Thermography

Bill Spight · **#141**

OK. Let's look at this yoseko like Berlekamp did, using a tax, t, on each move instead of plays in an environment.

Click Here To Show Diagram Code: [go]$$Wc Yoseko $$ ----------------- $$ | 1 X X O . O . | $$ | O 3 X X O O . | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

In 2 moves White gets a net local score of -17 + 2t, where t is the tax.

Click Here To Show Diagram Code: [go]$$Wc Yoseko $$ ----------------- $$ | 1 X X O 2 O 4 | $$ | O . X X O O 6 | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

If

takes and wins the ko with 2 net moves the net local score is 21 - 2t.

OC, the play does not have to go this way, but if it does we can find an equitable tax by solving the following equation.

-17 + 2t = 21 - 2t
t = 38/4 = 9½

Let m be the mast value. Then

m = -17 + 19 = 2

OC, these values are tentative.

Now suppose that :w5:

takes the ko back and wins it.

Click Here To Show Diagram Code: [go]$$Wc Ko $$ ----------------- $$ | 1 X X O 2 O 4 | $$ | O 7 X X O O . | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

takes ko

Each player has taken the ko once, so the net number of prisoners before :w7:

is 0. This way White has made only one extra play and has captured one extra stone, so the net local score is -18 + t. Solving for an equitable t we have

-18 + t = 21 - 2t
t = 39/3 = 13

m = -18 + 13 = -5

It seems that the position has morphed into a regular ko with a mast value of -5, where each play gains 13 points. These values are still tentative, OC.

Now suppose that :b6:

does not meekly let White capture, but captures the two White stones in the left top corner. Then :w7:

will throw in to make atari.

Click Here To Show Diagram Code: [go]$$Wc Ko $$ ----------------- $$ | 1 X X O 2 O 4 | $$ | O 6 X X O O . | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

takes ko,

@ 1

That leaves the following position with each player have made the same number of local plays, but Black has 2 extra White prisoners.

Click Here To Show Diagram Code: [go]$$Wc Ko $$ ----------------- $$ | O X X O . O X | $$ | 9 X X X O O . | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

2

prisoners

If White wins the ko the result, as expected, is -18 + t.

Now suppose that Black takes and wins the ko.

Click Here To Show Diagram Code: [go]$$Wc Ko $$ ----------------- $$ | O X X O 8 O X | $$ | . X X X O O 0 | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

2

prisoners

The result, as expected, is 21 - 2t, which changes neither m nor the equitable value of t.

:b6:

was a local ko threat. It did not change either the mast value or the equitable temperature, but it did let Black win the ko, which matters when t < 13.

We have found the right scaffold of the thermograph of the regular ko, which is v = 21 - 2t up to temperature 13, and v = -5 above that. The point being that at temperature 13 Black will not care if White wins the ko.

Now for non-ko positions a right scaffold that slopes upwards towards the right is unheard of. But such is the case here.

More to come.

Bill Spight · **#142**

OK. Suppose that Black plays first in the yoseko.

Click Here To Show Diagram Code: [go]$$Bc Black first $$ ----------------- $$ | . X X O 3 O 1 | $$ | O . X X O O 5 | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

OC, in actual play Black starts with a throw-in before taking the ko. If Black wins the ko the local score at temperature t is 20 - 3t. This is worse for Black than 21 - 2t when White plays first. Not a good sign.

Click Here To Show Diagram Code: [go]$$Bc White reply $$ ----------------- $$ | 2 X X O 3 O 1 | $$ | O . X X O O 5 | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

If White replies, we are in the regular ko that Black can take and win, for 21 - 2t, when t ≤ 13. So after :b1:

Black should not take and win the ko before White plays :w2:

. When should White play :w2:

? When

threatens to win the ko. I.e., when t ≤ 13.

