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 Post subject: Re: Values of moves #141 Posted: Wed Sep 19, 2018 12:22 pm
 Gosei

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These concepts and supporting diagrams are very clear, but fairly new. Is this a novel way of explaining local sente?
I'm digesting the concept of "a sente position" and "a gote position". I can see the relation to the old heuristic for local sente (follow-up move is bigger than move itself) and your way with diagrams is much clearer than that text.

However, this usage of sente is not related to "sente" in the meaning that the probability of playing it is 1, since that depends on the rest of the board? Or is it and does that probability not depend on the rest of the board but is it the generalization of what you have just shown (here you can decide, but not always).

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 Post subject: Re: Values of moves #142 Posted: Wed Sep 19, 2018 1:02 pm
 Lives in gote

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Thank you for your comments, Bill.

Bill Spight wrote:
Pio2001 wrote:
Example : we have two endgames to play.
Endgame A is sente for us. If we play it, we gain 5 points. If the opponent plays it, he gains 5 points.
Endgame B is double gote. If we play it, we gain 50 points, if the opponent plays it he gains 50 points.

This indicates that you do not really understand sente. Not your fault, OC, given what's out there. You may not understand gain, either. If so, nobody taught you, and you are making a reasonable guess.

I made a mistake : a sente move gains nothing ...since the points that the player has got in the follow-up position were already belonging to him before the move.

Here is an illustration of what I wanted to tell. Since Daal asked about playing a big gote vs a small sente, I assumed that we are not going to play anywhere else. So the temperature of the environment is zero.
I suppose that Black won't try to invade the top left corner after he is captured.

Click Here To Show Diagram Code
`[go]\$\$c Black to play. A is a small sente, B is a big gote.\$\$ ---------------------------\$\$ | X X X X X O . . . . . . . |\$\$ | X X X X X O . . . . . . . |\$\$ | X X X X X O . O . O . O . |\$\$ | X X X X X O . . . . . . . |\$\$ | X X X X X O O O O O O O O |\$\$ | O O O O b X X X X X X a . |\$\$ | O O O O O X . X . X O X O |\$\$ | O O O O O X X X X X O X O |\$\$ | O O O O O X O O O O O X O |\$\$ | O O O O O X O O O O O O O |\$\$ | X X X X X X O O O O O O O |\$\$ | O O O O O O O O O O O O O |\$\$ | O O O O O O O O O O O O . |\$\$ ---------------------------[/go]`

The white stones on the bottom right are alive, but if Black plays A, White must answer N8 in order to save them. So Black A is sente.
B is double gote, but it is a very big double gote.

So, should Black play A or B ?
If I am not mistaken, the value of A is 7 points (comparing Black A White N8 to White A) and the value of B is 49 points ( comparing Black B with White B and dividing by 2).

But the best move is A, because A is "sente enough" to force White to answer locally, even though he has the choice of playing the gote move B. This way, Black gets both A and B.

Bill Spight wrote:
Quote:
If you have some number, N, of a position such that the total score, S, of all of them together is the same, regardless of who plays first (they are miai), then the average value of each of them is S/N. That works for gote positions.

Actually, it is talking about positions. See my example of two of one position in this note: viewtopic.php?p=236716#p236716

Thanks. It does help,.. but I still don't get the meaning of "score". Is it the same as "local count" ?

Last edited by Pio2001 on Wed Sep 19, 2018 1:38 pm, edited 3 times in total.
 This post by Pio2001 was liked by 2 people: Bill Spight, daal
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 Post subject: Re: Values of moves #143 Posted: Wed Sep 19, 2018 1:06 pm
 Honinbo

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Knotwilg wrote:
These concepts and supporting diagrams are very clear, but fairly new. Is this a novel way of explaining local sente?

Yes. I came up with the diagrams and the idea of different strategies last winter. It has always been possible to use the diagrams to show convergence to the mean values in the limit for sente. Once I had the idea, I realized that the final diagram corresponds to calculations in the game tree.

Quote:
I'm digesting the concept of "a sente position" and "a gote position". I can see the relation to the old heuristic for local sente (follow-up move is bigger than move itself) and your way with diagrams is much clearer than that text.

Better definition: The reply is bigger than the reverse sente. I came up with that in the '70s.

Quote:
However, this usage of sente is not related to "sente" in the meaning that the probability of playing it is 1, since that depends on the rest of the board? Or is it and does that probability not depend on the rest of the board but is it the generalization of what you have just shown (here you can decide, but not always).

