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 Post subject: Re: Thermography #81 Posted: Thu Oct 08, 2020 3:07 am
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`[go]\$\$ -----------------\$\$ | . . . 3 1 a O |\$\$ | X X b . 2 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ ----------------[/go]`

Finally the three moves above seems correct whatever the temperature.

After this basic sequence:
-if temperature is above 1 white continue with "a" otherwise white play "b".
-between temperature 1 and 2, after white "a" black answers at "b"
-above temperature 2, after white "a" black plays tenuki.

This result is surprisingly quite simple isn't it?

 This post by Gérard TAILLE was liked by: Bill Spight
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 Post subject: Re: Thermography #82 Posted: Thu Oct 08, 2020 3:52 am
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Just a basic theoritical question.
For analysing a local yose area I often prefer to use an area counting. Assuming there no seki, my question is the following:
is the thermograph in "territory counting" strictly identical to the thermograph part above temperature 1 in "area counting" ?

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 Post subject: Re: Thermography #83 Posted: Thu Oct 08, 2020 7:52 am
 Honinbo

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Consider this case.

`[go]\$\$Bc\$\$ -----------------\$\$ | . . . . . . O |\$\$ | X X . . . . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . X X X O O O |\$\$ | . X O X X X O |\$\$ | . X O O O . O |\$\$ -----------------[/go]`

Let White play first.

`[go]\$\$Wc\$\$ -----------------\$\$ | . . . 4 2 5 O |\$\$ | X X . . 3 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . X X X O O O |\$\$ | . X O X X X O |\$\$ | . X O O O 1 O |\$\$ -----------------[/go]`

gains as much, on average, as the reverse sente, and lets White get the last play (locally) of that size. After the local temperature has dropped to 2.

Now let Black play first.

`[go]\$\$Bc Small trap\$\$ -----------------\$\$ | . . 3 . 1 4 O |\$\$ | X X . . 2 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . X X X O O O |\$\$ | . X O X X X O |\$\$ | . X O O O 5 O |\$\$ -----------------[/go]`

sets a small trap for White. loses ⅓ of a point on average, as discussed above. After the local temperature has dropped to ⅚.

`[go]\$\$Bc \$\$ -----------------\$\$ | . . 3 4 1 . O |\$\$ | X X . . 2 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . X X X O O O |\$\$ | . X O X X X O |\$\$ | . X O O O 5 O |\$\$ -----------------[/go]`

maintains the local temperature at 2. Below temperature 2 White plays on.

`[go]\$\$Bc \$\$ -----------------\$\$ | . . 3 4 1 8 O |\$\$ | X X 6 7 2 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . X X X O O O |\$\$ | . X O X X X O |\$\$ | . X O O O 5 O |\$\$ -----------------[/go]`

captures and .

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 Post subject: Re: Thermography #84 Posted: Thu Oct 08, 2020 8:09 am
 Honinbo

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Gérard TAILLE wrote:
Just a basic theoritical question.
For analysing a local yose area I often prefer to use an area counting. Assuming there no seki, my question is the following:
is the thermograph in "territory counting" strictly identical to the thermograph part above temperature 1 in "area counting" ?

Except for the count, yes. And for Japanese seki (edit: in the environment) you just have to adjust the count accordingly. There may be some kos or superkos that different rules treat differently, and that will affect the thermograph.

Edit: OIC. You mean if there is a seki or possible seki in the play. In that case a Japanese seki may well alter the thermograph.

_________________
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 Post subject: Re: Thermography #85 Posted: Thu Oct 08, 2020 8:30 am
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`[go]\$\$B\$\$ -----------------\$\$ | . . 3 6 1 4 O |\$\$ | X X 7 . 2 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ ----------------[/go]`

tenuky

Bill, when you analysed the sequence above you clearly took into account the resulting ko by using one third of the deiri value of the ko. That's sounds fine for me.

`[go]\$\$B counting a ko\$\$ -----------------\$\$ | . . 3 4 1 . O |\$\$ | X X 2 5 6 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

but after this sequence above I do not understand why you never take into account this ko.

Let me try to count it.

white wins the ko:
`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . 3 B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

tenuki
and the score for black is -8

black connects the ko
`[go]\$\$B counting a ko\$\$ -----------------\$\$ | . 3 B 1 B 2 O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

and the score for black is -1

I conclude that each move in the ko is worth 2⅓

But we have to be aware that after:
`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . a B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

black may also defend at "a"
Let's count this new position:
`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . B B W B . O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

black to play
`[go]\$\$B counting a ko\$\$ -----------------\$\$ | . B B 3 B 4 O |\$\$ | X X W 1 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

tenuki
and the score for black is -1

white to play
`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . B B W B 1 O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

and the score for black is -6

`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . B B W B . O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

Eventually the score of this position is -3½

`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . 3 B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

tenuki

comparing with this sequence leading to the black score -8 it means that
`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . a B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

the black defense at "a" is worth (8 - 3½)/2 = 2¼

Seeing this black defense is worth 2¼ which is less than the value 2⅓ of a move in the ko I conclude that black will never defends like this because when black chose to keep sente that meant the temperature was above 2⅓.

