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 Post subject: Engame move values vs endgame move gains
Post #1 Posted: Sun Jul 28, 2019 7:55 am 
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Discussion splitted from https://lifein19x19.com/viewtopic.php?p=247210#p247210

Quote:
lightvector wrote:
Bill Spight wrote:
Playing a local sente with sente gains nothing, in terms of points.


For those who are confused about this detail - have you ever noticed that when pros or top amateurs estimate the score, they always pre-subtract out the sente pushes and other sente intrusions, even if the opponent hasn't played them yet? (See any number of online Go commentary videos, or if you've been to a Go club or Congress you may have seen strong dan players or pros do this in-person). Pretty much every strong amateur or pro that I've ever encountered counts this way.

That's because a very good "baseline" is that whenever a player has a clear sente move, they assume for estimation purposes that player will get it. So when that player actually does play that move in sente, there is no gain. Relative to that baseline, they have only gotten exactly what they already counted that player to get!

That's basically what "sente gains nothing" means.

Pio2001 wrote:
Even today, I feel confused, even about the modern "miai values". For example, when I compare a sente move with a value of 1 point and a gote one with a value of 20 points.
If I apply the traditional rule that says that a sente move is worth twice a gote move, and even if I use the modern "tally" calculation, all the theory says that the gote move is worth much more that the sente move, while it is obvious to anyone that it is better to play the sente first, in order to get both.


The simple answer is that you might be mistaken about what "modern" counting theory says :) . There are TWO important values for locally-sente moves, not one - the reverse sente value (also known as the miai value, or the per-move gain), and the threat value - the gain of the followup move if unanswered.

So let's say in your example the local-sente move has a reverse-sente value of 1 point and a threat value of 7 points. In that case, modern theory says to play it any time when the biggest moves elsewhere on the board are worth between 1 and 7 points. Ideally as late as possible to preserve ko threats, but definitely don't let it sit until moves elsewhere are all worth less than 1 point, then the opponent will be able to take it and you will lose out.

If you played it while there was a 20 point gote on the board, that would be a huge mistake, since the opponent would ignore it and take the 20 point gote. If on the other hand, the threat value was 30 points, then you could certainly play it now if you didn't mind using up the ko threat - in that case, theory would say to play it any time when moves elsewhere are worth between 1 and 30 points instead of 1 and 7 points. But you could also still wait, so long as there would still be other moves worth between 1 and 30 points after the 20-point gote was gone.

Does that make sense? (This is basically what Bill said, but restated in case a different way of wording it helps it stick).



Thanks for the explanations, lightvector.

Let's apply all this to the following example, White to play :

Attachment:
Endgame.png
Endgame.png [ 12.38 KiB | Viewed 315 times ]


Two endgame moves are possible : A and B.

A is gote for Black and for White.
B is gote for Black and sente for White.

It is clear that the correct play is White G1 (sente), Black H1 (answer to White G1), then White A11 (gote).

If I follow the explanation of Robert Jasiek in his book Endgame 2 - Values, we have :

Upper left :
Local count after Black A : 4 points
Local count after White A : 0 points
Local count as it is : (0+4)/2 = 2 points for Black
Tally : 2
Move value = (4-0)/2 = 2 points per excess move

Lower right :
Local count after White G1 Black H1 : 15 points
Local count after Black G1 : 16 points
Local count as it is : 15 points
Tally : 1
Move value = (16-15)/1 = 1 point per excess move

Page 115, Robert Jasiek writes :
Quote:
The moves in local gote, local sente, ordinary ko or ko threat endgames can be compared directly with each other by their move values.

And next :
Quote:
usually, play a move with the largest move value


Which gives the wrong sequence ! According to this, A should be played before B, because the move value is superior.

Mind that Robert makes a perfectly clear distinction between the move value and the move gain. Here, we are talking about the values, not the gains.
He even writes, page 62, that

Quote:
A gain may or may not be equal to the move value. If they are unequal, a gain improves our evaluation of a move. For example if a player starts his local sente sequence, but the opponent replies elsewhere on the board, the local value shift of counts is described by the gain of the player's local play rather than the move value.


