Thermography

Talk about improving your game, resources you like, games you played, etc.
Post Reply
Bill Spight
Honinbo
Posts: 10905
Joined: Wed Apr 21, 2010 1:24 pm
Has thanked: 3651 times
Been thanked: 3373 times

Re: Thermography

Post by Bill Spight »

Gérard TAILLE wrote:
Bill Spight wrote:
Gérard TAILLE wrote: BTW I asked me the following problem: what are the solutions of the equation
G + G = 0
Of course we have the two obvious solutions G = 0 and G = *
Does it exist other solutions or do you have a proof that we have only these two solutions?
Combinatorial games form a group, so for every game G there exists a game, -G. In go, you just switch the colors of the stones. :)

What do you mean Bill?
My question was about the equation G + G = 0, not the equation G - G = 0.
Well, if G + G = 0 then G = -G.

For all impartial games, which have symmetrical trees, G = -G. :) So all impartial games satisfy that equation.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
Top
Bill Spight
Honinbo
Posts: 10905
Joined: Wed Apr 21, 2010 1:24 pm
Has thanked: 3651 times
Been thanked: 3373 times

Re: Thermography

Post by Bill Spight »

Gérard TAILLE wrote:
Bill Spight wrote:
Gérard TAILLE wrote: For the equation
G + G + G = 0
does it exist another solution than G = 0 ?
I don't know, but I don't think so. G has to be fuzzy, and it cannot be impartial
What does mean impartial Bill?
Sorry, I think I accidentally cut out some of my earlier answer. Impartial games are those where at each turn, each play has the same options. Each impartial game is its own negative.

So if G is impartial, then G + G = 0.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
Top
Gérard TAILLE
Gosei
Posts: 1346
Joined: Sun Aug 23, 2020 2:47 am
Rank: 1d
GD Posts: 0
Has thanked: 21 times
Been thanked: 57 times

Re: Thermography

Post by Gérard TAILLE »

I try to understand infinitesimals but it is not that easy

Edit
Click Here To Show Diagram Code
[go]$$
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | . X . . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
How do you analyse this position?
Top
Gérard TAILLE
Gosei
Posts: 1346
Joined: Sun Aug 23, 2020 2:47 am
Rank: 1d
GD Posts: 0
Has thanked: 21 times
Been thanked: 57 times

Re: Thermography

Post by Gérard TAILLE »

Gérard TAILLE wrote:I try to understand infinitesimals but it is not that easy

Edit
Click Here To Show Diagram Code
[go]$$
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | . X . . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
How do you analyse this position?
Oops, I believe this position is equal to ↑↑ which is not obvious is it?
Top
Bill Spight
Honinbo
Posts: 10905
Joined: Wed Apr 21, 2010 1:24 pm
Has thanked: 3651 times
Been thanked: 3373 times

Re: Thermography

Post by Bill Spight »

Gérard TAILLE wrote:I try to understand infinitesimals but it is not that easy

Edit
Click Here To Show Diagram Code
[go]$$
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | . X . . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
How do you analyse this position?
Well first, let's look at the play at temperature 1 (temperature 0 in the chilled game).
Click Here To Show Diagram Code
[go]$$B Black first
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | 1 X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 2 X 3 . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
Black first moves in gote to a position worth +4 (+3 in chilled go.) Black can transpose :b1: and :b3:.
Click Here To Show Diagram Code
[go]$$W White first
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | 4 X . . . . . . . . |
$$ | 1 X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 3 X 2 . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
White to play can move to a position worth +3 in sente. Not that this play is White's sente, OC. ;) This tells us that this go infinitesimal is greater than 0 (from Black's point of view). The numerical score is still +3.

:w1: is correct. :b2: and :b4: transpose.
Click Here To Show Diagram Code
[go]$$W White moves to star
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | a X . . . . . . . . |
$$ | 1 X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 3 X 2 . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
The go infinitesimal after :w1: - :w3: is star (*). If :w2: is at a instead, then after :w3: that go infinitesimal is also *. So the go infinitesimal after :w1: is also *.
Click Here To Show Diagram Code
[go]$$W White moves to upstar
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | a X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 1 X b . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
After :w1: here the go infinitesimal at a is up (↑) and the one at b is *. ↑ + * is written ↑*. (In fact, * plus almost anything may be written with that thing followed by *. :)) Now,

↑* > * , i.e.