`[go]\$\$B counting a ko\$\$ -----------------\$\$ | . . . . 1 . O |\$\$ | X X . . . . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

Finally when black, above temperature 2⅓ plays 1, the score of black is not -3 but rather -3⅓

If all that is true then the thermogrph corrected is the following
Attachment:

grille3.png [ 25.92 KiB | Viewed 2019 times ]

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 Post subject: Re: Thermography #86 Posted: Thu Oct 08, 2020 9:27 am
 Honinbo

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Gérard TAILLE wrote:
`[go]\$\$B\$\$ -----------------\$\$ | . . 3 6 1 4 O |\$\$ | X X 7 . 2 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ ----------------[/go]`

tenuky

Bill, when you analysed the sequence above you clearly took into account the resulting ko by using one third of the deiri value of the ko. That's sounds fine for me.

`[go]\$\$B counting a ko\$\$ -----------------\$\$ | . . 3 4 1 . O |\$\$ | X X 2 5 6 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

but after this sequence above I do not understand why you never take into account this ko.

Since ko thermography is complicated and we are just getting started (I am including many of our readers in that. ), I avoided discussion of ko fights, except for suggesting the traditional assumption of no ko threats. This position confounds ko with sente, which makes it fairly advanced.

Quote:
Let me try to count it.

white wins the ko:
`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . 3 B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

tenuki
and the score for black is -8

black connects the ko
`[go]\$\$B counting a ko\$\$ -----------------\$\$ | . 3 B 1 B 2 O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

and the score for black is -1

I conclude that each move in the ko is worth 2⅓

Nope. Sente is involved.

Quote:
But we have to be aware that after:
`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . a B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

black may also defend at "a"

Good catch.

Quote:
Let's count this new position:
`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . B B W B . O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

black to play
`[go]\$\$B counting a ko\$\$ -----------------\$\$ | . B B 3 B 4 O |\$\$ | X X W 1 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

tenuki
and the score for black is -1

In real life Black might play at 4 instead of connecting at 3, threatening the life of White's group. But assuming no ko threats, White will just take and win the ko. So let fill the ko. With sente, as your indicates. Black has played only one more move than White, unlike with a regular ko.

Quote:
white to play
`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . B B W B 1 O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

and the score for black is -6

`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . B B W B . O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

Eventually the score of this position is -3½

Well done! In calculating the count you correctly took sente into account.

Edit: Here I missed the miscalculation of the score when White wins the ko. It is -5, not -6.

Note also that each play in the ko gains 2½ points. Playing the ko raises the local temperature.

Edit: That means that each play in the ko gains only 2 points, not 2½ points. Since 2 < 2⅓, Black's connection in the corner reduces the temperature, not raises it. I corrected my mistake in my next note.

Quote:
`[go]\$\$W counting a ko \$\$ -----------------\$\$ | . 3 B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

tenuki

comparing with this sequence leading to the black score -8 it means that
`[go]\$\$W counting a ko\$\$ -----------------\$\$ | . a B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

the black defense at "a" is worth (8 - 3½)/2 = 2¼

That might be so if Black a were gote, but it is sente. You can see that by the fact that 2¼ < 2½.

Edit: Again incorrect, based upon the inaccurate calculation.

Black a threatens to take and win the ko, also in sente.

So, assuming no ko threats, if White takes the ko, play goes like this.

`[go]\$\$Wc counting a ko II\$\$ -----------------\$\$ | . 2 B 1 B 3 O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

The local score is -6 with one net play by White.

Edit: Correction. The local score is -5. The rest is fine.

`[go]\$\$Wc No ko\$\$ -----------------\$\$ | . . B . B 1 O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

achieves the same result without the ko.

In a real game White might take the ko to eliminate the possible Black ko threat in this position. But the thermograph is the same.

_________________
At some point, doesn't thinking have to go on?

Visualize whirled peas.

Everything with love. Stay safe.

Last edited by Bill Spight on Thu Oct 08, 2020 3:02 pm, edited 2 times in total.
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 Post subject: Re: Thermography #87 Posted: Thu Oct 08, 2020 10:19 am
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[quote="Bill Spight"]
`[go]\$\$B counting a ko\$\$ -----------------\$\$ | . 1 B W B a O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

Oops I do not see how can be sente.
Instead of answering at "a" white can be the first to play in the environment, answering at "a" only after black takes the ko can't she?
That is the basic reason why I think the ko gives white a slight advantage comparing to the analyse without ko.

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 Post subject: Re: Thermography #88 Posted: Thu Oct 08, 2020 11:42 am
 Honinbo

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Gérard TAILLE wrote:
Bill Spight wrote:
`[go]\$\$B counting a ko\$\$ -----------------\$\$ | . 1 B W B a O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

Oops I do not see how can be sente.
Instead of answering at "a" white can be the first to play in the environment, answering at "a" only after black takes the ko doesn't it?

Actually, my characterization of here as sente is not accurate. It was based on a miscount. Let's do it right.

`[go]\$\$Bc counting a ko\$\$ -----------------\$\$ | . . B . B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

1 prisoner

This position, assuming no ko threats, has a count of -3, counting one White prisoner which Black has captured.