There is a potential snag, however. If t = 0 Black gets 21 points if White plays :w2:

, but only 20 points if Black has to take and win the yoseko, anyway. Under the Japanese 1989 rules, however, if the position after :b1:

is left at the end of the game to hypothetical play, White is considered to be dead and Black gets 22 points without having to take and win the ko. So White has to play :w2:

even at temperature 0.

So the Black scaffold for the thermograph of the original position is v = 21 - 2t when t ≤ 13, as for the regular ko. As we have seen, that is the same as the White scaffold, but when should Black play :b1:

? Black can play any time when t ≤ 13, but the lower the temperature the better.

Click Here To Show Diagram Code: [go]$$Wc White threat $$ ----------------- $$ | 1 X X O . O . | $$ | O 3 X X O O . | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

White to play threatens to capture the Black stones in 2 moves for a local score of -17 + 2t. Black can afford to let White do so when

-17 + 2t ≥ 21 - 2t
t ≥ 38/4 = 9½

t = 9½ is the equitable temperature we found before and thought might be the temperature for below which someone would play. The mast value is 2, as we surmised.

The curious thing is that below that temperature the left and right walls of the thermograph coincide. No matter who plays first the minimax result will be 21 - 2t. In an actual game, however, as the play proceeds the ambient temperature tends to drop over time. So in practice, it is White, not Black, who will tend to initiate play in this position.

However, if White can win the regular ko the result to keep an eye on is -18 + t. At, say, t = 9½ that will mean a local score of -8½ instead of 2. That is a huge difference and so White will be on the lookout for the opportunity to create ko threats.

But here we are simply concerned with the thermograph of this ko, given no external ko threats. Here it is.

Attachment:

yosekoTG000.png [ 4.81 KiB | Viewed 10297 times ]

Where the two sides of the thermograph coincide the thermograph is magenta.

Gérard TAILLE · **#143**

Bill Spight wrote:

OK. Suppose that Black plays first in the yoseko.

Click Here To Show Diagram Code: [go]$$Bc Black first $$ ----------------- $$ | . X X O 3 O 1 | $$ | O . X X O O 5 | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

OC, in actual play Black starts with a throw-in before taking the ko. If Black wins the ko the local score at temperature t is 20 - 3t. This is worse for Black than 21 - 2t when White plays first. Not a good sign.

Click Here To Show Diagram Code: [go]$$Bc White reply $$ ----------------- $$ | 2 X X O 3 O 1 | $$ | O . X X O O 5 | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

If White replies, we are in the regular ko that Black can take and win, for 21 - 2t, when t ≤ 13. So after :b1:

Black should not take and win the ko before White plays :w2:

. When should White play :w2:

? When

threatens to win the ko. I.e., when t ≤ 13.

There is a potential snag, however. If t = 0 Black gets 21 points if White plays :w2:

, but only 20 points if Black has to take and win the yoseko, anyway. Under the Japanese 1989 rules, however, if the position after :b1:

is left at the end of the game to hypothetical play, White is considered to be dead and Black gets 22 points without having to take and win the ko. So White has to play :w2:

even at temperature 0.

So the Black scaffold for the thermograph of the original position is v = 21 - 2t when t ≤ 13, as for the regular ko. As we have seen, that is the same as the White scaffold, but when should Black play :b1:

? Black can play any time when t ≤ 13, but the lower the temperature the better.

Click Here To Show Diagram Code: [go]$$Wc White threat $$ ----------------- $$ | 1 X X O . O . | $$ | O 3 X X O O . | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

White to play threatens to capture the Black stones in 2 moves for a local score of -17 + 2t. Black can afford to let White do so when

-17 + 2t ≥ 21 - 2t
t ≥ 38/4 = 9½

t = 9½ is the equitable temperature we found before and thought might be the temperature for below which someone would play. The mast value is 2, as we surmised.

The curious thing is that below that temperature the left and right walls of the thermograph coincide. No matter who plays first the minimax result will be 21 - 2t. In an actual game, however, as the play proceeds the ambient temperature tends to drop over time. So in practice, it is White, not Black, who will tend to initiate play in this position.

