . . . . . . . . . . X O O X O . . | $$ | . . X , . . . . . , . . X O . X O . . | $$ | . . . . . . . X . . . 9 . O X . X O . | $$ | . 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]

Magicwand · Post by **Magicwand** » Fri Nov 09, 2012 6:56 pm

Click Here To Show Diagram Code: [go]$$Bcm111 white : 1 black : 1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 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 . | $$ | . . . X . . . . . O O O X X O O O . . | $$ | . . . . . . . . . . X . X O X X X O . | $$ | . . . . . . . . . . . . X O O X O . . | $$ | . . X , . . . . . , . . X O . X O . . | $$ | . . . . . . . X . . . X . O X . X O . | $$ | . O . X . . X O O X . . . . O . X . . | $$ | . . . . . . O X X . . . 0 . . O X . . | $$ | . . 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]

hyperpape · Post by **hyperpape** » Fri Nov 09, 2012 7:16 pm

Bonobo wrote:
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.

lovelove · Post by **lovelove** » Fri Nov 09, 2012 7:19 pm

Click Here To Show Diagram Code: [go]$$Bcm121 white : 1 black : 1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 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 . | $$ | . . . X . . . . . O O O X X O O O . . | $$ | . . . . . . . . . . X . X O X X X O . | $$ | . . . . . . . . . . . . X O O X O . . | $$ | . . X , . . . . . , . . X O . X O . . | $$ | . . . . . . . X . . . X . O X . X O . | $$ | . O . X . . X O O X . . . . O . X . . | $$ | . . . . . . O X X . . . O . . O X . . | $$ | . . O . X . O O . . . . 1 . 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]

Magicwand · Post by **Magicwand** » Sat Nov 10, 2012 5:50 am

Click Here To Show Diagram Code: [go]$$Bcm121 white : 1 black : 1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 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 . | $$ | . . . X . . . . . O O O X X O O O . . | $$ | . . . . . . . . . . X . X O X X X O . | $$ | . . . . . . . . . . . . X O O X O . . | $$ | . . X , . . . . . , . . X O . X O . . | $$ | . . . . . . . X . . . X . O X . X O . | $$ | . O . X . . X O O X . 2 . . O . X . . | $$ | . . . . . . O X X . . . O . . O X . . | $$ | . . O . X . O O . . . . X . 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]

lovelove · Post by **lovelove** » Sat Nov 10, 2012 6:22 am

Click Here To Show Diagram Code: [go]$$Bcm121 white : 1 black : 1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 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 . | $$ | . . . X . . . . . O O O X X O O O . . | $$ | . . . . . . . . . . X . X O X X X O . | $$ | . . . . . . . . . . . . X O O X O . . | $$ | . . X , . . . . . , . . X O . X O . . | $$ | . . . . . . . X . . . X . O X . X O . | $$ | . O . X . . X O O X . O . . O . X . . | $$ | . . . . . . O X X . 3 . O . . O X . . | $$ | . . O . X . O O . . . . X . 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]

Life In 19x19

#183 - Magicwand vs Lovelove

Re: Magicwand vs Lovelove

Re: Magicwand vs Lovelove

Re: Magicwand vs Lovelove

Re: Magicwand vs Lovelove

Deep in my heart I must be a triple digit kyu

Re: Deep in my heart I must be a triple digit kyu

Re: Magicwand vs Lovelove

Re: Magicwand vs Lovelove

Re: Magicwand vs Lovelove

Re: Magicwand vs Lovelove

Re: Magicwand vs Lovelove

Re: Deep in my heart I must be a triple digit kyu

Re: Magicwand vs Lovelove

Re: Magicwand vs Lovelove

Re: Magicwand vs Lovelove