`[go]\$\$Bc Black wins the ko\$\$ -----------------\$\$ | . 3 B 1 B 2 O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

1 prisoner

The local score is -1. With one net play Black has gained 2 points on average.

Now suppose that White wins the ko in 2 moves.

`[go]\$\$Wc White wins the ko\$\$ -----------------\$\$ | . 3 B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

1 prisoner

The local score is -8. If this line of play is correct, there is a difference of 7 points in 3 plays, for an average gain per play of 2⅓ points. (And the original value of -3 is wrong. It should be -3⅓.)

But suppose that connects in the top left corner.

`[go]\$\$Wc Black connects in the corner\$\$ -----------------\$\$ | . 2 B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

1 prisoner

Now we have a new ko.

`[go]\$\$Wc White wins the ko\$\$ -----------------\$\$ | . B B W B 1 O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

1 prisoner, 1 prisoner

The position after has a score of only -5, not -6. What were we thinking?

Let Black take and win the ko, with sente.

`[go]\$\$Bc Black wins the ko\$\$ -----------------\$\$ | . B B W B 4 O |\$\$ | X X W 1 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

1 prisoner, 1 prisoner

fills the ko with sente. Alternatively, White can play at 4. The result is -1 with one net Black play in either case, OC.

That means that each play in the ko (except Black filling it) gains 2 points, not 2½ points.

`[go]\$\$Wc Black connects in the corner\$\$ -----------------\$\$ | . 2 B W B . O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

1 prisoner, 1 prisoner

And that means that the position after is worth -3, on average. And that means that gains 2½ points.

`[go]\$\$Wc White takes the ko, with sente\$\$ -----------------\$\$ | . 2 B 1 B . O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

1 prisoner

And that means that the position after is worth 5½ points, and is indeed gote, gaining 2½ points. And that means that raises the local temperature from 2 to 2½. is the sente, not .

Anyway, before White takes the ko the local temperature is 2. raises it to 2½, then brings it back down to 2. It is true that can tenuki, but the sente exchange, - , has not altered the count. Only now, Black can take and win the ko with sente.

_________________
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Visualize whirled peas.

Everything with love. Stay safe.

 This post by Bill Spight was liked by: Gérard TAILLE
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 Post subject: Re: Thermography #89 Posted: Thu Oct 08, 2020 2:17 pm
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This time I quite agree with you Bill

Before temperature drops to 4 black plays in sente:
`[go]\$\$B \$\$ -----------------\$\$ | . . 3 4 1 . O |\$\$ | X X 2 5 6 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

when temperature drops between 2 and 2.5 white continue in sente:
`[go]\$\$W \$\$ -----------------\$\$ | . 2 B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

but here is the point. Can white gain something, even if the following capture of the ko by black is sente ?
From a theorical point of view it seems possible.
Assume white waits until we reach the temperature 2+ε, I mean the temperature of the smallest point above temperature 2.
Then the following sequence will take place:

`[go]\$\$W\$\$ -----------------\$\$ | . 2 B 1 B 5 O |\$\$ | X X W 4 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

takes point 2+ε
connects
takes point at temperature 2

As you can see, with this strategy white can gain ε points.

In any case, without any calculation, when seeing the position
`[go]\$\$B\$\$ -----------------\$\$ | . B B . B a O |\$\$ | X X W 1 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

white can answer by the safe "a" move but, undoubtely white might in certain circumstancies, be confident that black cannot really lose another move by playing at "a" even for a far larger ko.

That means that, from a theoritical point of view you can assume that this possibility allows white to gain say ε points (in practise ε may be equal to zero but sometimes ε may be greater than zero).

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 Post subject: Re: Thermography #90 Posted: Thu Oct 08, 2020 4:27 pm
 Honinbo

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Gérard TAILLE wrote:
This time I quite agree with you Bill

Before temperature drops to 4 black plays in sente:
`[go]\$\$B \$\$ -----------------\$\$ | . . 3 4 1 . O |\$\$ | X X 2 5 6 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

It now appears that the following sequence may be dominant play for White.

`[go]\$\$B \$\$ -----------------\$\$ | . . 3 4 1 . O |\$\$ | X X a . 2 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

However, White can possibly reach the same ko position by playing at a when the temperature is above 2 but below 2.5. This sequence does not affect your argument below.

Quote:
when temperature drops between 2 and 2.5 white continue in sente:
`[go]\$\$W \$\$ -----------------\$\$ | . 2 B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

but here is the point. Can white gain something, even if the following capture of the ko by black is sente ?
From a theorical point of view it seems possible.
Assume white waits until we reach the temperature 2+ε, I mean the temperature of the smallest point above temperature 2.
Then the following sequence will take place:

`[go]\$\$W\$\$ -----------------\$\$ | . 2 B 1 B 5 O |\$\$ | X X W 4 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

takes point 2+ε
connects
takes point at temperature 2

As you can see, with this strategy white can gain ε points.

In any case, without any calculation, when seeing the position
`[go]\$\$B\$\$ -----------------\$\$ | . B B . B a O |\$\$ | X X W 1 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

white can answer by the safe "a" move but, undoubtely white might in certain circumstancies, be confident that black cannot really lose another move by playing at "a" even for a far larger ko.