The probabilistic interpretation can be derived from the idea of temperature or of an ideal environment, which are abstractions or idealizations of the rest of the board. That is, the reply is bigger than the reverse sente, and the reply is equal to the sente play, so the sente play is larger than the reverse sente, and can be played earlier, as a rule, as the ambient temperature of the rest of the board drops.

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 Post subject: Re: Values of moves #144 Posted: Wed Sep 19, 2018 1:13 pm
 Honinbo

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Pio2001 wrote:
Thanks. It does help,.. but I still don't get the meaning of "score". Is it the same as "local count" ?

Score means score. A local region can have a score even while the rest of the board is not finished. In the case of miai, maybe constant value would be good, instead. But the point is that each player can guarantee that score in the combination of local regions, even if they have not been played out yet.

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The Adkins Principle:

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— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Values of moves #145 Posted: Wed Sep 19, 2018 1:29 pm
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For me, a score is something like "Black wins by 4.5 points", or "White wins by 25.5 points".
Correct me if I'm wrong, but I assume that you mean Black's points minus White's points, including territory and dead stones present in the local region, not including komi or handicap compensation, the local region being defined as a given set of intersections... What Robert Jasiek calls the "count" in a "locale".

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 Post subject: Re: Values of moves #146 Posted: Wed Sep 19, 2018 3:35 pm
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I would also like to ask a question about the notion of "gain".

In the modern endgame theory (as presented by Robert Jasiek in his book Endgame 2 - Values), the gain is the difference between the count(*) after a play and the count before the play (or the opposite of the count, from White's point of view).

But the count of an endgame position that is one player's sente is inherited from the sente follower (the position after the sente play). Which means that when we count an unfinished position, we use what we know about the possible evolution of this position.

Here, let's make a parallel with the game of Othello. In Othello softwares, during the opening and middle game, the software gives an evaluation of the count of the whole board, as far as it can guess according to its evaluation function.
Then, during the endgame, the software can explore the complete tree of possibilities, and it then gives the exact count, that is the final score of the game after perfect play. This count only changes if one player makes a mistake.
From this omniscient point of view, the outcome of the game is known with certainty, and the gain of all remaining moves is always zero.

In go, we estimate the count of local unfinished positions under a set of sensible hypothesis. When a player moves, we update our knowledge of the situation and calculate the new count. It defines the gain of the move.
But this only makes sense if we ignore something. If we could count perfectly, with all available information, all moves would gain zero by definition, since we would already know the final score of the whole game,

So, what is the information that is ignored when we define the "gain" ? Or, to put it otherwise, what are the hypothesis that we make when we define the gain ?

(*) The "count" is Black's points minus White's points, counted in a given arbitrary subset of the goban.

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 Post subject: Re: Values of moves #147 Posted: Wed Sep 19, 2018 4:44 pm
 Honinbo

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Pio2001 wrote:
So, what is the information that is ignored when we define the "gain" ?

1) Whose turn it is.

2) Other independent regions of the board.

_________________
The Adkins Principle:

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

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Values of moves #148 Posted: Wed Sep 19, 2018 4:48 pm
 Honinbo

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Knotwilg wrote:
However, this usage of sente is not related to "sente" in the meaning that the probability of playing it is 1, since that depends on the rest of the board? Or is it and does that probability not depend on the rest of the board but is it the generalization of what you have just shown (here you can decide, but not always).

Actually, as I was driving to a meeting this afternoon, I realized that the probabilistic semantics was staring us in the face, in the final diagrams. In the sente strategy diagram one player has made 100% of the initial moves in each position. In the gote strategy diagram each player has made 50% of the initial moves.

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— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Values of moves #149 Posted: Wed Sep 19, 2018 9:05 pm
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This diagram is a good way of looking at my previous simple sente / reverse-sente situation. (I tweaked some of the values from my original post to avoid fractions.)
Code:
Start
/ \
/   \
/     \
/       \
A         0
/ \
/   \
/     \
/       \
100        4

From the starting position, W to play (first branch to the right) can create a terminal position worth 0. B to play (first branch to the left) can create an intermediate position A, which requires deeper analysis. From the intermediate position, W to play can create a terminal position worth 4, while B to play can create a terminal position worth 100.

The task now is to assign values to the starting and intermediate positions (nodes) and to all the moves (branches), given the values of the terminal positions. In order to do that, each branch must be assigned a probability.