However, if White can win the regular ko the result to keep an eye on is -18 + t. At, say, t = 9½ that will mean a local score of -8½ instead of 2. That is a huge difference and so White will be on the lookout for the opportunity to create ko threats.

But here we are simply concerned with the thermograph of this ko, given no external ko threats. Here it is.

Attachment:

yosekoTG000.png

Where the two sides of the thermograph coincide the thermograph is magenta.

It is not easy to understand Bill.
Assuming a non-ko environment I understand that neither black nor white have a good reason to play first and the final result will be in any case a local score of 21. In such case my common sense tells me that the thermograph is only a vertical line above 21 maybe with a magenta color to a certain temperature.
This non-vertical double wall you draw is really strange, isn't it?

Bill Spight · **#144**

Gérard TAILLE wrote:

Bill Spight wrote:

OK. Suppose that Black plays first in the yoseko.

Click Here To Show Diagram Code: [go]$$Bc Black first $$ ----------------- $$ | . X X O 3 O 1 | $$ | O . X X O O 5 | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

OC, in actual play Black starts with a throw-in before taking the ko. If Black wins the ko the local score at temperature t is 20 - 3t. This is worse for Black than 21 - 2t when White plays first. Not a good sign.

Click Here To Show Diagram Code: [go]$$Bc White reply $$ ----------------- $$ | 2 X X O 3 O 1 | $$ | O . X X O O 5 | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

If White replies, we are in the regular ko that Black can take and win, for 21 - 2t, when t ≤ 13. So after :b1:

Black should not take and win the ko before White plays :w2:

. When should White play :w2:

? When

threatens to win the ko. I.e., when t ≤ 13.

There is a potential snag, however. If t = 0 Black gets 21 points if White plays :w2:

, but only 20 points if Black has to take and win the yoseko, anyway. Under the Japanese 1989 rules, however, if the position after :b1:

is left at the end of the game to hypothetical play, White is considered to be dead and Black gets 22 points without having to take and win the ko. So White has to play :w2:

even at temperature 0.

So the Black scaffold for the thermograph of the original position is v = 21 - 2t when t ≤ 13, as for the regular ko. As we have seen, that is the same as the White scaffold, but when should Black play :b1:

? Black can play any time when t ≤ 13, but the lower the temperature the better.

Click Here To Show Diagram Code: [go]$$Wc White threat $$ ----------------- $$ | 1 X X O . O . | $$ | O 3 X X O O . | $$ | X X X O O O O | $$ | O O O X X X X | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ | ? ? ? ? ? ? ? | $$ -----------------[/go]

White to play threatens to capture the Black stones in 2 moves for a local score of -17 + 2t. Black can afford to let White do so when

-17 + 2t ≥ 21 - 2t
t ≥ 38/4 = 9½

t = 9½ is the equitable temperature we found before and thought might be the temperature for below which someone would play. The mast value is 2, as we surmised.

The curious thing is that below that temperature the left and right walls of the thermograph coincide. No matter who plays first the minimax result will be 21 - 2t. In an actual game, however, as the play proceeds the ambient temperature tends to drop over time. So in practice, it is White, not Black, who will tend to initiate play in this position.

However, if White can win the regular ko the result to keep an eye on is -18 + t. At, say, t = 9½ that will mean a local score of -8½ instead of 2. That is a huge difference and so White will be on the lookout for the opportunity to create ko threats.

But here we are simply concerned with the thermograph of this ko, given no external ko threats. Here it is.

Attachment:

yosekoTG000.png

Where the two sides of the thermograph coincide the thermograph is magenta.

It is not easy to understand Bill.

No, it's not. You come up with very interesting positions. :rambo:

Quote:

Assuming a non-ko environment I understand that neither black nor white have a good reason to play first and the final result will be in any case a local score of 21.