That means that, from a theoritical point of view you can assume that this possibility allows white to gain say ε points (in practise ε may be equal to zero but sometimes ε may be greater than zero).

For clarity, here is the position before .

`[go]\$\$Wc\$\$ -----------------\$\$ | . B B W B . O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

The number of prisoners is equal.

Because of the absence of ko threats, Black cannot make a ko for the life of the group.

takes the last move before the temperature drops to 2, gaining 2+ε. Our model environment assumes a sufficiently large number of simple gote at temperature 2, followed by a sufficiently large number of simple gote at a slightly lower temperature, etc.

Suppose that Black takes the ko in the following sequence.

`[go]\$\$Wc\$\$ -----------------\$\$ | . B B W B 5 O |\$\$ | X X W 4 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

connects.

Black has gained 2 points on average in this exchange. White now plays in the environment, taking a 2 point gote. We estimate White's gain from doing so as 1 point. So our estimate of White's gain, starting with is 2+ε - 2 + 1 = 1+ε.

Note that this estimate is the same as the one if Black took a simple 2 point gote instead of this ko.

Suppose now that takes a play in the environment and White wins the ko, and then Black plays in the environment again. Both Black plays gain 2 points, because there are plenty of 2 point plays in the environment.

`[go]\$\$Wc\$\$ -----------------\$\$ | . B B W B 5 O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

gains 2 points, on average.

White's expected gain from this sequence is 2+ε - 2 + 2 - 1 = 1+ε, the same as above.

Now let take the ko but play in the environment, and then wins the ko with sente.

`[go]\$\$Wc\$\$ -----------------\$\$ | . B B W B 7 O |\$\$ | X X W 4 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

elsewhere, connects.

White's expected gain from this sequence is 2+ε - 2 + 2 - 1 = 1+ε, still the same.

OC, this is the same as if there were a simple 2 point gote on the board instead of the ko.

----

Now let's use my original model of the environment as a set of simple gote, each gaining gi, such that g0 ≥ g1 ≥ g2 ≥ . . . . Let g1 = 2 and takes g0.

`[go]\$\$Wc Sequence 1\$\$ -----------------\$\$ | . B B W B 5 O |\$\$ | X X W 4 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

connects.

White's expected gain is g0 - 2 + g1 - g2/2 = g0 - g2/2.

`[go]\$\$Wc Sequence 2\$\$ -----------------\$\$ | . B B W B 5 O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

elsewhere

White's expected gain is g0 - g1 + 2 - g2/2 = g0 - g2/2, the same as above.

`[go]\$\$Wc Sequence 3\$\$ -----------------\$\$ | . B B W B 7 O |\$\$ | X X W 4 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

elsewhere, connects.

White's expected gain is g0 - 2 + g1 - g2/2 = g0 - g2/2, the same as above.

All same same.

The result is the same as if the ko were a simple 2 point gote.

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 Post subject: Re: Thermography #91 Posted: Fri Oct 09, 2020 10:24 am
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Bill Spight wrote:
Now let's use my original model of the environment as a set of simple gote, each gaining gi, such that g0 ≥ g1 ≥ g2 ≥ . . . . Let g1 = 2 and takes g0.

`[go]\$\$Wc Sequence 1\$\$ -----------------\$\$ | . B B W B 5 O |\$\$ | X X W 4 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

connects.

I like very much your set of simple gote g0 ≥ g1 ≥ g2 ≥ . . . . because it is very simple to analyse.

`[go]\$\$Wc Sequence 1\$\$ -----------------\$\$ | . . B . B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

So let's consider the local area above and let's add an environment made of simple gote g1 ≥ g2 ≥ g3 ≥ . . . .
The temperature of the environment is of course t = g1.
In addition is it a good understanding that no ko threat exists in the environment? In other words if a ko fight takes place in the local area then an answer to this ko by a move in the environment can be only a move taking the biggest gote.

If this is true, before commenting your last post I need another information
`[go]\$\$Wc Sequence 1\$\$ -----------------\$\$ | . 2 B 1 B a O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

You understood from my earlier posts, that white takes the ko with as soon as temperature drops to 2⅓.
Because you consider gains 2½ I conclude is sente.
Now, white considering that a move at "a" gains only 2 points, she plays tenuki until temperature drops to 2.
My question is the following:
At which temperature will black takes the ko and what will be the final score for black if, after black has taken the ko, white continues to wait until temperature drops to 2 before answering at "a" ?
Of course if black takes the ko between temperature 2 and 2⅓ then if black continues by playing herself at "a" the two following white moves will be obviously white takes the ko and white connects.

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 Post subject: Re: Thermography #92 Posted: Fri Oct 09, 2020 12:54 pm
 Honinbo

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Gérard TAILLE wrote:
Bill Spight wrote:
Now let's use my original model of the environment as a set of simple gote, each gaining gi, such that g0 ≥ g1 ≥ g2 ≥ . . . . Let g1 = 2 and takes g0.

`[go]\$\$Wc Sequence 1\$\$ -----------------\$\$ | . B B W B 5 O |\$\$ | X X W 4 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

connects.