Naively, or as a starting hypothesis, we might assign probability 50% to each branch. This is the normal assumption for a simple sequence of gote moves, which either side might reasonably be expected to play. Just for illustration, this gives
Code:
Start=26
/ \
+26 /   \ -26
/     \
/       \
A=52       0
/ \
+48 /   \ -48
/     \
/       \
100        4

This result is not reasonable, so we reject the assumption that all moves (branches) have 50% probability.

The reason this result is unreasonable is that W has the option of avoiding it, by choosing the right branch from the intermediate position. Since the intermediate position arises only after a B move, and since it would then be the largest move on the board, W will certainly exercise the option, rather than giving B a 50% chance of making 100 points. In other words, W will treat the preceding B move as sente.

After pruning the branch which will never occur, we get the following simplified diagram:
Code:
Start
/ \
/   \
/     \
/       \
A         0
\
\
\
\
4

Now there is no need to evaluate the intermediate position, since it leads with 100% probability to the terminal position with value 4. But what probabilities do we assign to the two initial branches?

Since we have determined that the initial B move is sente, we should assign it probability 100%, for purposes of calculating position values. We finally end up with this diagram. The starting position has the same value as the sente terminal position, and the reverse-sente move has value 4.
Code:
Start = 4
/ \
sente  /   \  reverse-sente
/     \  value = -4
/       \
4         0

Yes, there is a slight paradox here -- we are assigning a value to a move (reverse-sente), based on calculations which assume it will never occur. But that is a reasonably accurate description of reverse-sente, is it not?

 This post by mitsun was liked by 2 people: Bill Spight, daal
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 Post subject: Re: Values of moves #150 Posted: Wed Sep 19, 2018 9:56 pm
 Honinbo

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mitsun wrote:
This diagram is a good way of looking at my previous simple sente / reverse-sente situation. (I tweaked some of the values from my original post to avoid fractions.)

Thank you for a good explanation.
Quote:

Code:
Start
/ \
/   \
/     \
/       \
A         0
/ \
/   \
/     \
/       \
100        4

From the starting position, W to play (first branch to the right) can create a terminal position worth 0. B to play (first branch to the left) can create an intermediate position A, which requires deeper analysis. From the intermediate position, W to play can create a terminal position worth 4, while B to play can create a terminal position worth 100.

The task now is to assign values to the starting and intermediate positions (nodes) and to all the moves (branches), given the values of the terminal positions. In order to do that, each branch must be assigned a probability.

A probabilistic semantics may be desirable (or maybe not), but it is not necessary.

Code:
Count=4
/ \
+48 /   \ -4
/     \
/       \
A=52       0
/ \
+48 /   \ -48
/     \
/       \
100        4

It may be shown, without probabilities, that the value of this position, V < 4, but that the only number that can be assigned as a mean value is 4. (This is more than most go players want to know. )

Quote:
After pruning the branch which will never occur, we get the following simplified diagram:
Code:
Start
/ \
/   \
/     \
/       \
A         0
\
\
\
\
4

This is fine, as long as the convention is that the missing branch of nodes such as A lead to a sufficiently Big value.

Quote:
Now there is no need to evaluate the intermediate position, since it leads with 100% probability to the terminal position with value 4. But what probabilities do we assign to the two initial branches?

Since we have determined that the initial B move is sente, we should assign it probability 100%, for purposes of calculating position values. We finally end up with this diagram. The starting position has the same value as the sente terminal position, and the reverse-sente move has value 4.
Code:
Start = 4
/ \
sente  /   \  reverse-sente
/     \  value = -4
/       \
4         0

I don't like this diagram. It relies too much on words and numbers to be understood, and makes it look like a sente is a gote. There is no branch indicating a White reply.

Quote:
Yes, there is a slight paradox here -- we are assigning a value to a move (reverse-sente), based on calculations which assume it will never occur. But that is a reasonably accurate description of reverse-sente, is it not?

There is a non-zero chance that White will play the reverse sente. I have seen this kind of probability written this way.

P(sente) = 1 - ε ,

where ε represents the small chance that White will play the reverse sente. Whether this is more than most go players want to know, I can't say. I have certainly met arguments of this sort: "But White might play the reverse sente!"

_________________
The Adkins Principle:

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

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Values of moves #151 Posted: Wed Sep 19, 2018 10:19 pm
 Honinbo

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Pio2001 wrote:
For me, a score is something like "Black wins by 4.5 points", or "White wins by 25.5 points".

Many sports have a scoreboard that shows the score or scores before anybody has won or lost.