Given a tax of t, neither side has an incentive to play locally. And the local score, with the tax, is 21 - 2t. In real life, the t's represent tenukis, the value of which tend to drop over time, so White has the incentive to lose the ko as quickly as possible, when t < 9½, as a rule.

Quote:

In such case my common sense tells me that the thermograph is only a vertical line above 21 maybe with a magenta color to a certain temperature.

That's because you are not taking the tax into account.

Quote:

This non-vertical double wall you draw is really strange, isn't it?

Yup.

Actually, it represents a phenomenon that Berlekamp discovered, and many, if not most, pros are aware of. (Edit: I don't mean the Berlekamp was the first to discover it, although he was probably the first to express it precisely.

) I don't think that any pro has written about it. Perhaps because it is not easy to explain, and it does not come up all that often.

Bill Spight · **#145**

This position has been discussed here. https://www.lifein19x19.com/viewtopic.p ... 65#p260965

In a way, it's easy, but in a way, it's not. :b1:

-

-

form a unit, like a first line hane-and-connect form a unit, but that fact in this position is not immediately obvious, if you are not used to such positions.

Let's draw the themograph.

The position after :b1:

-

is familiar. Let's start with that.

Attachment:

half point gote 000.png [ 3.51 KiB | Viewed 10214 times ]

By convention the scores are represented from Black's point of view, and increase as we go to the left. The vertical dimension represents the temperature which is an indicator of how much a play gains. We may think of the horizontal dimension as the value of positions and the vertical dimension as the value of plays.

Black to play can move to a local score of 1 with gote. This move is indicated by the inclined blue wall. White to play can move to a local score of 0 with gote. That is indicated by the inclined red wall. The walls come together at a height (temperature) of ½, which indicates how much each play gains on average. They also come together at a territorial value (count) of ½, which indicates the average value of the position. Since it is not a final score, we call it a count. Above the point where the walls come together the black mast rises vertically. The black mast indicates that neither player will make a local play when larger plays are available elsewhere (as a rule).

Now let's back up to the position after :b1:

. This is also a familiar position.

Attachment:

three quarter point 000.png [ 3.54 KiB | Viewed 10214 times ]

The left wall indicates a move to a local score of 2 with gote. The move gains ¾ point. The top part of the right wall indicates a move by White with gote to the position after :w2:

. Note the inflection point in the right wall at a count of 1 and a temperature of ½. The right wall of this thermograph indicates the information from the left wall and mast of the thermograph we just drew of the position after :b1:

-

. The inflection point indicates that when moves elsewhere gain ½ point or less Black will reply to :w2:

, as a rule. That is, in that case White will play :w2:

with sente. The black mast rises above temperature ¾ at a count of 1¼.

Finally, the thermograph of the original position.

Attachment:

half point gote 999.png [ 3.51 KiB | Viewed 10214 times ]

The left wall of this thermograph is derived from the right wall of the previous thermograph.

This thermograph is exactly like the thermograph of the position after :b1:

-

, except for the blue mast between temperature ½ and temperature ¾. Above that the mast is black. The blue mast indicates that when the largest play elsewhere gains between ½ and ¾, Black can play :b1:

with sente, as a rule. Black does not need to do so, except perhaps as a ko threat.

Otherwise we may consider the sequence, :b1:

-

-

, as a unit.

Gérard TAILLE · **#146**

Good point Bill,

Bill Spight wrote:

BTW if white plays first the miai value of the area drops to 0 but it remains a ko threat and the thermograph is not the thermograph of a dame is it?

Attachment:

ko threat.png [ 2.14 KiB | Viewed 10183 times ]

Maybe we can say that the value of the position is 0⁺ to show it is a little better for black that a dame?

RobertJasiek · **#147**

Bill Spight wrote:

Otherwise we may consider the sequence, :b1: - :w2: - :b3:, as a unit.

We may do so because it is a 'traversal sequence'. (I have not checked if CGT reversal applies, which might be an alternative reason.)