I like very much your set of simple gote g0 ≥ g1 ≥ g2 ≥ . . . . because it is very simple to analyse.

`[go]\$\$Wc Sequence 1\$\$ -----------------\$\$ | . . B . B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

So let's consider the local area above and let's add an environment made of simple gote g1 ≥ g2 ≥ g3 ≥ . . . .
The temperature of the environment is of course t = g1.

Actually, you can set t to any of the gis.

Quote:
In addition is it a good understanding that no ko threat exists in the environment?

You have to say something about the ko threat situation.

Quote:
In other words if a ko fight takes place in the local area then an answer to this ko by a move in the environment can be only a move taking the biggest gote.

If this is true, before commenting your last post I need another information
`[go]\$\$Wc Sequence 1\$\$ -----------------\$\$ | . 2 B 1 B a O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

You understood from my earlier posts, that white takes the ko with as soon as temperature drops to 2⅓.

I understood from that post that White takes the ko between temperature 2½ and 2. Maybe you have an earlier post in mind.

Quote:
Because you consider gains 2½ I conclude is sente.

In the sense that it raises the local temperature until White replies, but you can also consider it to be ambiguous, because when White replies the local temperature has not dropped. (See https://senseis.xmp.net/?AmbiguousPosition ).

Quote:
Now, white considering that a move at "a" gains only 2 points, she plays tenuki until temperature drops to 2.
My question is the following:
At which temperature will black takes the ko and what will be the final score for black if, after black has taken the ko, white continues to wait until temperature drops to 2 before answering at "a" ?

As indicated, with no ko threats this position is equivalent to a simple 2 point gote. That being the case it is played in descending order with the gote in the environment.

If White has enough sufficiently large ko threats, White could fight the ko and possibly gain by delaying winning the ko at a. OC, in this case those threats would have to be humungous, since if Black fills the ko she threatens to kill the White group.

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 Post subject: Re: Thermography #93 Posted: Fri Oct 09, 2020 3:16 pm
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Bill Spight wrote:
Gérard TAILLE wrote:
Bill Spight wrote:
Now let's use my original model of the environment as a set of simple gote, each gaining gi, such that g0 ≥ g1 ≥ g2 ≥ . . . . Let g1 = 2 and takes g0.

`[go]\$\$Wc Sequence 1\$\$ -----------------\$\$ | . B B W B 5 O |\$\$ | X X W 4 W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

connects.

I like very much your set of simple gote g0 ≥ g1 ≥ g2 ≥ . . . . because it is very simple to analyse.

`[go]\$\$Wc Sequence 1\$\$ -----------------\$\$ | . . B . B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

So let's consider the local area above and let's add an environment made of simple gote g1 ≥ g2 ≥ g3 ≥ . . . .
The temperature of the environment is of course t = g1.

Actually, you can set t to any of the gis.

Quote:
In addition is it a good understanding that no ko threat exists in the environment?

You have to say something about the ko threat situation.

Quote:
In other words if a ko fight takes place in the local area then an answer to this ko by a move in the environment can be only a move taking the biggest gote.

If this is true, before commenting your last post I need another information
`[go]\$\$Wc Sequence 1\$\$ -----------------\$\$ | . 2 B 1 B a O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

You understood from my earlier posts, that white takes the ko with as soon as temperature drops to 2⅓.

I understood from that post that White takes the ko between temperature 2½ and 2. Maybe you have an earlier post in mind.

Quote:
Because you consider gains 2½ I conclude is sente.

In the sense that it raises the local temperature until White replies, but you can also consider it to be ambiguous, because when White replies the local temperature has not dropped. (See https://senseis.xmp.net/?AmbiguousPosition ).

Quote:
Now, white considering that a move at "a" gains only 2 points, she plays tenuki until temperature drops to 2.
My question is the following:
At which temperature will black takes the ko and what will be the final score for black if, after black has taken the ko, white continues to wait until temperature drops to 2 before answering at "a" ?

As indicated, with no ko threats this position is equivalent to a simple 2 point gote. That being the case it is played in descending order with the gote in the environment.

If White has enough sufficiently large ko threats, White could fight the ko and possibly gain by delaying winning the ko at a. OC, in this case those threats would have to be humungous, since if Black fills the ko she threatens to kill the White group.

Finally it seems we have now identified the unexpected best sequence when the temperature drops regularly:

`[go]\$\$Bc Sequence 1\$\$ -----------------\$\$ | . . . . . . O |\$\$ | X X . . . . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

At high temperature black should be able to play in sente

eather
`[go]\$\$B\$\$ -----------------\$\$ | . . . 3 1 4 O |\$\$ | X X . . 2 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

or
`[go]\$\$B\$\$ -----------------\$\$ | . . 3 4 1 . O |\$\$ | X X 2 5 6 . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

with this second sequence, when temperature drops between between 2½ and 2 white can follow in sente by

`[go]\$\$W\$\$ -----------------\$\$ | . 2 B 1 B . O |\$\$ | X X W B W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

and we reach the position
`[go]\$\$B\$\$ -----------------\$\$ | . B B W B . O |\$\$ | X X W . W . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . . X X X X |\$\$ | . . . . . . . |\$\$ -----------------[/go]`

which can viewed as a 2 gote area with a local score of -3 for black point of view.

