Hi,
I have another tsumego from 321go:

"What is the value of playing at A?" (not saying for which colour)
(Then it gives a "3" as answer.)

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . . . . . . . . |
$$ | . . . . . . X . . |
$$ | . . , . . . X O . |
$$ | . . . . . . X O . |
$$ | . . . X , X X O . |
$$ | . . . . . X O O . |
$$ | X X X X X O , . . |
$$ | a O O O X O . O . |
$$ | . . O O O . . . . |
$$ +-------------------+[/go]

The general chapter seems to be about counting, the exercises before that were about either counting territory after finding 1 move, or making territory plus capturing 1 stone.
They were NOT about living.

But I see no advantage for black or white taking "A".
If black takes A, white can connect.
If white takes A, she reduces her liberties while winning nothing.

So, why does it make points for anyone to play at "A", and why 3??
3 can't mean capturing the whole white group.

Hi Jika,

( Tap the Show buttons to see hidden contents. )

Please, Ed. A play at "a" only gains 1½ pts.

Jika, by value of a move they mean the difference between the territorial value when Black plays first and the territorial value when White plays first. As Ed shows, that difference is 3 points. The differerence is also called the swing value.

A related question is what is the territorial value of the original local position? Since the local position is a gote, it is the average of the value after Black plays first (0) and the value after White plays first (-3, from Black's perspective), or -1½ pts. When Black plays first, she gains 1½ pts. (on average), moving from a position worth -1½ to a position worth 0. Likewise, when White plays first he also gains 1½ pts., moving from a position worth -1½ to a position worth -3.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Hi Bill,

Sorry if any of the following is already covered in your This 'n That thread on endgame studies.

I agree with the posts that have been written, but I want to try to say things in an easier way. Not sure if it'll help, but I'll try.

So let's simplify things, and finish the borders on the rest of the board:

Click Here To Show Diagram Code

[go]$$B
$$ +-------------------+
$$ | . . . . . . X O . |
$$ | . . . . . . X O . |
$$ | . . , . . . X O . |
$$ | . . . . . . X O . |
$$ | . . . X , X X O . |
$$ | . . . . . X O O . |
$$ | X X X X X O , . . |
$$ | a O O O X O . O . |
$$ | . . O O O . . . . |
$$ +-------------------+[/go]

To see in practical terms how much 'a' is worth, above, compare the difference in score if white plays:

Click Here To Show Diagram Code

[go]$$B Diagram A
$$ +-------------------+
$$ | . . . . . . X O . |
$$ | . . . . . . X O . |
$$ | . . , . . . X O . |
$$ | . . . . . . X O . |
$$ | . . . X , X X O . |
$$ | . . . . . X O O . |
$$ | X X X X X O , . . |
$$ | W O O O X O . O . |
$$ | . . O O O . . . . |
$$ +-------------------+[/go]

to if black plays:

Click Here To Show Diagram Code

[go]$$B Diagram B
$$ +-------------------+
$$ | . . . . . . X O . |
$$ | . . . . . . X O . |
$$ | . . , . . . X O . |
$$ | . . . . . . X O . |
$$ | . . . X , X X O . |
$$ | . . . . . X O O . |
$$ | X X X X X O , . . |
$$ | 1 O O O X O . O . |
$$ | 3 2 O O O 4 . . . |
$$ +-------------------+[/go]

The black territory in both cases is identical. But the white territory is different: In Diagram A, white has 17 points on the board (surrounding 17 empty intersections). In Diagram B, white has 14 points on the board (surrounding 14 empty intersections).

17 - 14 is 3, so that's where the 3 points comes from.

In a real game, the borders aren't finished off like they are right before you score the game. So people usually look at just that local area and count the point difference.

_________________
be immersed

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

First, thank you all!

Sometimes I get the feeling that my beginner's questions trigger a much more high level discussion, which is good, because it would mean that you find benefits for your own play.

But, hm, these calculations seem quite advanced for me...

@Ed: I did not count the F1 point. I overlooked that it is protected, so I did not count it as white's territory, and even thought black could take it to prevent white from connecting!

@Bill: Is it important to learn these calculations at my stage (given the above mistakes)?

@Kirby: This is helpful. In addition to not seeing F1, I also did not realize how strong white is to the right.

Excuse: the original diagram is on the corner of a bigger board, so the H-stones are towards the middle of the board, not towards the border.

These exercises from 321go seem to be very heterogeneous:
Most are simply "close a gap or kill stones so you win the territory.
Then it is quite obvious what to do.
And they only want me to count the points the winner gets there.

The other kind of exercises, like this one, are "open", and I seem to miss important points (like F1) or I do not understand how long I have to play out the situation to "see" the result.

Now I'm going back to those exercises I was not able to solve.

PS: What are the conventions of "he" or "she"?
I've seen "she" used for white, or is it interchangeable?
And is it important (will people jump down my throat if I forget to name both genders? And, going into political correctness, what about the usage of the third gender?)

