Zugzwang

Bill Spight · Post by **Bill Spight** » Mon Nov 23, 2020 10:13 am

Gérard TAILLE wrote:
Bill Spight wrote:
Gérard TAILLE wrote:2) if a subgame is not completely resolved (as the subgame G = {+5|+12}) at the end of the game then the result of the subgame will be 0 (seki).

How building the corresponding CGT game allowing to get the same result as the real game, knowing that G = {+5|+12} = +6 for a CGT game?
The key is to resolve the game at temperature -1. My rules and Lasker-Maas rules do that. Lasker-Maas rules are quite straightforward. Black plays to +5 on the board with a Black captive, for a net result of +6. If White does not have Black captive to give her, they can trade stones.
OK Bill I see but your rule or Lasker-Maas rule is not J89.
So, if I understood correctly, because in J89 rule there are no ending phase of the game allowing to resolve such subgame by playing at temperature -1, then we cannot modelize the J89 rule by a CGT game can we?

Well, even though CGT is based upon not passing, the players can always stop play when the only plays left are in numbers and score the game. So you can accommodate any assignment of scores, even if they are not based upon CGT sub-zero play.

So if {+5|+12} were possible under the J89 go rules, it would be worth +5.

Gérard TAILLE · Post by **Gérard TAILLE** » Mon Nov 23, 2020 10:46 am

Bill Spight wrote: Well, even though CGT is based upon not passing, the players can always stop play when the only plays left are in numbers and score the game. So you can accommodate any assignment of scores, even if they are not based upon CGT sub-zero play. So if {+5|+12} were possible under the J89 go rules, it would be worth +5.

I do not understand Bill.
if G = {+5|+12} were possible under the J89 go rules then it would be worth +5 under this J89 rule.
But in any CGT game we have always {+5|+12} = +6.
Assume a game ends with 10 G games. Under J89 black will win by 50 points, with a lot of passes for white.
How will be played the CGT game? (I mean without white passes).

Bill Spight · Post by **Bill Spight** » Mon Nov 23, 2020 11:00 am

Gérard TAILLE wrote:
Bill Spight wrote: Well, even though CGT is based upon not passing, the players can always stop play when the only plays left are in numbers and score the game. So you can accommodate any assignment of scores, even if they are not based upon CGT sub-zero play. So if {+5|+12} were possible under the J89 go rules, it would be worth +5.
I do not understand Bill.
if G = {+5|+12} were possible under the J89 go rules then it would be worth +5 under this J89 rule.
But in any CGT game we have always {+5|+12} = +6.

Right. but that is only because CGT games are no pass games. Since J89 allows passes to end play, and only allows its peculiar form of hypothetical play for scoring purposes, we can accept the J89 scores and erect a CGT model on them. (Except for ko positions, OC.)

In chess, a checkmate is worth +1 or -1, even though the winner probably has a large number of moves available, while the loser has none. We just accept the chess score for our model.

Gérard TAILLE · Post by **Gérard TAILLE** » Mon Nov 23, 2020 2:18 pm

Bill Spight wrote:
Gérard TAILLE wrote:
Bill Spight wrote: Well, even though CGT is based upon not passing, the players can always stop play when the only plays left are in numbers and score the game. So you can accommodate any assignment of scores, even if they are not based upon CGT sub-zero play. So if {+5|+12} were possible under the J89 go rules, it would be worth +5.
I do not understand Bill.
if G = {+5|+12} were possible under the J89 go rules then it would be worth +5 under this J89 rule.
But in any CGT game we have always {+5|+12} = +6.
Right. but that is only because CGT games are no pass games. Since J89 allows passes to end play, and only allows its peculiar form of hypothetical play for scoring purposes, we can accept the J89 scores and erect a CGT model on them. (Except for ko positions, OC.)

In chess, a checkmate is worth +1 or -1, even though the winner probably has a large number of moves available, while the loser has none. We just accept the chess score for our model.

Is it the same problem in GO with area counting with position like the following?

Click Here To Show Diagram Code: [go]$$B $$ ----------------------- $$ | . O O X . . . . . . | $$ | X . O X . . . . . . | $$ | X X O X . . . . . . | $$ | . . O X . . . . . . | $$ | O O O X . . . . . . | $$ | X X X X . . . . . . | $$ | . . . . . . . . . . | $$ | . . . . . . . . . . | $$ | . . . . . . . . . . | $$ | . . . . . . . . . . | $$ -----------------------[/go]

Here again black should continue to move while white must pass.