Quote:
Correct me if I'm wrong, but I assume that you mean Black's points minus White's points, including territory and dead stones present in the local region, not including komi or handicap compensation, the local region being defined as a given set of intersections... What Robert Jasiek calls the "count" in a "locale".

I cannot vouch for Jasiek's usage. Berlekamp introduced the term, count, for the non-final value of a game or independent go position. When I was learning about the endgame, books simply called that territory, but these days sticklers in the West prefer to use territory only for final values; so I use count in self-defense.

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The Adkins Principle:

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

— Winona Adkins

"Once in a very great while his eyes light up for a moment, and he says "Whee!" very quietly."
— Lion Miller

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 Post subject: Re: Values of moves #152 Posted: Wed Sep 19, 2018 10:36 pm
 Oza

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Bill Spight wrote:
I don't like this diagram. It relies too much on words and numbers to be understood...
More words I say! More words and diagrams like the examples that you and pio2001 offered of sente vs. gote positions. They are precisely what makes the diagram halfway intelligible to people like me.

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 Post subject: Re: Values of moves #153 Posted: Wed Sep 19, 2018 11:19 pm
 Lives in gote

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Bill Spight wrote:
Code:
Start = 4
/ \
sente  /   \  reverse-sente
/     \  value = -4
/       \
4         0

I don't like this diagram. It relies too much on words and numbers to be understood, and makes it look like a sente is a gote. There is no branch indicating a White reply.

Yes, on reflection I do not like it either. As you say, the left branch makes it look like B invested a move, when in fact he did not. Better to keep the node and single branch.

Code:
Start = 4
/ \
sente  /   \  reverse-sente
/     \  value = -4
/       \
S         0
\
\
\
\
4

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 Post subject: Re: Values of moves #154 Posted: Wed Sep 19, 2018 11:53 pm
 Tengen

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Pio2001 wrote:
I assume that you mean Black's points minus White's points [...] What Robert Jasiek calls the "count"

The count of a settled (local) position. Counts of unsettled positions are derived from counts of subsequent positions.

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 Post subject: Re: Values of moves #155 Posted: Thu Sep 20, 2018 12:31 am
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Here are the graphs for the two positions Bill provided as Go diagrams earlier. The node counts and branch move values are for the gote assumption, with probability 50% for every branch.
Code:

o 5.25                  o 2.75? really 3
/ \                     / \
/   \ -2.75             /   \ gote -1.25,
/     \                 /     \ really sente
/       \               /       \
8         o 2.5         4         o 1.5
/ \                     / \
/   \ -2.5              /   \ -1.5
/     \                 /     \
5       0               3       0

Bill demonstrated that the W branch is local gote in the first graph and local sente in the second graph. Is there an easy way to see this from the graphs? I guess the contradiction in the second graph is that the gote count of the starting position (2.75) is less than a terminal position (3) which B can always guarantee reaching, by treating the W move as sente.

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 Post subject: Re: Values of moves #156 Posted: Thu Sep 20, 2018 2:55 am
 Oza

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Can I remind people that the starting question of this thread, virtually unanswered, was: What is the easiest way to determine a rough value of a move in order to compare alternatives. I am more interested in "ballpark" than "correct."

We seem to have descended, rapidly and predictably, into counting how many angels can dance on the head of a pin. Angels are, admittedly, a step up from fleas, but in my view of the angelology only the archangel Bill has the right to stand on the pinhead. Although one other angel is surreptitiously trying to claim equal status, it is evident that the other angels don't really know what the archangel knows and don't even understand each other. In short they haven't earned their wings yet.

Does this matter? Well, one celebrated example in real life of the folly of counting angels was the fall of Constantinople when the Byzantine courtiers argued over the meaning of sente while the Turks were left undisturbed to plot their successful invasion of the city.

I don't mind being the barbarian at the gates and so will attempt to give daal an answer to his question. It's something I call the principle of affected areas. I gleaned it from Japanese books, but I have mangled it horribly since then, and have no idea whether it is truly useful. It's certainly not correct but might possibly be called ballpark. I don't know the origin of that American term but I assume that it refers to being in a baseball stadium and making a stab at guessing how many spectators are there. My method is more akin to being on the moon and guessing how many people are in all the ballparks together. Still, I do fondly believe it contains the germ of an idea that could work for daal.

daal wanted to know how to decide on whether to play A, B or C above. I assume he regards A as sente, however tentatively, for both sides, B as sente for Black but a gote area for White, and C is gote for Black (only fleas and angels worry about reverse sente). In real life I expect he would play in the order A, B, C. But (because of the inescapable angelic chatter) he would harbour some doubts as to whether he should be playing C first. He therefore wants a method that would enable him to feel less guilty about harbouring those doubts and that would once in a while actually let him play a better move. Failing that, a method that would enable him to see some sense in pro play would not go amiss.

