Hi Bill,

Going back to scoring:I didn't know anything about group tax until you mentioned it ( on multiple occasions, in various threads ). From your research and current understanding, do you feel a scoring method that includes group tax is the 'best' way to score ? In the sense that both sides must play it all out and, removing stones off the board if necessary, until there are no more legal moves remaining on the board that can affect the win/loss situation ? In other words, until every stone remaining on the board is "alive", or "un-removable", else it would affect the win/loss ?

Back to the reduced board from the bot game:

Click Here To Show Diagram Code

[go]$$B 5.5 komi, zero prisoners
$$ ---------------------
$$ | . X O O . X X X . |
$$ | X . X O O O X X X |
$$ | X X X X X O X X X |
$$ | O O O O X O O O O |
$$ | . O . O X O O O O |
$$ | X X X O X O X X . |
$$ ---------------------[/go]

Yes: no special exception rules needed for bent four, so of course the ko is allowed, so both players will not make any more moves here; and pass.

Thanks, Ed.

Black has another sente, and White has a couple of plays, as well. Are some of these plays better than the others?

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

Visualize whirled peas.

Everything with love. Stay safe.

Well, the oldest known forms of go used what we today call a group tax, whether by area scoring or territory scoring. And the group tax lasted into the 20th century in China. How bad can it be? Also, nearly all forms of no pass go have a group tax, because if you have to fill an eye point that puts your group in atari (except as a sacrifice) you might as well resign.

Today I advocate Button Go, an intermediate form of go that reconciles territory and area scoring, and, IMHO, combines the best features of both.




You don't have to go that far. You can reach a scorable position before that point.



Even with some form of no pass go the play reaches a point where the players can stop play and score. That point is typically when all the dame have been filled. It can also happen earlier, if the players agree. (And are correct. )

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

Visualize whirled peas.

Everything with love. Stay safe.

Thanks, Bill. What is Button Go, and is it related in any way to AGA's passing-one-stone-per-pass ?Yes, i, as a human, don't have to go that far, but indeed if the rules require it, then at the end, we reach a board where no single legal move that would affect the win/loss exists; then we use area scoring. ( I don't understand how to use territory scoring and avoid special cases (hacks) for things like bent-4-in-the-corner. ) My understanding is this would resolve all (?!?) of the special hacks in Japanese rules, like that infamous 0.5 ko case where Go Seigen was awarded a loss, not based on the board and logic, but based on magic, arbitrary human ruling.

About No Pass Go

In my previous note I said that no pass go normally reaches a position where the players can stop play and score the game. Well, that was how games ended when I learned go. We did not pass and there was no two, three, or four pass rule to end play. We simply agreed to stop play and score the game. Not only that, but nearly all forms of no pass go have territory, and also have a group tax. Also, no pass go may have dead stones that affect the score. A precursor of ancient territory scoring with a group tax may have been some form of no pass go.

Straight no pass go is, IMO, too difficult for humans, besides having a very long and perhaps tedious endgame. Most endgames would involve playing inside the opponent's territory in order to reduce its value, or to increase its value by a small amount, if there is no better play.

At the risk of repeating myself, here is a small No Pass Go problem that illustrates that feature.

Click Here To Show Diagram Code

[go]$$B No pass go. Who wins?
$$ ---------------
$$ | . . X . . X . |
$$ | X X X X X X X |
$$ | O O O O O O O |
$$ | . O . O . . . |
$$ ---------------[/go]

Who wins with perfect play?

Why?

Enjoy!

_________________
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,

The simplest form of Button Go has a token called a button, which is worth ½ pt. by area scoring. At her or his turn a player may take the button instead of making a play on the board. Taking the button lifts a ko or superko ban, just as a board play does. Normally the button is taken after the last dame is filled and has the effect that it does not matter who gets the last dame.