Bill Spight · Post by **Bill Spight** » Mon Nov 23, 2020 2:51 pm

Gérard TAILLE wrote:Is it the same problem in GO with area counting with position like the following?

$$B
$$ -----------------------
$$ | . O O X . . . . . . |
$$ | X . O X . . . . . . |
$$ | X X O X . . . . . . |
$$ | . . O X . . . . . . |
$$ | O O O X . . . . . . |
$$ | X X X X . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------------- $$ | . O O X . . . . . . | $$ | X . O X . . . . . . | $$ | X X O X . . . . . . | $$ | . . O X . . . . . . | $$ | O O O X . . . . . . | $$ | X X X X . . . . . . | $$ | . . . . . . . . . . | $$ | . . . . . . . . . . | $$ | . . . . . . . . . . | $$ | . . . . . . . . . . | $$ -----------------------[/go]
Here again black should continue to move while white must pass.

Well, in CGT White cannot pass.

But there is no play at negative temperature with area scoring. OC, area rules could award Black two more points in the corner without requiring her to play there, After all, they allow removal of dead stones without play, so why not? I.e., Black could just place two stones in the corner for counting without actually playing them. I really don't know what, say, the Chinese rules say about that. {shrug}

----

Anyway, by my territory rules and Lasker-Maas rules Black has 2 points in this corner.

Also by Berlekamp's rules.

Gérard TAILLE · Post by **Gérard TAILLE** » Mon Nov 23, 2020 2:54 pm

Bill Spight wrote:
Gérard TAILLE wrote:Is it the same problem in GO with area counting with position like the following?

$$B
$$ -----------------------
$$ | . O O X . . . . . . |
$$ | X . O X . . . . . . |
$$ | X X O X . . . . . . |
$$ | . . O X . . . . . . |
$$ | O O O X . . . . . . |
$$ | X X X X . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------------- $$ | . O O X . . . . . . | $$ | X . O X . . . . . . | $$ | X X O X . . . . . . | $$ | . . O X . . . . . . | $$ | O O O X . . . . . . | $$ | X X X X . . . . . . | $$ | . . . . . . . . . . | $$ | . . . . . . . . . . | $$ | . . . . . . . . . . | $$ | . . . . . . . . . . | $$ -----------------------[/go]
Here again black should continue to move while white must pass.
Well, in CGT White cannot pass. But there is no play at negative temperature with area scoring. OC, area rules could award Black two more points in the corner without requiring her to play there, After all, they allow removal of dead stones without play, so why not? I.e., Black could just place two stones in the corner for counting without actually playing them. I really don't know what, say, the Chinese rules say about that. {shrug}

----

Anyway, by my territory rules and Lasker-Maas rules Black has 2 points in this corner. Also by Berlekamp's rules.

Bill, do you have a link to understand in details how, in your rule, you play the last phase of the endgame and how you calculate the result of the game ?

Bill Spight · Post by **Bill Spight** » Mon Nov 23, 2020 3:22 pm

Gérard TAILLE wrote:
Bill Spight wrote:
Gérard TAILLE wrote:Is it the same problem in GO with area counting with position like the following?

$$B
$$ -----------------------
$$ | . O O X . . . . . . |
$$ | X . O X . . . . . . |
$$ | X X O X . . . . . . |
$$ | . . O X . . . . . . |
$$ | O O O X . . . . . . |
$$ | X X X X . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ | . . . . . . . . . . |
$$ -----------------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------------- $$ | . O O X . . . . . . | $$ | X . O X . . . . . . | $$ | X X O X . . . . . . | $$ | . . O X . . . . . . | $$ | O O O X . . . . . . | $$ | X X X X . . . . . . | $$ | . . . . . . . . . . | $$ | . . . . . . . . . . | $$ | . . . . . . . . . . | $$ | . . . . . . . . . . | $$ -----------------------[/go]
Here again black should continue to move while white must pass.
Well, in CGT White cannot pass. But there is no play at negative temperature with area scoring. OC, area rules could award Black two more points in the corner without requiring her to play there, After all, they allow removal of dead stones without play, so why not? I.e., Black could just place two stones in the corner for counting without actually playing them. I really don't know what, say, the Chinese rules say about that. {shrug}

----

Anyway, by my territory rules and Lasker-Maas rules Black has 2 points in this corner. Also by Berlekamp's rules.
Bill, do you have a link to understand in details how, in your rule, you play the last phase of the endgame and how you calculate the result of the game ?