In the next chapter, about Traditional endgame theory, the problem is the same. He writes, page 131 :

Quote:
Multiply by 2 the move value of playing in sente or reverse sente in a local sente to compare it with the move value of playing in a local gote

And, page 132 :
Quote:
After calibration, usually, play a move with the largest move value.


Here, A has a value of 4 points double gote, and B has a value of 1 point sente. Which means that A should be worth twice as much as B (4 vs 2). Again, wrong move order.

He then gives an example, page 134 example 3, where this exact method is applied... unfortunately, in that example, the gote move has a value of 7 points, and the sente one 4x2 points, which gives the right move order by accident !

But Robert is not alone. In his book "Yose, Fins de Partie au jeu de go", Dai Junfu makes the same mistake, although with a disclaimer about the inaccuracy of this method.


In "Rational Endgame, Antti Törmänen says, page 27, taking a sente move as an example, that
Quote:
[it] has no comparable points value at all. It simply enforces the expected outcome of the position.


So he avoids the mistake, but without giving an accurate method of comparison besides reading.


If I follow your explanations, lightvector, the correct calculation should use the "gain", as defined by Robert Jasiek, but move by move, as shown by Antti Törmänen (though Antti doesn't give the calculation, just the right move order). Robert Jasiek's book agrees with this (page 62), although he seems to have forgotten it 53 pages later.

In our example, we would have

Local count after White G1 = mean value between the two possible continuations :
Continuation Black H1 : local count = 15 points
Continuation White H1 : local count = -5 points
Mean value = (15+ (-5))/2 = Local count after White G1 = 5 points.

The answer Black H1 thus gains 15-5 = 10 points, while in the upper left corner, a move by Black gains 4-2 = 2 points.
Since the answer Black H1 is the move with the highest gain for Black, we can say that White G1 was sente (following Antti Törmänen's statement "Sente is relative to the whole board position" (p 27), which is what Robert Jasiek calls "global sente").

So we can still assume that the local count of the initial position in the bottom right is inherited from the result of the sente sequence, and is 15 points.

Now we can calculate the gain of White G1 : 5-15 = -10 points for Black, thus 10 points for White.

The gain of White A is easier to calculate : 2 points.

Now we can tell that the right move order is given by the decreasing gains :

Gain of White A : 2 points
Gain White B : 10 points
White must play B

Then Black has two choices :
Black answers B : 10 points
Black plays A : 2 points
Black must answer B with H1.

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 Post subject: Re: Engame move values vs endgame move gains
Post #2 Posted: Sun Jul 28, 2019 9:04 am 
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As always, we start with the territorial values (counts).

A (gote position) has a count of 2. B (White sente position) has a count of 15.

A play in A by Black gains 2 pts., for a local score of 4. A play in A by White gains 2 pts., for a local score of 0. The reverse sente by Black in B gains 1 pt., for a local score of 16.

How much does the sente play by White gain in B? To answer that question we find the territorial count after that move. If Black replies the result is 15, as advertised. If White carries out the threat the result is -5. The territorial count is the average of 15 and -5, or 5. White started from a position worth, on average, 15 pts. and moved to a position worth, on average, 5 pts., for a (temporary) gain of 10 pts. Black's reply will also gain 10 pts., to take the local score to 15. White's gain is temporary because it gives Black a bigger play than she had before White made the play, destabilizing the local position.

Edit: I couldn't stand to wade through your whole note before writing the above. Having done so, I see that we are in agreement. :)

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 Post subject: Re: Engame move values vs endgame move gains
Post #3 Posted: Sun Jul 28, 2019 9:32 am 
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Maybe Bill would have a different answer, but the way I understand it is that in practice, numeric-based endgame theories cannot be 100% prescriptive on exactly what moves you should make. It CANNOT be, because plain numeric values are fundamentally insufficient. For example it is quite easy to construct positions such that you should play A before B if A and B are the only positions, but if C is present, then you should play B before A - therefore no possible way of assigning numeric values can possibly be perfect. In general, you need reading.

So the mistake is that you are thinking of move values/gains as being 100% prescriptive. Instead, they are simply a useful guideline, and they provide a precise way to sum up losses and gains in whatever line of play *does* occur, even if they are not 100% prescriptive about what exactly that line should be.