You can also implement the button by making the first pass special, in that if White makes the first pass he gains 1 pt., but Black does not. This has already been done in international competition. With AGA style scoring a somewhat more complicated form of Button Go, Two Button Go, may be used with the same effect. Edit: You can implement Double Button Go with AGA pass stones by making the last pass special. If the player to make the last pass also made the first pass, she or he does not have to hand over a pass stone. White does not have to make the last pass. Because of that, we may consider that Double Button rule as a simplification of AGA rules.

See https://senseis.xmp.net/?ButtonGo .



Well, Go Seigen's view may also be considered arbitrary. In fact, by areas scoring he would have lost, as well.

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

Visualize whirled peas.

Everything with love. Stay safe.

A very funny ko, if you want to call it a ko. White does not have to fight the ko, does he?

_________________
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, I just read NoPassGo for the first time; No pass Go is rather different from regular Go.

Evaluation problem.

Click Here To Show Diagram Code

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

What is best play by both sides?

Click Here To Show Diagram Code

[go]$$Bc Black first
$$ --------------------------
$$ | . . . . . 2 1 3 . . . X .
$$ | O O O O O X O . X X . X .
$$ | X X X X X O O O X . X . .
$$ | . . . , X X X X X X . . .[/go]

Net local score = -1

Click Here To Show Diagram Code

[go]$$Wc White first
$$ --------------------------
$$ | . . . . . 3 5 1 4 . . X .
$$ | O O O O O X O 2 X X . X .
$$ | X X X X X O O O X . X . .
$$ | . . . , X X X X X X . . .[/go]

Net local score = -3

How much does each play gain?

The original position has a count of -2; so each play gains 1 pt. on average.

Are other plays as good as these?

Black can play with sente as a ko threat. But otherwise, the sente plays are not as good.

Click Here To Show Diagram Code

[go]$$Bc Sente 1-a
$$ --------------------------
$$ | . . . . . 2 a 1 . . . X .
$$ | O O O O O X O b X X . X .
$$ | X X X X X O O O X . X . .
$$ | . . . , X X X X X X . . .[/go]

is sente, threatening a descent to 2. After Black can play at a, or if Black plays elsewhere, White can play at b.

Click Here To Show Diagram Code

[go]$$Bc Sente 1-b
$$ --------------------------
$$ | . . . . . . 2 1 . . . X .
$$ | O O O O O X O . X X . X .
$$ | X X X X X O O O X . X . .
$$ | . . . , X X X X X X . . .[/go]

White could also reply with , leaving a net local score of -2. The problem is not the sente, per se, it is that gives White two incomparable options, and White can choose which is better, depending upon the rest of the board.

The other sente is even worse.

Click Here To Show Diagram Code

[go]$$Bc Sente 2
$$ --------------------------
$$ | . . . . . 2 b a . . . X .
$$ | O O O O O X O 1 X X . X .
$$ | X X X X X O O O X . X . .
$$ | . . . , X X X X X X . . .[/go]

After , if Black plays elsewhere White has the option of playing at a. And i if Black plays at a White has the choice of replying at b or not. gives White two choice points.

In short, the sente plays are not so good because they give White good choices.



What about the other play for White?

Click Here To Show Diagram Code

[go]$$Wc White alternative
$$ --------------------------
$$ | . . . . . 3 . 2 . . . X .
$$ | O O O O O X O 1 X X . X .
$$ | X X X X X O O O X . X . .
$$ | . . . , X X X X X X . . .[/go]

This play for White yields the same result after as the sequence starting with the kosumi.

Click Here To Show Diagram Code

[go]$$Wc White main line
$$ --------------------------
$$ | . . . . . 3 5 1 4 . . X .
$$ | O O O O O X O 2 X X . X .
$$ | X X X X X O O O X . X . .
$$ | . . . , X X X X X X . . .[/go]

However, in the main line Black might make a mistake and play elsewhere after , allowing White to play at 4. That is assuming that Black will not make use of as a ko threat later. That is unlikely, since White normally makes this play at temperature 1, and if Black plays elsewhere, White can usually play at 4 right away. OTOH, if White has enough sufficiently large ko threats White might be komonster and be able to gain a point by delaying the connection at . As usual, ko complicates matters.