Bill Spight · **#148**

Gérard TAILLE wrote:

Good point Bill,

Bill Spight wrote:

BTW if white plays first the miai value of the area drops to 0 but it remains a ko threat and the thermograph is not the thermograph of a dame is it?

Attachment:

ko threat.png

Right.

The blue mast extends up to ½.

Quote:

Maybe we can say that the value of the position is 0⁺ to show it is a little better for black that a dame?

That's what I used to do, before learning CGT. Right now the colored mast seems to be a good representation. The things is not to reduce the game tree in such a way as to eliminate the ko threat.

Bill Spight · **#149**

RobertJasiek wrote:

Bill Spight wrote:

Otherwise we may consider the sequence, :b1:

-

-

, as a unit.

We may do so because it is a 'traversal sequence'. (I have not checked if CGT reversal applies, which might be an alternative reason.)

It is a CGT reversal, because the position after :b1:

-

is equal to the original. We can see that with a difference game.

Gérard TAILLE · **#150**

Bill Spight wrote:

RobertJasiek wrote:

Bill Spight wrote:

Otherwise we may consider the sequence, :b1:

-

-

, as a unit.

We may do so because it is a 'traversal sequence'. (I have not checked if CGT reversal applies, which might be an alternative reason.)

It is a CGT reversal, because the position after :b1:

-

is equal to the original. We can see that with a difference game.

I am not sure to understand Bill.
Don't you proof position after :b1:

-

is not equal to the original due to the color of the mast?

Bill Spight · **#151**

RobertJasiek wrote:

Bill Spight wrote:

{Other than when is a ko threat} we may consider the sequence, :b1:

-

-

, as a unit.

We may do so because it is a 'traversal sequence'. (I have not checked if CGT reversal applies, which might be an alternative reason.)

Gérard TAILLE wrote:

Bill Spight wrote:

It is a CGT reversal, because the position after :b1:

-

is equal to the original. We can see that with a difference game.

I am not sure to understand Bill.
Don't you proof position after :b1:

-

is not equal to the original due to the color of the mast?

They are equal as combinatorial games, not as ko threats. Thermography has been extended beyond combinatorial games to kos and superkos.

Gérard TAILLE · **#152**

What about this well known position?

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

To simplify the problem assume area counting.
How do you draw the thermograph? What miai value? How do you show that white cannot avoid playing at temperature 0 in order to gain some more area?

Bill Spight · **#153**

Gérard TAILLE wrote:

What about this well known position?

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

To simplify the problem assume area counting.
How do you draw the thermograph? What miai value? How do you show that white cannot avoid playing at temperature 0 in order to gain some more area?

See https://lifein19x19.com/viewtopic.php?t=11301

Also https://lifein19x19.com/viewtopic.php?t ... 8&#p194948 and the next four notes.

Also https://lifein19x19.com/viewtopic.php?p=246125#p246125

You may also be interested in the discussion between Robert and me here and thereabouts. https://lifein19x19.com/viewtopic.php?p=225084#p225084

Bill Spight · **#154**

Here is an sgf file for Three-Points-Without-Capturing, assuming no ko threats.

Here is the game tree: {-3|-3||-2}. This is a standoff, as neither player wishes to play first. In CGT this reduces to { |-2}. That is, White to play moves to a local score of -2. In go terms that is equivalent to filling your own territory. If filling your own territory costs one point, you had one more point to start with. { |-2} = -3. The fact that go players came up with the same value is very interesting, isn't it? :cool:

BTW, in CGT the dame when Black plays first is significant. {-3|-2} = -2½. You get a similar effect with rules that penalize Black one point for passing first, but not White. Then the first pass is worth {-1|0} = -½ in CGT.

Let's try to construct the thermograph for this position.