(I hope I'm not being too intrusive, or wide of the mark, with these speculations, daal.)

To be more precise, daal would like to know whether he can play the triangled stone below and be sure that White will answer at A, or should he worry that White might ignore it and play something like the square-marked monkey jump, in which case he should revert to B. There are some tactical nuances, of course, but barbarians don't worry about things like aji that can bite you in the bum. We have two Shredded Wheats for breakfast.

The principle of affected areas, as shown below, tells us. An SDK certainly, and possibly even a DDK, can easily surmise that if White ignores Black and plays the monkey jump, Black can jump into the new triangled point and (because White then has to worry about the safety of his entire group) set off a sequence that leads to something like the square-marked stones being played in sente (with some filling in round the edges towards the end of the game), so that Black can return to the lower side to answer the monkey jump. We can then easily visualise, again without precise calculation of tactics, that the triangle-marked stones will appear on the board. The marked areas are the "affected" areas and we can see that the area in the upper right is bigger then the one in the lower left, so Black is justified in starting at A and not worrying about the monkey jump.

I will leave daal to work out a case where his A may be sente locally but the resulting affected area is not as big as the monkey jump area below, and so he needs to play C (e.g. he can stick a white stone somewhere in the top right corner so that it makes a Black invasion less profitable).

Now another aspect of what daal was asking about, which seems to have been mostly ignored, is that we would like to know how to choose between big moves at any stage of the game, and not just the endgame - and not even just the boundary plays.

Below is an example from real life. For those who want to see the whole game it is from the Oza on 2017-07-13, Takao Shinji playing Son Makoto.

White has just played move 96 to end a ko in the top left. Black needs to add a move at A to save his group. But he demurred and played B. The principle of affected areas, used in a ballpark way, can tell us why.

If we count the affected area in the upper left if White plays there first, it is about 20 points. It is, however, quite easy to see that Black should be concerned about what may happen on the centre right. He has a couple of stones stranded there on the right, and his group in the centre is not yet quite sure of life. It seems obvious there is some urgency in the area and just by inspection we can see the potential Black area affected if White plays there first ("affected" because Black would have to answer - a non-urgent area is where there are e.g. miai and so can be shared whoever goes first) could easily exceed 20 points. If we want to be a little more serious about this but still avoid doing lots of arithmetic, we can even apply QARTS theory. Black has a one-eyed group in the centre that's not safe so we count up to -10 for that, and a no-eyed group on the right so we count -15 for that. Combined, that gives us a but more than the 20 or so affected points in the upper left.

LeelaZero even agrees with the pro players, with the small exception that it would prefer to start at C. It rates A, B and C as all very close to each other, but B or C do rank marginally ahead of A. But, even if A had emerged ahead of B and C in this bot ranking, we can see at the very least that the pro not playing at A was not a typo and was not a blunder, but was a rational choice.

As I said, I have mangled this method horribly. I have never made any attempt to refine it as I so rarely play, so I don't know for certain whether it is refinable. Even if refined, I don't expect it to be anywhere accurate enough to satisfy the angels.

Just in case, the angels are getting too exhausted at flapping their wings in irate consternation, I do understand your aims. I just don't have the time to share them. Or to put it another way: I do like Abba's song; I just can't play it as well as I'd like.

I have a dream, a move to play
To help me cope with anything.
If you see the wonder of a boundary play,
You can fake the future even if you fail.
I believe in angels, something good in this thermography.
I have a dream.
When I know the time is right for me,
I'll play sente.
I have a dream, a fantasy,
To help me through reality...

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 Post subject: Re: Values of moves #157 Posted: Thu Sep 20, 2018 3:26 am
 Tengen

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John Fairbairn wrote:
The principle of affected areas

Instead of a principle, it is your assumption of avoiding continued mutual reduction.

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 Post subject: Re: Values of moves #158 Posted: Thu Sep 20, 2018 4:01 am
 Honinbo

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Tygem: 커비라고해
As a side note, I'm reminded of an endgame heuristic I heard awhile back:

Play moves on "higher" lines first. So if you have endgame moves on the 3rd line, 2nd line, and 1st line, a rough heuristic is to start with the 3rd line moves, then move on to 2nd, then do 1st line moves.