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

Visualize whirled peas.

Everything with love. Stay safe.

My answer :

No Pass Go problem

Click Here To Show Diagram Code

[go]$$B No pass go. Who wins?
$$ ---------------
$$ | . . X . . X . |
$$ | X X X X X X X |
$$ | O O O O O O O |
$$ | . O . O . . . |
$$ ---------------[/go]

Who wins with perfect play?

Note: Tryss has solved the problem with Black to play.

Unhidden:

White.

Why?

Ahem.

If we all played no pass go, SDKS would see that White wins, no matter who plays first. But since we do not all play no pass go, let me explain.

Black has 2 pts. of territory. I.e., 1.5 + 1.5 + 1 - 2 = 2. To avoid confusion, let me refer to an empty point on the board as a space, so we don't mistake it for a point of territory. The one space eye in the top right is 1 pt. of territory. Each two space eye is worth 1.5 pts. of territory. Adding them together we get 4 pts. and then subtracting 2pts. for the group tax we get 2 pts. of territory. If you are familiar with chilled go ( https://senseis.xmp.net/?Chilling ) you know that some positions have fractional scores ( https://senseis.xmp.net/?Numbers ). The same is true in straight no pass go.

Now let's evaluate White's position. White scores are negative, so we have -1 -1 -2 + v + 2 = -2 + v. (v is an infinitesimal called down. See https://senseis.xmp.net/?DOWN ) Adding the Black and White results together we get the value of the whole board: 2 - 2 + v = v. v may be an infinitesimal, but it is negative, which means that White wins, no matter who plays first. No pass go SDKs would be familiar with those values and would agree that White wins.

Let me show that and explain the values as I go.

Click Here To Show Diagram Code

[go]$$W No pass go, White first
$$ ---------------
$$ | 6 2 X 4 3 X . |
$$ | X X X X X X X |
$$ | O O O O O O O |
$$ | 5 O 7 O . 1 . |
$$ ---------------[/go]

After each player has two 1 space eyes. Black to play must fill an eye and loses.

eliminates the v, leaving White with 2 pts. of territory and a net score of 0 pts. on the whole board. If it's your turn and the score is 0, you lose. (In fact, the definition of a 0 game is that the second player wins.) It is Black's turn, so White wins.

plays in one of the 1.5 pt. eyes, leaving a 1 pt. eye. That is, loses 0.5 pt. Knowledgeable players, like our SDKs, would not bother to make plays that lose points, but would simply score the game.

plays in the other 1.5 pt. eye, leaving a 2 pt. eye. OC, in regular go that is worth 3 pts., but the value of the dead stone is different in no pass go, and differs according to the eye. We do not bother to evaluate it by itself.

captures the stone, leaving a 1 pt. eye. That means that Black has 2 moves in that eye and White has none. 1 move = 1 pt. of territory, so that eye is worth 2 pts.

Now each player fills a 1 pt. eye until Black would have to play self atari. White to play wins the game.

Click Here To Show Diagram Code

[go]$$B No pass go, Black first
$$ ---------------
$$ | . . X . . X . |
$$ | X X X X X X X |
$$ | O O O O O O O |
$$ | . O . O 2 1 . |
$$ ---------------[/go]

plays in the 3 space eye, leaving its value as -2 + *. * (pronounced STAR) is an infinitesimal that we have in regular go, namely a dame. Either player can play on a dame, reducing its territory to 0.

plays in the 3 space eye, reducing its value to -2, as we have already seen.

At this point we can see that each player has 2 pts., for a whole board score of 0, with Black to play. As knowledgeable players we do not bother to play the game out, but declare White the winner.

Note: v is a game in itself. White can play from v to 0, winning that game. Black can play from v to *, but then White can reply to 0, also winning. Since White wins, no matter who plays first, v is negative.

Edit: I have not shown that after Black plays in the 3 space White eye it is worth -2 + *. We have seen that White plays to -2 from there. Now to show that Black to play also moves to -2.