In my rules a pass lifts all ko and superko bans, so to stop play there is a three repetition rule, which usually means three consecutive passes. In the first phase of play passes are free. If the players cannot agree about scoring, e.g, about dead stones (which are removed and counted) or one way passes or whatever, or even if either player requests resumption of play, there is an encore that also ends with three repetitions, and passes cost one point (via pass stones). However, if the same player starts and begins the encore, the other player must hand over a prisoner. At the end of the encore all stones on the board are considered to be alive and all empty points surrounded by stones of one player are the territory of that player.

Gérard TAILLE · Post by **Gérard TAILLE** » Tue Nov 24, 2020 2:29 am

Bill Spight wrote: In my rules a pass lifts all ko and superko bans, so to stop play there is a three repetition rule, which usually means three consecutive passes. In the first phase of play passes are free. If the players cannot agree about scoring, e.g, about dead stones (which are removed and counted) or one way passes or whatever, or even if either player requests resumption of play, there is an encore that also ends with three repetitions, and passes cost one point (via pass stones). However, if the same player starts and begins the encore, the other player must hand over a prisoner. At the end of the encore all stones on the board are considered to be alive and all empty points surrounded by stones of one player are the territory of that player.

If I understand correctly that means that seki are counted more like area counting than territory counting. That means that your rule lies somewhere between chinese rule and japonese rule, doesn't it?
BTW it seems it is the same in the Lasker-Maas rule.

Bill Spight · Post by **Bill Spight** » Tue Nov 24, 2020 4:26 am

Gérard TAILLE wrote:
Bill Spight wrote: In my rules a pass lifts all ko and superko bans, so to stop play there is a three repetition rule, which usually means three consecutive passes. In the first phase of play passes are free. If the players cannot agree about scoring, e.g, about dead stones (which are removed and counted) or one way passes or whatever, or even if either player requests resumption of play, there is an encore that also ends with three repetitions, and passes cost one point (via pass stones). However, if the same player starts and begins the encore, the other player must hand over a prisoner. At the end of the encore all stones on the board are considered to be alive and all empty points surrounded by stones of one player are the territory of that player.
If I understand correctly that means that seki are counted more like area counting than territory counting. That means that your rule lies somewhere between chinese rule and japonese rule, doesn't it?
BTW it seems it is the same in the Lasker-Maas rule.

Aside from one way dame, which rarely occur, the main difference is that territory is counted in seki. That makes my rules and Lasker-Maas rules a form of chilled go for area scoring.

A hybrid between area and territory scoring is Button Go.

See https://senseis.xmp.net/?ButtonGo You can implement Button Go without a physical token with a simple alteration of AGA rules. Instead of requiring White to make the last pass say that if the last player to pass is the same as the first player to pass, then the last pass is free. And then, if play resumes, if the last player to pass in the resumption is the same as the first player in the resumption, that pass is free.

Edit: In CGT terms 6½ komi may be written {-7|-6}. A play in the komi loses ½ point and is equivalent to taking the button. OC, taking the button gains ½ point in area scoring.

Gérard TAILLE · Post by **Gérard TAILLE** » Wed Nov 25, 2020 7:26 am

I tried to build a game with the proposed zugswang position.
Here it is.
The sequence is not optimal OC but I tried to avoid any stupid move in order to have a sequence which looks "natural".

Gérard TAILLE · Post by **Gérard TAILLE** » Thu Nov 26, 2020 9:16 am

Gérard TAILLE wrote:I tried to build a game with the proposed zugswang position.
Here it is.
The sequence is not optimal OC but I tried to avoid any stupid move in order to have a sequence which looks "natural".

How do you count the above game with buttonGo rule?