This result is a little unexpected maybe due to some miscalculation of position scores from both of us.

The very common monkey appears really a quite difficult move to analyse in a real environment where you can be faced to ko threats and to miai or tedomari considerations!

Very good job Bill.

BTW Bill, does it exist some theory in which we add in the ideal environment of gote areas, the same number of ko threats for black and white, with value decreasing regularly.
Such environment will be interesting to handle a local ko fight which impose for one of the player to find greater ko threats than the other player.

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 Post subject: Re: Thermography #94 Posted: Fri Oct 09, 2020 4:37 pm
 Honinbo

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Gérard TAILLE wrote:
BTW Bill, does it exist some theory in which we add in the ideal environment of gote areas, the same number of ko threats for black and white, with value decreasing regularly.
Such environment will be interesting to handle a local ko fight which impose for one of the player to find greater ko threats than the other player.

It may be somewhat different from what you have in mind, but in 2000 Professor Berlekamp proposed a neutral threat environment (NTE), where each side has an equal and opposite non-removable ko threat to each such ko threat of the other side. Bill Fraser and I worked on the theory. I discovered the first and, to my knowledge, only proof in NTE, namely, that for basic approach kos where White to play can win the ko in one move for a local score of 0 and the score if Black wins is x, the mean value and temperature of the ko is x/F, where F is a Fibonacci number. x/5 for the one move approach ko, x/8 for the two move approach ko, x/13 for the three move approach ko, etc. I presented this in a paper in 2002 at the third Computers and Games workshop in Edmonton, Canada. The proceedings were published by Springer.

AFAIK, no further research has been done on NTE. It is not something that is easy to calculate at the table, as it involves algebra, and in addition is not realistic. Unlike regular plays at go, ko threats are typically relatively few and not close in value to each other.

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 Post subject: Re: Thermography #95 Posted: Sat Oct 10, 2020 10:58 am
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Bill Spight wrote:
Gérard TAILLE wrote:
BTW Bill, does it exist some theory in which we add in the ideal environment of gote areas, the same number of ko threats for black and white, with value decreasing regularly.
Such environment will be interesting to handle a local ko fight which impose for one of the player to find greater ko threats than the other player.

It may be somewhat different from what you have in mind, but in 2000 Professor Berlekamp proposed a neutral threat environment (NTE), where each side has an equal and opposite non-removable ko threat to each such ko threat of the other side. Bill Fraser and I worked on the theory. I discovered the first and, to my knowledge, only proof in NTE, namely, that for basic approach kos where White to play can win the ko in one move for a local score of 0 and the score if Black wins is x, the mean value and temperature of the ko is x/F, where F is a Fibonacci number. x/5 for the one move approach ko, x/8 for the two move approach ko, x/13 for the three move approach ko, etc. I presented this in a paper in 2002 at the third Computers and Games workshop in Edmonton, Canada. The proceedings were published by Springer.

AFAIK, no further research has been done on NTE. It is not something that is easy to calculate at the table, as it involves algebra, and in addition is not realistic. Unlike regular plays at go, ko threats are typically relatively few and not close in value to each other.

OK Bill I understand that we can try to build a model with ko threats but at the end it will almost surely not be interesting in practice.
In any case a tool like thermograph or difference games cannot be a miracle tool telling you where to play wtihout any error but il could (has to) be a useful tool giving you a good guess for the best move => real gain of time by reading first the probable best sequence.
Thermography approach needs some training but my feeling is that it is really a very good tool in order to begin the reading of sequences in the best conditions (I mean beginning by the probable best moves). Of course if the local situation is rather complex it doesn't harm to calculate a thermograph which is not 100% correct but quite near from the correct one.
Concerning difference games I can easily see some examples allowing to eliminate dominated moves but for the time being it seems to me difficult to use it in practice. Thermography looks to me far more efficient and I prefer to train myself on this tools keeping difference games only as an interesting tool for a theorical point of view.
Do somebody know what pro think about these tools in practise ?

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 Post subject: Re: Thermography #96 Posted: Sat Oct 10, 2020 12:01 pm
 Honinbo

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Gérard TAILLE wrote:
Bill Spight wrote:
Gérard TAILLE wrote:
BTW Bill, does it exist some theory in which we add in the ideal environment of gote areas, the same number of ko threats for black and white, with value decreasing regularly.
Such environment will be interesting to handle a local ko fight which impose for one of the player to find greater ko threats than the other player.

It may be somewhat different from what you have in mind, but in 2000 Professor Berlekamp proposed a neutral threat environment (NTE), where each side has an equal and opposite non-removable ko threat to each such ko threat of the other side. Bill Fraser and I worked on the theory. I discovered the first and, to my knowledge, only proof in NTE, namely, that for basic approach kos where White to play can win the ko in one move for a local score of 0 and the score if Black wins is x, the mean value and temperature of the ko is x/F, where F is a Fibonacci number. x/5 for the one move approach ko, x/8 for the two move approach ko, x/13 for the three move approach ko, etc. I presented this in a paper in 2002 at the third Computers and Games workshop in Edmonton, Canada. The proceedings were published by Springer.