Click Here To Show Diagram Code

[go]$$B No pass go, Black first
$$ ---------------
$$ | . X . X . X . |
$$ | X X X X X X X |
$$ | O O O O O O O |
$$ | . O . O 1 X . |
$$ ---------------[/go]

I have altered the board to make it simpler. Black now has four 1 pt. eyes, for the same 2 pts. of territory.

After the eye is worth -5 in regular go, but only -2 in no pass go. Now to show that.

Click Here To Show Diagram Code

[go]$$B No pass go, Zero game?
$$ ---------------
$$ | . X . X . X . |
$$ | X X X X X X X |
$$ | O O O O O O O |
$$ | . O . O X X . |
$$ ---------------[/go]

If the bottom right eye is worth -2, then the whole board is worth 0 and the second player wins.

Click Here To Show Diagram Code

[go]$$W No pass go, White first
$$ ---------------
$$ | . X . X . X . |
$$ | X X X X X X X |
$$ | O O O O O O O |
$$ | . O . O X X 1 |
$$ ---------------[/go]

captures the two Black stones, leaving an eye worth -1.5. Knowledgeable players could now stop and score the board. The whole board has a net score of 0.5, so Black wins by ½ pt. So far, so good.

Click Here To Show Diagram Code

[go]$$B No pass go, Black first.
$$ ---------------
$$ | . X . X . X 1 |
$$ | X X X X X X X |
$$ | O O O O O O O |
$$ | . O . O X X 2 |
$$ ---------------[/go]

must fill a 1 pt. eye. Now captures the two Black stones, leaving a -1.5 pt. eye. The whole board has a net score of -0.5, so White wins by ½ pt.

The second player wins, as advertised. So the bottom right eye is equivalent to two 1 pt. eyes. (Edit: As long as White is alive, OC.)

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

Visualize whirled peas.

Everything with love. Stay safe.

A nice endgame position

Click Here To Show Diagram Code

[go]$$Bc
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O . O X .
$$ . X O O . O . X .
$$ . X O . O X . X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . . . . . . . .[/go]

Evaluate the position and play.

Enjoy!

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

Visualize whirled peas.

Everything with love. Stay safe.

A nice endgame position

Click Here To Show Diagram Code

[go]$$B
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O . O X .
$$ . X O O . O . X .
$$ . X O . O X . X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . . . . . . . .[/go]

Evaluate the position and play.

(Unhidden.)

Click Here To Show Diagram Code

[go]$$B Black first
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O . O X .
$$ . X O O . O 1 X .
$$ . X O . O X . X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . . . . . . . .[/go]

makes double ko life. White has 3 pts. of territory.

Click Here To Show Diagram Code

[go]$$W White first
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O . O X .
$$ . X O O . O 1 X .
$$ . X O . O X . X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . . . . . . . .[/go]

plays on the same spot.

Click Here To Show Diagram Code

[go]$$W White first, Black reply
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O . O X .
$$ . X O O . O W X .
$$ . X O . O B 2 X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . . . . . . . .[/go]

saves the stone. White gets 4 pts. of territory.

Click Here To Show Diagram Code

[go]$$W White first, White follow-up
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O . O X .
$$ . X O O . O W X .
$$ . X O . O B 3 X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . . . . . . . .[/go]

captures the stone, for 6 pts. of territory for White.

The position after is gote, with an average White territory of (4 + 6)/2 = 5. A play by either side gains 1 pt.

The original position is ambiguous between sente and gote. As a sente, its average White territory is 4 pts., the result after White plays and Black replies. As a gote, it is the average of 3 pts. and 5 pts., which is also 4 pts. Each play gains 1 pt. In fact, this position is our old friend, UP, in a different guise.

----

Black's mistake.

Click Here To Show Diagram Code

[go]$$B Black connects, White replies
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O . O X .
$$ . X O O . O 2 X .
$$ . X O . O X 1 X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . . . . . . . .[/go]

White gets 4 pts. of territory.