If you always play the max gain move, the specific way you lose out relative to optimal play is due to *tedomari* - getting the last play before a drop in temperature. Whenever the global temperature (the gain of the most urgent remaining move left on the board) drops from X to Y after your move instead of staying at around X, you will do (X-Y) points better than "expected" because the next move your opponent can get will only give them Y points instead of X points.

I think that ko aside, tedomari is basically the *only* way you can lose out by always playing max-gain moves (Bill can correct me if I'm wrong).

You have all the numbers right in your case I think, except I would interpret one of them differently.
You have:
A: A double-gote position where playing gains 2 points for either side.
B: A sente position for white where black playing gains 1 point and white playing gains nothing beyond baseline expectation but has a 10 points followup threat. (I would not attempt to call the sente move as gaining 10 points, end of story, instead I would keep both "1" and "10" in mind as relevant numbers).

If you play A first, the temperature drops from 2 to 1 (black's biggest remaining move drops from 2 points to 1 point).
If you play B first in sente, then A, the temperature drops from 2 points to 0 points as you play A (black has no remaining useful moves at all).

So the reason why playing B first in sente is better in this case is that by doing so, the temperature drops *an extra point*. You gain nothing yourself immediately, but you make it so that when it gets to black's initiative, black's biggest remaining move is smaller (in fact, nonexistent!). Tedomari gave you extra value in that black had nothing to do using his move!

Let's compare with this position:
Click Here To Show Diagram Code
[go]$$c
$$ ----------------------------
$$ | O X . . . X O . . . . . . |
$$ | O X . . . X O O O . . . . |
$$ | a X . . . X c X O . . . . |
$$ | O X . , . X O O O , . . . |
$$ | O X . . . X O O . . . . . |
$$ | O X X X X X X O O O O O O |
$$ | O O O O O O X X X X X X X |
$$ | . . . . . O X . . . . . . |
$$ | . . . . . O X . . . . . . |
$$ | . . . , . O X . . , . . . |
$$ | . . . . . O X X X X X X X |
$$ | . . . . . O X X O O O O O |
$$ | . . . . . O b . . O . X . |
$$ ----------------------------[/go]


Now we've added:
C: A double-gote position where playing gains 1 point for either side.

Now, it doesn't matter if you play A or B first:
* If you play A first (2 points gain), black plays C (1 point gain), and then you push at B in sente and gain nothing further.
* If you play B in sente first (0 point gain), then play A (2 point gain), then black plays C (1 point gain). Same thing.

Notice how as once there was another move of gain *between* 1 point and 10 points, you no longer had to play your sente right away. You could just as well leave it until later.


So the basic strategy is: Often play the move whose play gains you the most, but try to be the player who gets tedomari (makes the last move before significant temperature drops), and/or have it be bigger when you do get it.

And part of doing that is:

Usually play your sente moves (even though they gain you nothing after considering the opponent's reply) during a time when the biggest other moves for your opponent are worth between the reverse-sente value (1 in the above case) and the threat value (10 in the above case), and often waiting as late as possible. And I'd recommend you NOT attempt to reduce sente moves to just a single number, both numbers are useful.

And the way you determine "how late should I wait?" is you read - if you read playing A and you see that B is the biggest move left for the opponent, probably you should play B in sente first to deny that option to the opponent. But if it's not the biggest (because move C is still there), then perhaps you can also wait a little longer. Also sometimes, even among among gote moves, you should play a move of strictly lower gain than some other move you have, if it means you can deny a significant gain to the opponent via tedomari later.

Because again, to re-emphasize, although move values let you precisely account gains and losses, they cannot solely determine strategy.
Does that help?


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 Post subject: Re: Engame move values vs endgame move gains
Post #4 Posted: Sun Jul 28, 2019 10:00 am 
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Thank you both. Very interesting.

However, I'm still confused between the value and the gain. For me (if I understood properly Robert Jasiek's definitions), the value is the difference between White's playing first result and Black playing first result, divided by the tally (we consider two different sequences), while the gain is the difference between the local count after and before (only one sequence is considered).
Above, White B has a value of 1 point, but gains 10 points. The numbers are quite different !