↑* - * = ↑ > 0 .

So for White * dominates ↑*. That's why :w1: in this diagram is incorrect in CGT.

When Black plays first things get tricky. ;)
Click Here To Show Diagram Code
[go]$$B Black first, I
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 2 X 1 . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
:b1:, OC, raises the local temperature, forcing :w2:. The resulting infinitesimal is ↑, which is greater than 0. So this looks pretty good for Black. If White does not play :w2:, then Black at 2 gets a chilled score of 9 - 2 = 7, a gain of 4 points over the original score of 3.
Click Here To Show Diagram Code
[go]$$B Black first, II
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | 1 X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 2 X . . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
:b1: carries the same size threat as :b1: in the previous diagram, but the result after :w2: is different. This way, the infinitesimal is *, which is confused with 0. Since ↑ > 0, we might think that the first diagram is better for Black, but ↑ <> * (up is confused with star). So we can write the original infinitesimal this way:

{{4|↑},{4|*}||*}

Surely we can simplify this. :) Especially since we know that it is greater than 0.

We can do so if either of the Black options reverses, so that Black continues play in a unit sequence. That is so if this infinitesimal is greater than or equal to * or ↑. We can guess the answer, but let's prove it.

First let's try *. The question boils down to this: Can White to play win the difference game? If not, the infinitesimal is greater than or equal to *. Subtracting * is the same as adding it, so let's play this game.

{{4|↑},{4|*}||*} + *

White to play wins by playing to * on the left, as * + * = 0.

Now let's try ↑. The negative of ↑ is ↓ = {*|0}. Here is the game.

{{4|↑},{4|*}||*} + {*|0}

We already know that the left game is greater than 0, so White cannot win by playing to 0 on the right. If White plays to * on the left, Black wins by playing to * on the right. White first cannot win. That gives us the following sequence of play.
Click Here To Show Diagram Code
[go]$$B Black first, I
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | 3 X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 2 X 1 . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
We may consider :b1: - :b3: as a unit.

That means that this infinitesimal reduces to

{0,{4|*}||*}

Gérard, you come up with the most interesting positions.
:D :bow: :bow: :bow:

Edited for correctness. :)

Edit2: Well, almost. I just took another look, and {4|*} > 0, so we can reduce it still further. :)

{4|*||*}
Last edited by Bill Spight on Wed Nov 11, 2020 6:41 pm, edited 3 times in total.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
Top
Bill Spight
Honinbo
Posts: 10905
Joined: Wed Apr 21, 2010 1:24 pm
Has thanked: 3651 times
Been thanked: 3373 times

Re: Thermography

Post by Bill Spight »

Gérard TAILLE wrote:
Gérard TAILLE wrote:I try to understand infinitesimals but it is not that easy

Edit
Click Here To Show Diagram Code
[go]$$
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | . X . . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
How do you analyse this position?
Oops, I believe this position is equal to ↑↑ which is not obvious is it?
It's actually less than ↑↑.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
Top
Gérard TAILLE
Gosei
Posts: 1346
Joined: Sun Aug 23, 2020 2:47 am
Rank: 1d
GD Posts: 0
Has thanked: 21 times
Been thanked: 57 times

Re: Thermography

Post by Gérard TAILLE »