Click Here To Show Diagram Code

[go]$$B Black connects, Black follow-up, White replies
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O 4 O X .
$$ . X O O . O 3 X .
$$ . X O . O X B X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . . . . . . . .[/go]

Black makes a ko, which White fills, for 3 pts. of territory.

Click Here To Show Diagram Code

[go]$$B Black plays the ko
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O 5 O X .
$$ . X O O 6 O B X .
$$ . X O . O X B X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . . . . . . . .[/go]

This is a sente ko, as if Black won the second ko White would die. The result after is an average of 1⅓ pts. for White, 2 pts. of territory minus 1 pt. for the captured stone plus ⅓ pt. for in the remaining ko. So in the previous diagram gains 3 - 1⅓ = 1⅔ pts. on average. So the position after is also worth 1⅓ pts. for White, So is sente, raising the local temperature to 1⅔.

Now, returns to a position worth 4 pts. for White, which means that loses no points. Why, then is a mistake? After all, the original position is ambiguous. Why is not just another ambigous play?

A difference game supplies the answer.

Click Here To Show Diagram Code

[go]$$ Difference game
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O . O X .
$$ . X O O . O B X .
$$ . X O . O X . X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . O O O O O . .
$$ . O O X X X O O .
$$ . O X . X . X O .
$$ . O X X . X . O .
$$ . O X . X O W O .
$$ . O O X X X O O .
$$ . . O O O O O . .
$$ . . . . . . . . .[/go]

To set up the difference game we have mirrored the original position. In the original position Black has played and in the mirror position White has played . If is at least as good as , then Black to play cannot win the difference game, and if is at least as good as , then White to play cannot win the difference game.

Click Here To Show Diagram Code

[go]$$B Black first
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O . O X .
$$ . X O O . O B X .
$$ . X O . O X . X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . O O O O O . .
$$ . O O X X X O O .
$$ . O X . X . X O .
$$ . O X X . X 1 O .
$$ . O X . X O W O .
$$ . O O X X X O O .
$$ . . O O O O O . .
$$ . . . . . . . . .[/go]

wins the difference game by 1 pt.

Click Here To Show Diagram Code

[go]$$W White first
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O . O X .
$$ . X O O . O B X .
$$ . X O . O X . X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . O O O O O . .
$$ . O O X X X O O .
$$ . O X . X 2 X O .
$$ . O X X . X 1 O .
$$ . O X . X O W O .
$$ . O O X X X O O .
$$ . . O O O O O . .
$$ . . . . . . . . .[/go]

After , makes jigo. So is at least as good as , but not vice versa. That means that is a mistake, even if it is a sente which loses no points.

----

White's mistake.

Click Here To Show Diagram Code

[go]$$W White takes
$$ . . . . . . . . .
$$ . . X X X X X . .
$$ . X X O O O X X .
$$ . X O . O . W X .
$$ . X O O . O 2 X .
$$ . X O . O B 1 X .
$$ . X X O O O X X .
$$ . . X X X X X . .
$$ . . . . . . . . .[/go]

replies to , leaving a position worth on average 3⅓ pts. to White. White has 3 pts. of territory plus 1 pt. for the stone, minus ⅓ pt. for each of and . The local temperature has dropped to ⅓. is a sente which loses ⅔ pt., and so is a mistake.

_________________
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.

Safari web browser converts some fractions. Also, Mac OSX has some fractions available, along with different scripts and symbols.

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

Visualize whirled peas.

Everything with love. Stay safe.

Another nice endgame position.

Click Here To Show Diagram Code

[go]$$
$$ . . . . . . . . . .
$$ . O O O O O O O O .
$$ . O X . . . . . O .
$$ . O X O O . . O O .
$$ . O O O X X X X X .
$$ . . . . . . . . . .[/go]

Outside stones are safe.

Evaluate the position. What is the best play by each side?

Enjoy.

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

Visualize whirled peas.

Everything with love. Stay safe.

A difficult endgame position.

Click Here To Show Diagram Code

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

The outside region is Black's territory.

Enjoy! (If you can. )

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

Visualize whirled peas.

Everything with love. Stay safe.