In the following quotes, are we talking about values or about gains ?

lightvector wrote:
So the mistake is that you are thinking of move value as being 100% prescriptive.

lightvector wrote:
If you always play the max value move


lightvector wrote:
Notice how as once there was another move of value *between* 1 point and 10 points, you no longer gained any value from playing your sente right away. You could just as well leave it until later.


lightvector wrote:
So the basic strategy is: Often play the move whose play gains you the most, but try to be the player who gets tedomari


lightvector wrote:
Usually play your sente moves (even though they gain you nothing after considering the opponent's reply) during a time when the biggest other moves for your opponent are worth between the reverse-sente value (1 in the above case) and the threat value (10 in the above case)


lightvector wrote:
if you read playing A and you see that B is the biggest-value move left for the opponent,

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 Post subject: Re: Engame move values vs endgame move gains
Post #5 Posted: Sun Jul 28, 2019 10:26 am 
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Pio2001 wrote:
[Robert Jasiek] writes, page 131 :

Quote:
Multiply by 2 the move value of playing in sente or reverse sente in a local sente to compare it with the move value of playing in a local gote


Pio2001 wrote:
But Robert is not alone. In his book "Yose, Fins de Partie au jeu de go", Dai Junfu makes the same mistake, although with a disclaimer about the inaccuracy of this method.


I just realize that while Robert talks about "sente or reverse sente", Dai only talks about reverse sente, not sente. Which agrees with Antti's statement about a sente move :

Quote:
[it] has no comparable points value at all. It simply enforces the expected outcome of the position.


Is it correct to assume that we can compare the value of a gote and a reverse sente move (using the tally or the multiplication by 2, which are the same thing), but not the values of a gote and a sente move ?

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 Post subject: Re: Endgame move values vs endgame move gains
Post #6 Posted: Sun Jul 28, 2019 11:06 am 
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lightvector wrote:
Maybe Bill would have a different answer, but the way I understand it is that in practice, numeric-based endgame theories cannot be 100% prescriptive on exactly what moves you should make. It CANNOT be, because plain numeric values are fundamentally insufficient.


Absolutely. :) The wonderful thing is that gains work so well. :D

Quote:
In general, you need reading {to play perfectly}.


But there are guidelines to help simplify the task of reading. For instance, since both A and the White follower (threat) of B are simple gote, and playing the threat gains more than playing A, it is correct for White to play B before A, even if there are other plays on the board unless ko considerations apply.

Edit: BTW, your example is a good illustration of the fact that White does not have to play his sente. But as long as the choice is between A and B, and there is no ko now or later in the game tree, it is correct for White to play the sente (B). It is not uncommon for pro endgames to reach a point where the players both rush to play their sente. They have seen that either there is no ko to come, or that any ko is so small that their opponent could afford to eliminate the sente play (potential ko threat) before the ko fight starts.


Quote:
If you always play the max gain move, the specific way you lose out relative to optimal play is due to *tedomari* - getting the last play before a drop in temperature. Whenever the global temperature (the gain of the most urgent remaining move left on the board) drops from X to Y after your move instead of staying at around X, you will do (X-Y) points better than "expected" because the next move your opponent can get will only give them Y points instead of X points.

I think that ko aside, tedomari is basically the *only* way you can lose out by always playing max-gain moves (Bill can correct me if I'm wrong).


Many years ago I thought it was clever to compose problems in which the largest play was not best, and it was difficult to discern that fact. Maybe it was, but it was not very helpful for practical play. Noticing these temperature drops is, IMHO, the main way that humans can detect times when the largest play is not best. Aside from noticing sente, OC.

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 Post subject: Re: Enigame move values vs endgame move gains
Post #7 Posted: Sun Jul 28, 2019 12:03 pm 
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For moves, I don't worry about any distinction between value and gain. As lightvector points out, single numbers are in general not sufficient to tell us what perfect play is. They are only guides.

FWIW, here is my thinking on the matter.

As always, we start with the values (counts) of local positions. How can we determine the count of a position by play? We know that the count does not depend upon whose turn it is, so we have to consider lines of play with each player playing first. In general, neither player wants to play from a position with a score, so we don't worry about those in this discussion.