Bill Spight wrote:
Click Here To Show Diagram Code
[go]$$B Black first, I
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 2 X 1 . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
:b1:, OC, raises the local temperature, forcing :w2:. The resulting infinitesimal is ↑, which is greater than 0. So this looks pretty good for Black. If White does not play :w2:, then Black at 2 gets a chilled score of 9 - 2 = 7, a gain of 4 points over the original score of 3.
Here is the point of my position Bill : the exchange :b1: :w2: in the above diagram is not that good for black because it is in fact a privilege for black
By avoiding this exchange black can keep in reserve the possibility after after :w1: in the following diagram to not answer at "a" !
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 1 X a . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
You said my position is less than ↑↑ but how you play the difference game?
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------------
$$ | O X . . . . O O O O |
$$ | . X . . . . O X O X |
$$ | 1 X X . . . O . O . |
$$ | O O X X X . O 4 O 2 |
$$ | 3 X . . X . X X X X |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
Top
Bill Spight
Honinbo
Posts: 10905
Joined: Wed Apr 21, 2010 1:24 pm
Has thanked: 3651 times
Been thanked: 3373 times

Re: Thermography

Post by Bill Spight »

Gérard TAILLE wrote:
Bill Spight wrote:
Click Here To Show Diagram Code
[go]$$B Black first, I
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 2 X 1 . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
:b1:, OC, raises the local temperature, forcing :w2:. The resulting infinitesimal is ↑, which is greater than 0. So this looks pretty good for Black. If White does not play :w2:, then Black at 2 gets a chilled score of 9 - 2 = 7, a gain of 4 points over the original score of 3.
Here is the point of my position Bill : the exchange :b1: :w2: in the above diagram is not that good for black because it is in fact a privilege for black
By avoiding this exchange black can keep in reserve the possibility after after :w1: in the following diagram to not answer at "a" !
Click Here To Show Diagram Code
[go]$$W
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 1 X a . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
You said my position is less than ↑↑ but how you play the difference game?
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------------
$$ | O X . . . . O O O O |
$$ | . X . . . . O X O X |
$$ | 1 X X . . . O . O . |
$$ | O O X X X . O 4 O 2 |
$$ | 3 X . . X . X X X X |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$W White to play and win
$$ -----------------------
$$ | O X . . . . O O O O |
$$ | . X . . . . O X O X |
$$ | 1 X X . . . O . O . |
$$ | O O X X X . O 3 O 2 |
$$ | . X . . X . X X X X |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
Top
Gérard TAILLE
Gosei
Posts: 1346
Joined: Sun Aug 23, 2020 2:47 am
Rank: 1d
GD Posts: 0
Has thanked: 21 times
Been thanked: 57 times

Re: Thermography

Post by Gérard TAILLE »

Bill Spight wrote:
Click Here To Show Diagram Code
[go]$$W White to play and win
$$ -----------------------
$$ | O X . . . . O O O O |
$$ | . X . . . . O X O X |
$$ | 1 X X . . . O . O . |
$$ | O O X X X . O 3 O 2 |
$$ | . X . . X . X X X X |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
You are right Bill.
I will look at other ideas for positions and I have also to look how to discover more easly equivalent positions.
Thank you again for your help.
Top
Bill Spight
Honinbo
Posts: 10905
Joined: Wed Apr 21, 2010 1:24 pm
Has thanked: 3651 times
Been thanked: 3373 times

Re: Thermography

Post by Bill Spight »

Correction. I wrote:
Gérard TAILLE wrote:I try to understand infinitesimals but it is not that easy
Click Here To Show Diagram Code
[go]$$
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | . X . . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
How do you analyse this position?
Moi wrote: This infinitesimal reduces to

{0,{4|*}||*}

Gérard, you come up with the most interesting positions.
:D :bow: :bow: :bow:

Edited for correctness. :)
Edit2: Well, almost. I just took another look, and {4|*} > 0, so we can reduce it still further. :)

{4|*||*}

IOW, this is canonical play.
Click Here To Show Diagram Code
[go]$$B Black first
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | 1 X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 2 X 3 . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
Click Here To Show Diagram Code
[go]$$W White first
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | 2 X . . . . . . . . |
$$ | 1 X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 3 X 4 . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
However, at temperature 1 Black does not have to play :b3: in the first diagram, nor does she have to play :b4: in the second diagram. The former is why Black can get the last play in this diagram.
Click Here To Show Diagram Code
[go]$$B Black to play and win
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | 1 X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | 2 X . . X . . . . . |
$$ | O O X X X - - . . . |
$$ | O O O O O O - X X X |
$$ | . . . . . . O O O 3 |
$$ | . . . . . . . . O . |
$$ | . . . . . . . . O X |
$$ -----------------------[/go]
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
Top
Gérard TAILLE
Gosei
Posts: 1346
Joined: Sun Aug 23, 2020 2:47 am
Rank: 1d
GD Posts: 0
Has thanked: 21 times
Been thanked: 57 times