Click Here To Show Diagram Code: [go]$$ ----------------- $$ | . . X X O O . | $$ | . X . X O O X | $$ | . X . X X X O | $$ | . X X X O O O | $$ | . X O O O . . | $$ | X . X O . O . | $$ | . X B O . . . | $$ -----------------[/go]

After the last black move white passes and takes the button
The game continue by

Click Here To Show Diagram Code: [go]$$ ----------------- $$ | . . X X O O 1 | $$ | . X . X O O X | $$ | . X . X X X O | $$ | . X X X O O O | $$ | . X O O O . . | $$ | X . X O . O . | $$ | . X X O . . . | $$ -----------------[/go]

Click Here To Show Diagram Code: [go]$$B $$ ----------------- $$ | . . X X 4 3 X | $$ | . X . X 5 2 X | $$ | . X . X X X O | $$ | . X X X O O O | $$ | . X O O O . . | $$ | X . X O . O . | $$ | . X X O . . . | $$ -----------------[/go]

Click Here To Show Diagram Code: [go]$$Wcm6 $$ ----------------- $$ | . . X X W 2 3 | $$ | . X . X X O 1 | $$ | . X . X X X O | $$ | . X X X O O O | $$ | . X O O O . . | $$ | X . X O . O . | $$ | . X X O . . . | $$ -----------------[/go]

at the left of

Assuming a 7,5 komi white wins in japonese rules by 0.5 point.

How do you define the komi in buttonGo? What is the result of the game?

Bill Spight · Post by **Bill Spight** » Thu Nov 26, 2020 10:28 am

Gérard TAILLE wrote:
Gérard TAILLE wrote:I tried to build a game with the proposed zugswang position.
Here it is.
The sequence is not optimal OC but I tried to avoid any stupid move in order to have a sequence which looks "natural".

How do you count the above game with buttonGo rule?

Click Here To Show Diagram Code: [go]$$W $$ ----------------- $$ | . . X X O O . | $$ | . X . X O O X | $$ | . X . X X X O | $$ | . X X X O O O | $$ | . X O O O . . | $$ | X . X O . O . | $$ | . X B O . . . | $$ -----------------[/go]

By territory scoring (NOT Japanese) Black has 10 points of empty territory on the board + 3 points in the top right corner + 4 points for prisoners = 17 points.

White has 7 points on the board + 2 points for prisoners - ½ point for the button = 8½ points.

Black is ahead by 8½ points.

The game continue by
$$B
$$ -----------------
$$ | . . X X O O 1 |
$$ | . X . X O O X |
$$ | . X . X X X O |
$$ | . X X X O O O |
$$ | . X O O O . . |
$$ | X . X O . O . |
$$ | . X X O . . . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------- $$ | . . X X O O 1 | $$ | . X . X O O X | $$ | . X . X X X O | $$ | . X X X O O O | $$ | . X O O O . . | $$ | X . X O . O . | $$ | . X X O . . . | $$ -----------------[/go]

$$B
$$ -----------------
$$ | . . X X 4 3 X |
$$ | . X . X 5 2 X |
$$ | . X . X X X O |
$$ | . X X X O O O |
$$ | . X O O O . . |
$$ | X . X O . O . |
$$ | . X X O . . . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------- $$ | . . X X 4 3 X | $$ | . X . X 5 2 X | $$ | . X . X X X O | $$ | . X X X O O O | $$ | . X O O O . . | $$ | X . X O . O . | $$ | . X X O . . . | $$ -----------------[/go]

$$Wcm6
$$ -----------------
$$ | . . X X W 2 3 |
$$ | . X . X X O 1 |
$$ | . X . X X X O |
$$ | . X X X O O O |
$$ | . X O O O . . |
$$ | X . X O . O . |
$$ | . X X O . . . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$Wcm6 $$ ----------------- $$ | . . X X W 2 3 | $$ | . X . X X O 1 | $$ | . X . X X X O | $$ | . X X X O O O | $$ | . X O O O . . | $$ | X . X O . O . | $$ | . X X O . . . | $$ -----------------[/go]
at the left of

In terms of area scoring Black has 29 points on the board and White has 20 points plus ½ point for the button. Black is ahead by 8½ points.

How do you define the komi in buttonGo? What is the result of the game?

Normally the komi is an integer. If it is 9 points on the 7x7, then White wins by ½ point.

Gérard TAILLE · Post by **Gérard TAILLE** » Thu Nov 26, 2020 10:41 am

Bill Spight wrote:
Gérard TAILLE wrote:
Gérard TAILLE wrote:I tried to build a game with the proposed zugswang position.
Here it is.
The sequence is not optimal OC but I tried to avoid any stupid move in order to have a sequence which looks "natural".