AFAIK, no further research has been done on NTE. It is not something that is easy to calculate at the table, as it involves algebra, and in addition is not realistic. Unlike regular plays at go, ko threats are typically relatively few and not close in value to each other.

OK Bill I understand that we can try to build a model with ko threats but at the end it will almost surely not be interesting in practice.
In any case a tool like thermograph or difference games cannot be a miracle tool telling you where to play wtihout any error but il could (has to) be a useful tool giving you a good guess for the best move => real gain of time by reading first the probable best sequence.
Thermography approach needs some training but my feeling is that it is really a very good tool in order to begin the reading of sequences in the best conditions (I mean beginning by the probable best moves). Of course if the local situation is rather complex it doesn't harm to calculate a thermograph which is not 100% correct but quite near from the correct one.
Concerning difference games I can easily see some examples allowing to eliminate dominated moves but for the time being it seems to me difficult to use it in practice. Thermography looks to me far more efficient and I prefer to train myself on this tools keeping difference games only as an interesting tool for a theorical point of view.

For analyzing a position Berlekamp recommended always starting with the thermograph. (Or thermographs for different ko threat assumptions.) IMO that is a good approach. OC, in an actual game doing more than finding the count and how much a play gains is not always useful.

When you are considering two different plays, difference games can be very useful, if they give a clear preference. When that happens you don't have to read the whole game tree to find that out. Very often, however, they will tell you that the two plays are incomparable, so you are still at square 1. (Or maybe a bit further along because of what you have learned by the analysis.) One advantage of difference games is that they do not always require optimal play to make a decision. Good enough play will do. Thermographs, however, require optimal play at each temperature to be correct. Working on them will help to find optimal play, though. And difference games easily generalize as heuristics for similar situations. For instance:

`[go]\$\$Wc White to play\$\$ -----------------\$\$ | . . . . . . O |\$\$ | X X . . . . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . X X X X . |\$\$ | . . X O O O O |\$\$ -----------------[/go]`

Once White realizes that the reverse sente gains 4 points, connecting on the bottom side is obvious if you have done certain simpler difference games.

IMO, doing thermographs and difference games can improve both your reading and intuition.

Quote:
Do somebody know what pro think about these tools in practise ?

The Japanese version of Berlekamp and Wolfe's Mathematical Go sold out in Japan in 3 days in 1994. And Berlekamp held some endgame tournaments in Korea and China. But I am not aware of any writing about these techniques or use of them by professionals.

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 Post subject: Re: Thermography #97 Posted: Sat Oct 10, 2020 2:05 pm
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Bill Spight wrote:
Working on them will help to find optimal play, though. And difference games easily generalize as heuristics for similar situations. For instance:

`[go]\$\$Wc White to play\$\$ -----------------\$\$ | . . . . . . O |\$\$ | X X . . . . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . X X X X . |\$\$ | . . X O O O O |\$\$ -----------------[/go]`

Once White realizes that the reverse sente gains 4 points, connecting on the bottom side is obvious if you have done certain simpler difference games.

`[go]\$\$Wc White to play\$\$ -----------------\$\$ | . . . . . . O |\$\$ | X X a . . . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . X X X X b |\$\$ | . . X O O O O |\$\$ -----------------[/go]`

I understand you compare the reverse sente at "a" and the connection at "b" and, with the help of a difference game, you conclude that the connection "b" is better than the reverse sente.
But let's take as environment a unique simple gote of value 4.
The reverse sente move at "a" is better isn't it?

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 Post subject: Re: Thermography #98 Posted: Sat Oct 10, 2020 3:35 pm
 Honinbo

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Gérard TAILLE wrote:
Bill Spight wrote:
Working on them will help to find optimal play, though. And difference games easily generalize as heuristics for similar situations. For instance:

`[go]\$\$Wc White to play\$\$ -----------------\$\$ | . . . . . . O |\$\$ | X X . . . . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . X X X X . |\$\$ | . . X O O O O |\$\$ -----------------[/go]`

Once White realizes that the reverse sente gains 4 points, connecting on the bottom side is obvious if you have done certain simpler difference games.

`[go]\$\$Wc White to play\$\$ -----------------\$\$ | . . . . . . O |\$\$ | X X a . . . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . X X X X b |\$\$ | . . X O O O O |\$\$ -----------------[/go]`

I understand you compare the reverse sente at "a" and the connection at "b" and, with the help of a difference game, you conclude that the connection "b" is better than the reverse sente.
But let's take as environment a unique simple gote of value 4.
The reverse sente move at "a" is better isn't it?

Well, I don't actually use a difference game for this board, I just know difference games for similar situations.

But my intention, despite the non-independence, was to use the bottom to indicate an environment for the top, given the lack of space on the small board.

So if the top faced an environment with only two 4 point gote, the reverse sente would be correct. And if this combination faced an environment with only one 4 point gote, the reverse sente would be correct, too.