Re: Thermography

Post by Gérard TAILLE »

Click Here To Show Diagram Code
[go]$$
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | . X . . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
Finally this position reduces to {4|*||*} which is somewhere between ↑ and ↑↑.
Taking a game with such infinetisimals as subgame, can CGT help to handle these infinitesimals for gaining tedomari or have we to read the game to choose the best move?
As an example I do not know if I can use the value 1 or 2 for the atomic weight of this infinitesimal and I do not know if I even can use the result of the atomic weight for a game with such subgame.
Top
Bill Spight
Honinbo
Posts: 10905
Joined: Wed Apr 21, 2010 1:24 pm
Has thanked: 3651 times
Been thanked: 3373 times

Re: Thermography

Post by Bill Spight »

Gérard TAILLE wrote:
Click Here To Show Diagram Code
[go]$$
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | . X . . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
Finally this position reduces to {4|*||*} which is somewhere between ↑ and ↑↑.
Taking a game with such infinetisimals as subgame, can CGT help to handle these infinitesimals for gaining tedomari or have we to read the game to choose the best move?
Well, most go infinitesimals are not as interesting as this one. ;)

Fortunately, playing go infinitesimals is much easier than playing the endgame as whole. In practice, playing them nearly perfectly in actual games should be as easy as falling off a log for an amateur dan player who has studied them. :) A few years ago I wrote an article, which turned into a pair of articles, for the startup online go magazine, Myosu, now unfortunately defunct, about a very ancient game, the game for a pair of gold-petaled bowls, which has been reviewed a number of times over the centuries. Near the end the White player made the wrong play in a complicated go infinitesimal. I spotted it immediately, and, since the other go infinitesimals were simple, it was easy to read out the whole board to the end. AFAICT, I was the first reviewer to find that mistake. But I had the advantage of having read Mathematical Go. :D
Gérard TAILLE wrote:As an example I do not know if I can use the value 1 or 2 for the atomic weight of this infinitesimal and I do not know if I even can use the result of the atomic weight for a game with such subgame.
My original play of the game at temperature 1 showed that it played a lot like an ↑. In a real game I would probably stop there and treat it much like one, delving more deeply only if necessary. :) OC, in our discussion I have to analyze it thoroughly, and even then I made a couple of slips. ;) But finding its reduced form was quite satisfying and a lot of fun. :)

In reducing it we discovered a couple of interesting things. It is confused with *, but greater than ↑. OC, ↑ has an atomic weight of 1 and * has an atomic weight of 0, so this game appears to have an atomic weight of 1. I find calculating atomic weight by the definition to be difficult and tedious, but if this infinitesimal is confused with ↑* it will have an atomic weight of 1. Let's see.

{4|*||*} + * + {*|0}

White to play can win by playing to * on the left, since * + * = 0 and {*|0} < 0.

Black to play can win by playing to * on the right, since {4|*||*} > 0.

So {4|*||*} has atomic weight 1, it is greater than ↑ and confused with * and ↑*. That should be enough information to play it nearly flawlessly in a real game without much effort. :)
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
Top
Gérard TAILLE
Gosei
Posts: 1346
Joined: Sun Aug 23, 2020 2:47 am
Rank: 1d
GD Posts: 0
Has thanked: 21 times
Been thanked: 57 times

Re: Thermography

Post by Gérard TAILLE »