How do you count the above game with buttonGo rule?

$$W
$$ -----------------
$$ | . . X X O O . |
$$ | . X . X O O X |
$$ | . X . X X X O |
$$ | . X X X O O O |
$$ | . X O O O . . |
$$ | X . X O . O . |
$$ | . X B O . . . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$W $$ ----------------- $$ | . . X X O O . | $$ | . X . X O O X | $$ | . X . X X X O | $$ | . X X X O O O | $$ | . X O O O . . | $$ | X . X O . O . | $$ | . X B O . . . | $$ -----------------[/go]
By territory scoring (NOT Japanese) Black has 10 points of empty territory on the board + 3 points in the top right corner + 4 points for prisoners = 17 points.

White has 7 points on the board + 2 points for prisoners - ½ point for the button = 8½ points.

Black is ahead by 8½ points.

The game continue by
$$B
$$ -----------------
$$ | . . X X O O 1 |
$$ | . X . X O O X |
$$ | . X . X X X O |
$$ | . X X X O O O |
$$ | . X O O O . . |
$$ | X . X O . O . |
$$ | . X X O . . . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------- $$ | . . X X O O 1 | $$ | . X . X O O X | $$ | . X . X X X O | $$ | . X X X O O O | $$ | . X O O O . . | $$ | X . X O . O . | $$ | . X X O . . . | $$ -----------------[/go]

$$B
$$ -----------------
$$ | . . X X 4 3 X |
$$ | . X . X 5 2 X |
$$ | . X . X X X O |
$$ | . X X X O O O |
$$ | . X O O O . . |
$$ | X . X O . O . |
$$ | . X X O . . . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$B $$ ----------------- $$ | . . X X 4 3 X | $$ | . X . X 5 2 X | $$ | . X . X X X O | $$ | . X X X O O O | $$ | . X O O O . . | $$ | X . X O . O . | $$ | . X X O . . . | $$ -----------------[/go]

$$Wcm6
$$ -----------------
$$ | . . X X W 2 3 |
$$ | . X . X X O 1 |
$$ | . X . X X X O |
$$ | . X X X O O O |
$$ | . X O O O . . |
$$ | X . X O . O . |
$$ | . X X O . . . |
$$ -----------------
Click Here To Show Diagram Code
[go]$$Wcm6 $$ ----------------- $$ | . . X X W 2 3 | $$ | . X . X X O 1 | $$ | . X . X X X O | $$ | . X X X O O O | $$ | . X O O O . . | $$ | X . X O . O . | $$ | . X X O . . . | $$ -----------------[/go]
at the left of
In terms of area scoring Black has 29 points on the board and White has 20 points plus ½ point for the button. Black is ahead by 8½ points.

How do you define the komi in buttonGo? What is the result of the game?
Normally the komi is an integer. If it is 9 points on the 7x7, then White wins by ½ point.

I understood that the komi for 7x7 game is 9 points only with area scoring. In territory scoring it seems the komi is 8 points.

If I understand correctly and I choose to play a 7x7 game with a komi of 7.5 in japonese rules, then this komi becomes 8 points for buttonGo game.
That means that in case of zugswang, buttonGo may fail to give the same result of japonese rule. Fortunatly these zugswang positions occured never in practice so it doesn't matter. It was just a theoritical question OC.

Bill Spight · Post by **Bill Spight** » Thu Nov 26, 2020 11:21 am

Gérard TAILLE wrote:How do you define the komi in buttonGo? What is the result of the game?

Moi wrote:Normally the komi is an integer. If it is 9 points on the 7x7, then White wins by ½ point.

Gérard TAILLE wrote:I understood that the komi for 7x7 game is 9 points only with area scoring. In territory scoring it seems the komi is 8 points.

If I understand correctly and I choose to play a 7x7 game with a komi of 7.5 in japonese rules, then this komi becomes 8 points for buttonGo game.
That means that in case of zugswang, buttonGo may fail to give the same result of japonese rule. Fortunatly these zugswang positions occured never in practice so it doesn't matter. It was just a theoritical question OC.

Oh, that's not the only difference with Japanese rules. Button Go is a hybrid between area and territory scoring, and will count territory in seki.

As for the best komi on the 7x7 with Button Go, we could ask KataGo (lightvector).

lightvector · Post by **lightvector** » Thu Nov 26, 2020 8:19 pm

Bill Spight wrote: As for the best komi on the 7x7 with Button Go, we could ask KataGo (lightvector).

Under Tromp-Taylor-like rules with a button (first pass earns 0.5 points and does not count for ending the game), KataGo says 50% black winrate at 8.5 komi, 98% with 8 komi, 3% with 9 komi. Feel free to explore the variations with KataGo with any appropriate analysis interface if you like.

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