Attachment:

sanmoku 999.png [ 2.15 KiB | Viewed 10075 times ]

The left scaffold is to the right of the right scaffold at or above temperature 0. This indicates a standoff. Neither player will wish to play first. All we can say at this point is that the score of the position lies between -2 and -3, inclusive. CGT, as we have seen, evaluates this game as -3. The Japanese 1989 rules evaluate it as -2, by forcing White to play at temperature 0 to avoid a seki. Before that, as the name indicates, Japanese rules evaluated this as -3 at the end of play. (The ko threat situation is significant, OC.) The fact that the left scaffold is vertical at temperature 0 cannot be seen, as it is inclined above temperature 0.

To handle such games Berlekamp extended thermography downward to temperature -1, which he called subterranean thermography. Below temperature 0 the vertical blue scaffold shows up.

Attachment:

sanmoku888.png [ 2.86 KiB | Viewed 10075 times ]

Not only does the vertical blue line show up, the two scaffolds of the thermograph meet at a local score of -3. The mast rises vertically from that point.

Attachment:

sanmoku000.png [ 2.36 KiB | Viewed 10075 times ]

At temperature -1 we have a tax of -1 for each play. In go that means that each stone played is worth 1 point. However, it is not exactly the same as stone counting. With stone counting this position would be worth 0, not -3.

Anyway, subterranean thermography gives us the correct CGT mast for Three-Points-Without-Capturing with no ko threats. :cool:

Gérard TAILLE · **#155**

Bill Spight wrote:

To handle such games Berlekamp extended thermography downward to temperature -1, which he called subterranean thermography. Below temperature 0 the vertical blue scaffold shows up.

Attachment:

The attachment sanmoku888.png is no longer available

Not only does the vertical blue line show up, the two scaffolds of the thermograph meet at a local score of -3. The mast rises vertically from that point.

Attachment:

The attachment sanmoku000.png is no longer available

At temperature -1 we have a tax of -1 for each play. In go that means that each stone played is worth 1 point. However, it is not exactly the same as stone counting. With stone counting this position would be worth 0, not -3.

Anyway, subterranean thermography gives us the correct CGT mast for Three-Points-Without-Capturing with no ko threats. :cool:

First of all I suggest to take only area counting to avoid discussing japonese rule because it is not my point.

Maybe it is still clearer to draw the thermograph even under temperature = -1

Attachment:

t.png [ 7.29 KiB | Viewed 10050 times ]

But I see a problem. As soon as you take a tax < 0 you change the rule of the game.
Imagine you are playing a game with tax = -100. The game looks like a go game in the first part of the game but the goal being to get the last move the strategy will be clearly different as the game proceeds.

Just a very small example:

Click Here To Show Diagram Code: [go]$$B White to play $$ --------------------- $$ | . b . a O O . O . | $$ | X . X X O O O O O | $$ | X X X O X X X O . | $$ | . X O O . . X O O | $$ | X X O . . . X X X | $$ | O O O . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ ---------------------[/go]

with tax = -3 black "b" is better than black "a" isn't it?

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

My problem was to find the miai value (-3) by thermography but OC without changing the rule (I assume chinese rule in which the result is quite easy to calculate).

Bill Spight · **#156**

Gérard TAILLE wrote:

First of all I suggest to take only area counting to avoid discussing japonese rule because it is not my point.

Well, the Japanese rules are relevant.

Gérard TAILLE wrote:

To simplify the problem assume area counting.
How do you draw the thermograph? What miai value? How do you show that white cannot avoid playing at temperature 0 in order to gain some more area?

(Emphasis mine.)

The Japanese '89 rules require White to play at temperature 0 to avoid a ruling of seki. That's why this position is worth only -2 under them.

Quote:

Maybe is still clearer to draw the thermograph even under temperature = -1

Attachment:

t.png

But then { |-2} becomes worth -4 at temperature -2.

Quote:

But I see a problem. As soon as you take a tax < 0 you change the rule of the game.

The problems come, as with { |-2}, with a tax < -1.

Quote:

Imagine you are playing a game with tax = -100. The game looks like a go game in the first part of the game but the goal being to get the last move the strategy will be clearly different as the game proceeds.