Bill Spight wrote:
Gérard TAILLE wrote:
Click Here To Show Diagram Code
[go]$$
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | . X . . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
Finally this position reduces to {4|*||*} which is somewhere between ↑ and ↑↑.
Taking a game with such infinetisimals as subgame, can CGT help to handle these infinitesimals for gaining tedomari or have we to read the game to choose the best move?
Well, most go infinitesimals are not as interesting as this one. ;)
Thank you Bill, it is a pleasure, OC
Bill Spight wrote:
Gérard TAILLE wrote:As an example I do not know if I can use the value 1 or 2 for the atomic weight of this infinitesimal and I do not know if I even can use the result of the atomic weight for a game with such subgame.
My original play of the game at temperature 1 showed that it played a lot like an ↑. In a real game I would probably stop there and treat it much like one, delving more deeply only if necessary. :) OC, in our discussion I have to analyze it thoroughly, and even then I made a couple of slips. ;) But finding its reduced form was quite satisfying and a lot of fun. :)

In reducing it we discovered a couple of interesting things. It is confused with *, but greater than ↑. OC, ↑ has an atomic weight of 1 and * has an atomic weight of 0, so this game appears to have an atomic weight of 1. I find calculating atomic weight by the definition to be difficult and tedious, but if this infinitesimal is confused with ↑* it will have an atomic weight of 1. Let's see.

{4|*||*} + * + {*|0}

White to play can win by playing to * on the left, since * + * = 0 and {*|0} < 0.

Black to play can win by playing to * on the right, since {4|*||*} > 0.

So {4|*||*} has atomic weight 1, it is greater than ↑ and confused with * and ↑*. That should be enough information to play it nearly flawlessly in a real game without much effort. :)
Here is a game example
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------------
$$ | O X W W . . . O - - |
$$ | . X W X X X X O - - |
$$ | . X X - - - O O - - |
$$ | O O X X X - - - - - |
$$ | . X . . X - - - - - |
$$ | O O X X X - - - - - |
$$ | O O O O X - - - - - |
$$ | O X . . X - - - - - |
$$ | O O O O O O O X - - |
$$ | O . B . . . X X - - |
$$ -----------------------[/go]
The atomic weight of this game is zero. In this case because the threat of white marked stones is greater than the threat of black marked stone white to play normally wins tedomari but here it is not the case is it?
Top
Bill Spight
Honinbo
Posts: 10905
Joined: Wed Apr 21, 2010 1:24 pm
Has thanked: 3651 times
Been thanked: 3373 times

Re: Thermography

Post by Bill Spight »

Gérard TAILLE wrote:
Bill Spight wrote:
Gérard TAILLE wrote:
Click Here To Show Diagram Code
[go]$$
$$ -----------------------
$$ | O X . . . . . . . . |
$$ | . X . . . . . . . . |
$$ | . X X . . . . . . . |
$$ | O O X X X . . . . . |
$$ | . X . . X . . . . . |
$$ | O O X X X . . . . . |
$$ | O O O O O . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------[/go]
Finally this position reduces to {4|*||*} which is somewhere between ↑ and ↑↑.
Taking a game with such infinetisimals as subgame, can CGT help to handle these infinitesimals for gaining tedomari or have we to read the game to choose the best move?
Well, most go infinitesimals are not as interesting as this one. ;)
Thank you Bill, it is a pleasure, OC
Bill Spight wrote:
Gérard TAILLE wrote:As an example I do not know if I can use the value 1 or 2 for the atomic weight of this infinitesimal and I do not know if I even can use the result of the atomic weight for a game with such subgame.
My original play of the game at temperature 1 showed that it played a lot like an ↑. In a real game I would probably stop there and treat it much like one, delving more deeply only if necessary. :) OC, in our discussion I have to analyze it thoroughly, and even then I made a couple of slips. ;) But finding its reduced form was quite satisfying and a lot of fun. :)

In reducing it we discovered a couple of interesting things. It is confused with *, but greater than ↑. OC, ↑ has an atomic weight of 1 and * has an atomic weight of 0, so this game appears to have an atomic weight of 1. I find calculating atomic weight by the definition to be difficult and tedious, but if this infinitesimal is confused with ↑* it will have an atomic weight of 1. Let's see.

{4|*||*} + * + {*|0}

White to play can win by playing to * on the left, since * + * = 0 and {*|0} < 0.