One option: use Black/B, White/W, Black's/B's, White's/W's, etc.

Something like "White wants to defend W's corner"?

Hi Bill,(C): Territorial value = ( 's local points) - ( 's local points) = 2 - 3 = -1(B): Territorial value = ( 's local points) - ( 's local points) = 2 - 2 = 0.
How to calculate Swing_value = 0 ?

(A): confused: what are the 2 and 2½ in "Territorial value = 2 - 2½" ?

Thanks.

Not to worry. I knew nothing about them until I was 2 kyu.



No.



There is no overall standard. I go by yin and yang. Yin = feminine = black; yang = masculine = white. Others do the reverse. Others use only one pronoun.



Just be consistent.



As you wish.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

No matter who fills the dame the result is the same.



Black has 2 pts. White has 2½ pts.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Hi Bill,

Thanks for being patient with these 30k questions. The whole number 2 is clear (for both B and W).
How to derive the ½ for white?

B has exactly 2 points (clear).
W has at least 2 points (clear); 3 max (also clear).
I can see one can argue there's a 50% chance W will get the extra 1 point.
But how to derive the (magical?) 50% odds?
Say the probability lies between 0.0 and 1.0;
how to derive exactly ½, and not any other value between 0 and 1?

Is it from the average of:
((B var): territorial value if first; -1)
-- and --
((C var): territorial value if first; 0);
thus (-1 + 0)/2 ? ( for this double-gote situation ).

Just to confuse the discussion further (from a 50 k's perspective):

)

Maybe the situation in the first diagram is that B has taken the point where W could make an eye, so who gets the left over dame point does not matter, so it does not matter who's move it is?

But if white's possible eye-point is not taken yet, whoever's move it is will (considering the local situation only) take it with his/her next move; therefore there is a 50% chance for white taking it and getting an additional point, while black taking it would get him no points? (It would just create the situation of the first diagram, 2-2, plus 1 dame??)

This would explain the 50%, because considering a local move only, the likelihood of having the next move is 50%?

Please ignore if nonsense.

I managed to solve 3 exercises on this basis, but now I'm stuck with another one (sigh):



I thought the solution would be 7 (the max points for B):
white taking A creates 1 point (A1).
black taking A kills the three stones (3x2=6) plus takes A1 (6+1=7).
They can't have the same territorial value both at the same time, so 7-1 does not work either?!

So, why 8?
Or maybe it is 3?!
(50% chance that W gets A, giving him 0+1/2 on A1;
50% chance that B gets A, getting the three stones+1 point, so 0+1/2x7 (in my calculation, see above)=3 1/2)

I like maths, but right now I'm feeling totally confused.

The easy way is through the method of multiples (i.e., the mean value theorem).

Click Here To Show Diagram Code

[go]$$B 2(A) Score = -1
$$ +---------------------+
$$ | . O . O . 1 X . X . |
$$ | O O O O O O X X X X |
$$ | O O O O O O X X X X |
$$ | . O . O . 2 X . X . |
$$ +---------------------+[/go]

This board contains 2 copies of A. The score is -1. That means that A is worth ½ pt. on average. The same is true for 2N copies, no matter how large N is.

and are miai. It does not matter who plays first, or which copy they play in, the score will be the same.



There is more than one way to derive the probability. But IMO the clearest way to think about this is in terms of fuzzy logic, that is, in terms of possibilities. Unless we know better, the possibility that Black will play first in A is equal to the possibility that White will play first.

In any event, the mean value justifies the probabilities, not the other way around.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

@Jika: 7+1=8

In the endgame the board divides up into independent regions of play. Unless we can read the play out, we typically do not know who will play first in any given region. If the region is gote, we may assume that the chances are 50-50 that either player will play first. Since a gote dame gains nothing, it does not matter who fills it.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Hi Bill, Trying to work out a simpler version of post#15:

Click Here To Show Diagram Code

[go]$$ x
$$ +---------------------+
$$ | . O . O . O X . X . |
$$ | O O O O X X X X X X |
$$ +---------------------+[/go]

Click Here To Show Diagram Code

[go]$$W (a)
$$ +---------------------+
$$ | . O . O 1 O X . X . |
$$ | O O O O X X X X X X |
$$ +---------------------+[/go]

(a) Territorial value = ( 's local points) - ( 's local points) = 2 - 2 = 0

Click Here To Show Diagram Code

[go]$$B (b)
$$ +---------------------+
$$ | . O . O 1 O X . X . |
$$ | O O O O X X X X X X |
$$ +---------------------+[/go]

(b) Territorial value = ( 's local points) - ( 's local points) = 4 - 2 = 2

swing value = (b) - (a) = 2 - 0 = 2 (?)The territorial value of the original local position (x) is ((2 + 0)/2) = 1 ?

Hi, Ed.

Correct.

Correct.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.