How much are prisoners worth? If they are also worth 100 points then the strategy changes little. If they are worth 0, then the strategy changes a lot, even with no tax. See https://senseis.xmp.net/?NoPassGo for a game where the goal is to get the last move and prisoners count 0. It's strategy will be very similar to the one where each stone played is worth 100 points but each prisoner is worth only 1 point.

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Just a very small example:

Click Here To Show Diagram Code: [go]$$B White to play $$ --------------------- $$ | . b . a O O . O . | $$ | X . X X O O O O O | $$ | X X X O X X X O . | $$ | . X O O . . X O O | $$ | X X O . . . X X X | $$ | O O O . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ ---------------------[/go]

with tax = -3 black "b" is better than black "a" isn't it?

Yes, if prisoners count only 1 point.

Quote:

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

My problem was to find the miai value (-3) by thermography but OC without changing the rule (I assume chinese rule in which the result is quite easy to calculate).

Well, the only problem is the Japanese '89 rules.

Gérard TAILLE · **#157**

Bill Spight wrote:

Gérard TAILLE wrote:

First of all I suggest to take only area counting to avoid discussing japonese rule because it is not my point.

Well, the Japanese rules are relevant.

Gérard TAILLE wrote:

To simplify the problem assume area counting.
How do you draw the thermograph? What miai value? How do you show that white cannot avoid playing at temperature 0 in order to gain some more area?

(Emphasis mine.)

The Japanese '89 rules require White to play at temperature 0 to avoid a ruling of seki. That's why this position is worth only -2 under them.

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Maybe is still clearer to draw the thermograph even under temperature = -1

Attachment:

t.png

But then { |-2} becomes worth -4 at temperature -2.

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But I see a problem. As soon as you take a tax < 0 you change the rule of the game.

The problems come, as with { |-2}, with a tax < -1.

Quote:

Imagine you are playing a game with tax = -100. The game looks like a go game in the first part of the game but the goal being to get the last move the strategy will be clearly different as the game proceeds.

How much are prisoners worth? If they are also worth 100 points then the strategy changes little. If they are worth 0, then the strategy changes a lot, even with no tax. See https://senseis.xmp.net/?NoPassGo for a game where the goal is to get the last move and prisoners count 0. It's strategy will be very similar to the one where each stone played is worth 100 points but each prisoner is worth only 1 point.

Quote:

Just a very small example:

Click Here To Show Diagram Code: [go]$$B White to play $$ --------------------- $$ | . b . a O O . O . | $$ | X . X X O O O O O | $$ | X X X O X X X O . | $$ | . X O O . . X O O | $$ | X X O . . . X X X | $$ | O O O . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ ---------------------[/go]

with tax = -3 black "b" is better than black "a" isn't it?

Yes, if prisoners count only 1 point.

Quote:

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

My problem was to find the miai value (-3) by thermography but OC without changing the rule (I assume chinese rule in which the result is quite easy to calculate).

Well, the only problem is the Japanese '89 rules.

OK Bill let's take Japanese '89 rules.
You rose the problem of the value of prisoner. Why do you to change its value? When you use a positive tax, say tax = 9, you keep the value 1 of the prisoner or you change to the value 9 ?
Do thermography imply to change the prisoner value if tax is negative but not if tax is positive?
Do you agree that the game rule change if you use negative tax?
BTW the game changes also if tax is positive but maybe only by stopping the game when neither player accepts to move with the level of the tax. If tax is negative the problem is different because here the players will continue to play but by changing their strategy.

Bill Spight · **#158**

Gérard TAILLE wrote:

Bill Spight wrote:

Gérard TAILLE wrote:

First of all I suggest to take only area counting to avoid discussing japonese rule because it is not my point.

Well, the Japanese rules are relevant.

Gérard TAILLE wrote:

To simplify the problem assume area counting.
How do you draw the thermograph? What miai value? How do you show that white cannot avoid playing at temperature 0 in order to gain some more area?