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 Post subject: Re: Thermography #99 Posted: Sat Oct 10, 2020 4:15 pm
 Honinbo

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Similarly,

`[go]\$\$Wc White to play\$\$ -----------------\$\$ | . . . . . . O |\$\$ | X X . . . . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . X X X X 1 |\$\$ | . . X . O O O |\$\$ -----------------[/go]`

Because of my experience with those difference games, I can guess that is White's best play on this board. (It is 1 point better than the reverse sente. )

And if I am drawing the thermograph, I know that above temperature 3½ White plays the reverse sente first, but somewhere along the line is White's first play.

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At some point, doesn't thinking have to go on?

Visualize whirled peas.

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 Post subject: Re: Thermography #100 Posted: Sun Oct 11, 2020 8:07 am
 Lives in gote

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Bill Spight wrote:
When you are considering two different plays, difference games can be very useful, if they give a clear preference. When that happens you don't have to read the whole game tree to find that out. Very often, however, they will tell you that the two plays are incomparable, so you are still at square 1. (Or maybe a bit further along because of what you have learned by the analysis.) One advantage of difference games is that they do not always require optimal play to make a decision. Good enough play will do. Thermographs, however, require optimal play at each temperature to be correct. Working on them will help to find optimal play, though. And difference games easily generalize as heuristics for similar situations. For instance:

`[go]\$\$Wc White to play\$\$ -----------------\$\$ | . . . . . . O |\$\$ | X X . . . . O |\$\$ | . X O O O O O |\$\$ | . X X X O . . |\$\$ | . . . X O O O |\$\$ | . . X X X X . |\$\$ | . . X O O O O |\$\$ -----------------[/go]`

Once White realizes that the reverse sente gains 4 points, connecting on the bottom side is obvious if you have done certain simpler difference games.

IMO, doing thermographs and difference games can improve both your reading and intuition.

When reading your post here above I clearly understand that you agree thermography is very useful but I also understand that it may be a good idea to use also difference games and I take your example as an illustration of that last point.

Now reading your last posts I have the impression that you confirm thermograph is useful (I agree at 100%) but I cannot see a point concerning difference game.

Anyway, taking your example, let me try to explain in more details what appears useful for me with thermography

`[go]\$\$W\$\$ ------------------------\$\$ | . . . . . . O . . O X|\$\$ | X X a . . . O O O O X|\$\$ | . X O O O O O X X X X|\$\$ | X X X X X X X X X . X|\$\$ | X . . . . . . . . X X|\$\$ | X . . . . . . . . . X|\$\$ | X . . . . . . . . . X|\$\$ | X . . . . . . . . . X|\$\$ | b O . . . . . . O O c|\$\$ | X O O O O O O O O . X|\$\$ | X X X O . O . O O . X|\$\$ ------------------------[/go]`

First of all, though you find "graph" in the word "thermography", I consider that the thermograph itself is only a visual result of a fondamental analysis based on an ideal environment at temperature t.
In practice many players use thermography without knowing they use it.
Taking the now very well known area at the top of the board, any good player is able to say that, at the beginning of yose, this area is worth 4 points for black in sente. Thermography will explain this in other words : instead of the wording "at the beginning of yose ..." thermography will claim that at a "temperature above 2 then ...". Here is the genius of thermograpy : the value of an area depends on the temperature of the idea environment.
For the same configuration, if we are in the late yose, each player will recognize that the area is a good 3 points gote point. Thermography will precise that this fact will happen when temperature drops under 2.
As you see, without knowing thermography a good player knows the two major points of thermography
- we can give a value to a local area by assuming an ideal environment
- this value depends on the value of the best gote move in this environment

The difference between a pure thermography analysis and the analysis made by a real player is the following : the real player calculates the value of the local environment taking into account only a temperature equal or slightly under the current temperature, ignoring all others and saving a lot of time : if the current temperature is around say 4, who cares about the fact that under temperature 1 the area can be evaluated to 4 points in double sente?

Let's take now the above diagram, white to move. The upper part is the local area we are interested in, the bottom left is the four points gote you proposed and in the bottom right you see a point "c" I consider as a gote point with value g :
0 ≤ g ≤ 4
The temperature of the environment is equal to 4 and the value of our local area (against an ideal environment) is 4 points in reverse sente.

Here is a fondamental comment: though a real environment can very often be approximated by an ideal environment, a real environment can never be ideal. Amongs the various caracteristics of an ideal environment one is really essential: the gain expected from a play in the environment at temperature t, is equal to t/2.

In the above diagram if g = 0 (or very near from 0) then the gain from the environment (4) is far greater than expected value (t/2 = 2). I call such environment a tedomari environment. Taking the fact that a move at "a" is equal to a move at "b" (against an ideal environment) when g= 0 I do not hesitate to guess that the best move is at "b" because in tedomari environment the advantage to play in the environment grows.

In the other hand if g = 4 (or very near from 4) the gain from the environment (0) is far lower than expected value (t/2 = 2). I call such environment a miai environment. In that case I guess the best move is at "a" because in miai environment the advantage to play in the environment diminishes.

if g = 2 the environment looks neither tedomari nor miai and you have to read more to find the best move. Anyway you cannot consider the environment as ideal because after a move at "b" (by either player) the temperature drops suddenly to 2 and the environment becomes a tedomari environment!

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