The basic idea is that the "higher" line moves result in claiming more points.

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 Post subject: Re: Values of moves #159 Posted: Thu Sep 20, 2018 4:32 am
 Honinbo

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mitsun wrote:
Here are the graphs for the two positions Bill provided as Go diagrams earlier. The node counts and branch move values are for the gote assumption, with probability 50% for every branch.
Code:

o 5.25                  o 2.75? really 3
/ \                     / \
/   \ -2.75             /   \ gote -1.25,
/     \                 /     \ really sente
/       \               /       \
8         o 2.5         4         o 1.5
/ \                     / \
/   \ -2.5              /   \ -1.5
/     \                 /     \
5       0               3       0

Bill demonstrated that the W branch is local gote in the first graph and local sente in the second graph. Is there an easy way to see this from the graphs? I guess the contradiction in the second graph is that the gote count of the starting position (2.75) is less than a terminal position (3) which B can always guarantee reaching, by treating the W move as sente.

The final 5 and 3 provide lower bounds for the original counts.

The count of the position on the left lies between 8 and 5; the count of the position on the right lies between 4 and 3.

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 Post subject: Re: Values of moves #160 Posted: Thu Sep 20, 2018 10:41 am
 Oza

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John Fairbairn wrote:
Can I remind people that the starting question of this thread, virtually unanswered, was: What is the easiest way to determine a rough value of a move in order to compare alternatives. I am more interested in "ballpark" than "correct."
Thanks for the reminder. I had almost forgotten that I had asked the original question precisely because I am so bad at counting correctly.

Quote:
Does this matter? Well, one celebrated example in real life of the folly of counting angels was the fall of Constantinople when the Byzantine courtiers argued over the meaning of sente while the Turks were left undisturbed to plot their successful invasion of the city.
Just quoting this because it is so much fun.

Quote:
I don't mind being the barbarian at the gates and so will attempt to give daal an answer to his question. It's something I call the principle of affected areas. I gleaned it from Japanese books, but I have mangled it horribly since then, and have no idea whether it is truly useful. It's certainly not correct but might possibly be called ballpark. I don't know the origin of that American term but I assume that it refers to being in a baseball stadium and making a stab at guessing how many spectators are there. My method is more akin to being on the moon and guessing how many people are in all the ballparks together. Still, I do fondly believe it contains the germ of an idea that could work for daal.

I think so too. What I especially like about this idea is that the term "affected areas" is easy to intuitively grasp and remember to apply. As to "ballpark," my uncorroborated feeling is that it allegorically refers to the area where a ball is in bounds, i.e., within a large but not exactly defined region. I wonder if they should introduce komi for different sized baseball fields... Now there's a task for our friends!

Quote:
(I hope I'm not being too intrusive, or wide of the mark, with these speculations, daal.)
Not in the least.

Quote:
The principle of affected areas, as shown below, tells us. An SDK certainly, and possibly even a DDK, can easily surmise that if White ignores Black and plays the monkey jump, Black can jump into the new triangled point and (because White then has to worry about the safety of his entire group) set off a sequence that leads to something like the square-marked stones being played in sente (with some filling in round the edges towards the end of the game), so that Black can return to the lower side to answer the monkey jump. We can then easily visualise, again without precise calculation of tactics, that the triangle-marked stones will appear on the board. The marked areas are the "affected" areas and we can see that the area in the upper right is bigger then the one in the lower left, so Black is justified in starting at A and not worrying about the monkey jump.

I really appreciate this kind of explanation. An easy to follow and nicely illustrated text.

Quote:
Now another aspect of what daal was asking about, which seems to have been mostly ignored, is that we would like to know how to choose between big moves at any stage of the game, and not just the endgame - and not even just the boundary plays.
Indeed. I hadn't dared bring it up again what with so many move values beginning with a decimal point, but yes, in fact the reason I originally posted had less to do with endgame, and more to do with how to establish priorities.

Quote:
Below is an example from real life. For those who want to see the whole game it is from the Oza on 2017-07-13, Takao Shinji playing Son Makoto.
I don't know how much I will learn from it, but I have memorized the first 100 moves. Btw, Go4Go calls Takao's opponent in this game Sun Zhe.

Quote:
As I said, I have mangled this method horribly. I have never made any attempt to refine it as I so rarely play, so I don't know for certain whether it is refinable. Even if refined, I don't expect it to be anywhere accurate enough to satisfy the angels.
I am curious to hear their take on it though...

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