(Emphasis mine.)

The Japanese '89 rules require White to play at temperature 0 to avoid a ruling of seki. That's why this position is worth only -2 under them.

Quote:

Maybe is still clearer to draw the thermograph even under temperature = -1

Attachment:

t.png

But then { |-2} becomes worth -4 at temperature -2.

Quote:

But I see a problem. As soon as you take a tax < 0 you change the rule of the game.

The problems come, as with { |-2}, with a tax < -1.

Quote:

Imagine you are playing a game with tax = -100. The game looks like a go game in the first part of the game but the goal being to get the last move the strategy will be clearly different as the game proceeds.

How much are prisoners worth? If they are also worth 100 points then the strategy changes little. If they are worth 0, then the strategy changes a lot, even with no tax. See https://senseis.xmp.net/?NoPassGo for a game where the goal is to get the last move and prisoners count 0. It's strategy will be very similar to the one where each stone played is worth 100 points but each prisoner is worth only 1 point.

Quote:

Just a very small example:

Click Here To Show Diagram Code: [go]$$B White to play $$ --------------------- $$ | . b . a O O . O . | $$ | X . X X O O O O O | $$ | X X X O X X X O . | $$ | . X O O . . X O O | $$ | X X O . . . X X X | $$ | O O O . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ | . . . . . . . . . | $$ ---------------------[/go]

with tax = -3 black "b" is better than black "a" isn't it?

Yes, if prisoners count only 1 point.

Quote:

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

My problem was to find the miai value (-3) by thermography but OC without changing the rule (I assume chinese rule in which the result is quite easy to calculate).

Well, the only problem is the Japanese '89 rules.

OK Bill let's take Japanese '89 rules.

Let's not. They are an abomination.

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You rose the problem of the value of prisoner. Why do you to change its value?

To illustrate that with a tax less than -1, the value of a prisoner affects the strategy.

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When you use a positive tax, say tax = 9, you keep the value 1 of the prisoner or you change to the value 9 ?

Yes, because with a positive tax you want to reduce the value of a move for the purpose of finding the mean value of a game.

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Do thermography imply to change the prisoner value if tax is negative but not if tax is positive?

A negative tax is used to find the actual value of a number, not it average value. A tax less than -1 finds the wrong CGT values for some numbers, such as { |-2} = -3.

My idea of changing the prisoner value with a tax less than -1 was to show how increasing it to the negative of the tax made the strategy close to regular go, while keeping it the same made a high negative tax change the strategy to approach no pass go in the limit.

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Do you agree that the game rule change if you use negative tax?

It's a different game if the tax is less than -1, because the scores are different. In regular go the score for each prisoner is 1 point.

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BTW the game changes also if tax is positive but maybe only by stopping the game when neither player accepts to move with the level of the tax.

It's a different game, but similar enough to shed light on the regular game.

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If tax is negative the problem is different because here the players will continue to play but by changing their strategy.

A tax less than -1 changes the values of numbers (scores).

Gérard TAILLE · **#159**

Bill Spight wrote:

Gérard TAILLE wrote:

OK Bill let's take Japanese '89 rules.

Let's not. They are an abomination.

Why are we talking about prisonners?

Bill Spight · **#160**

Gérard TAILLE wrote:

Bill Spight wrote:

Gérard TAILLE wrote:

OK Bill let's take Japanese '89 rules.

Let's not. They are an abomination.

Why are we talking about prisonners?

Because each prisoner scores 1 point by traditional territory scoring. The current Japanese rules are not the only territory rules. There are Korean rules. Many go servers use their own territory rules. There are the Japanese '49 rules, there are Berlekamp's no pass go rules with prisoner return, there are Lasker-Maas rules, there are Spight rules, there are Ikeda rules, there are ancient Chinese and Japanese rules that used territory scoring with a group tax. The Japanese '89 rules are the only ones I know of that score this position as -2.

Besides, we have always been talking territory scores, right?

Thermography

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