Black to play can win by playing to * on the right, since {4|*||*} > 0.

So {4|*||*} has atomic weight 1, it is greater than ↑ and confused with * and ↑*. That should be enough information to play it nearly flawlessly in a real game without much effort. :)
Here is a game example
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------------
$$ | O X W W . . . O - - |
$$ | . X W X X X X O - - |
$$ | . X X - - - O O - - |
$$ | O O X X X - - - - - |
$$ | . X . . X - - - - - |
$$ | O O X X X - - - - - |
$$ | O O O O X - - - - - |
$$ | O X . . X - - - - - |
$$ | O O O O O O O X - - |
$$ | O . B . . . X X - - |
$$ -----------------------[/go]
The atomic weight of this game is zero. In this case because the threat of white marked stones is greater than the threat of black marked stone white to play normally wins tedomari but here it is not the case is it?
I don't know about normally, but with only the two long corridors White wins. I.e., their sum is negative. But, OC, the other sum is positive, so it's a question of which, if either, is greater.
Click Here To Show Diagram Code
[go]$$W White to play
$$ -----------------------
$$ | O X W W 4 3 1 O - - |
$$ | . X W X X X X O - - |
$$ | 5 X X - - - O O - - |
$$ | O O X X X - - - - - |
$$ | . X . . X - - - - - |
$$ | O O X X X - - - - - |
$$ | O O O O X - - - - - |
$$ | O X . 8 X - - - - - |
$$ | O O O O O O O X - - |
$$ | O . B 7 6 2 X X - - |
$$ -----------------------[/go]
With normal play Black gets the last play. :) :w5: at 6 leaves a positive sum on the table.
Click Here To Show Diagram Code
[go]$$W White to play, variation
$$ -----------------------
$$ | O X W W 6 5 3 O - - |
$$ | . X W X X X X O - - |
$$ | 1 X X - - - O O - - |
$$ | O O X X X - - - - - |
$$ | . X . . X - - - - - |
$$ | O O X X X - - - - - |
$$ | O O O O X - - - - - |
$$ | O X . 8 X - - - - - |
$$ | O O O O O O O X - - |
$$ | O . B 7 4 2 X X - - |
$$ -----------------------[/go]
:w1: here leads to a transposition, thanks to the :wc: stones.
Click Here To Show Diagram Code
[go]$$B Black to play
$$ -----------------------
$$ | O X W W 5 4 2 O - - |
$$ | . X W X X X X O - - |
$$ | 7 X X - - - O O - - |
$$ | O O X X X - - - - - |
$$ | 8 X . . X - - - - - |
$$ | O O X X X - - - - - |
$$ | O O O O X - - - - - |
$$ | O X . 9 X - - - - - |
$$ | O O O O O O O X - - |
$$ | O . B 6 3 1 X X - - |
$$ -----------------------[/go]
Normal play with Black first allows White to play :w4: with sente before replying with :w6:, but the positive sum remains on the board, and Black gets the last play.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
Top
Gérard TAILLE
Gosei
Posts: 1346
Joined: Sun Aug 23, 2020 2:47 am
Rank: 1d
GD Posts: 0
Has thanked: 21 times
Been thanked: 57 times

Re: Thermography

Post by Gérard TAILLE »

Here is a theoritical question on infinitesimals.

Firstly we know that we have ↑ || * and it may be difficult to compare a move in ↑ and a move in *. However we know also that the atomic weight of ↑ is equal to 1 and the atomic weight of * is equal to 0. As a consequence it may seem preferable for black to play in * rather that ↑ in order to not lose this atomic weight of 1.

Secondly we know that * is a special infinitesimal with the property * + * = 0. Taking a game G made of infinitesimals we can thus always assume that we have only 0 or 1 * in the game (the other * being miai).

Now is my question : Assume a game G + ↑ + * and, because I add here an *, assume there are no * in G. In this context (no * in G) can we say that a black move in * dominates a black move in ↑ ?
Top
Post Reply

Return to “Amateurs”