Suppose that one player makes the best play (or possibly sequence of plays) from a position that gains a certain number of points and the opponent replies with a play that gains the same number of points. The gains cancel out and the resulting position has the same value as the original position.

For a gote position the gain is the same for each player. There is a play that gains exactly what the play in the gote gains and yields the value of the original position, no matter who plays first. We may take that gain as the value of playing in the gote position.

For a sente position the gains for the players are different. But, as mentioned, we do not have to find a play that gains the same as the sente threat, because the reply to the threat does that. It is baked into the cake. :) Sente gains nothing, as they say. ;) So all we have to do is find a play that gains exactly the same as the reverse sente. We may take that gain as the value of playing the reverse sente.

Why do these values matter? Because they indicate when it becomes urgent to make a play in the local position we are considering. They are still only guides, OC. Yes, there is a number that indicates when it is safe to play the sente , as a rule. But usually we do not have to worry about calculating it, as long as the opponent cannot afford to play the reverse sente. And the gain of the reverse sente tells us when he might do that. Again, numbers are still only guides.

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 Post subject: Re: Engame move values vs endgame move gains
Post #8 Posted: Sun Jul 28, 2019 12:15 pm 
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Pio2001 wrote:
Is it correct to assume that we can compare the value of a gote and a reverse sente move (using the tally or the multiplication by 2, which are the same thing), but not the values of a gote and a sente move ?


The only things that the numbers give us a sure guide to are simple gote, or moves that reduce to simple gote.

We can compare other plays, but not simply by the numbers. For instance, above I said that, unless ko is a consideration, it is correct for White to play B in your example before A, even with other moves on the board. But I had to stipulate that A is a simple gote, as is the threat of B.

Here is another cute rule: Suppose that A is a simple gote, ko is not a consideration, and one player correctly plays in A. Then if the other player has one or more sente with threats that are simple gote that gain more than A, that play should play all those sente. (This pretty much follows from the above. :) If it were the other player's move, she would play all those sente before playing A. Better late than never. ;))

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Post #9 Posted: Sun Jul 28, 2019 12:18 pm 
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Bill Spight wrote:
For moves, I don't worry about any distinction between value and gain.


But the numbers are completely different. When lightvector says :

Quote:
Usually play your sente moves (even though they gain you nothing after considering the opponent's reply) during a time when the biggest other moves for your opponent are worth between the reverse-sente value (1 in the above case) and the threat value (10 in the above case)


If my opponent's biggest move is a sente with a value of 5 and a gain of 20, how do I know if it is worth between 1 and 10, since the first number is inside the interval, while the second number is outside ?

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Post #10 Posted: Sun Jul 28, 2019 12:40 pm 
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Pio2001 wrote:
Bill Spight wrote:
For moves, I don't worry about any distinction between value and gain.


But the numbers are completely different. When lightvector says :

Quote:
Usually play your sente moves (even though they gain you nothing after considering the opponent's reply) during a time when the biggest other moves for your opponent are worth between the reverse-sente value (1 in the above case) and the threat value (10 in the above case)


If my opponent's biggest move is a sente with a value of 5 and a gain of 20, how do I know if it is worth between 1 and 10, since the first number is inside the interval, while the second number is outside ?


The value of 5 is the gain of the reverse sente. (Edit: I think. I don't know what you are talking about, really.) It is called the value, I suppose, because it is the gain that matters most. In an ideal world it would be the only one that mattered, because the opponent would make a mistake if she played the reverse sente when other plays gained more. But in practice, sometimes it becomes important to play the sente, even though the second largest gote gains more than the reverse sente. Why the second largest gote? Because if you take the largest gote, it will be the largest gote left when your opponent considers whether to play the reverse sente or not.

Edit: Where do you get value of 5 and the gain of 20? Where does the range, 1 - 10 come from? Aren't those the gains of the reverse sente and the reply to the sente? Are you introducing another sente into the mix?

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Post #11 Posted: Sun Jul 28, 2019 1:21 pm 
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Bill Spight wrote:
Edit: Where do you get value of 5 and the gain of 20? Where does the range, 1 - 10 come from? Aren't those the gains of the reverse sente and the reply to the sente? Are you introducing another sente into the mix?


The values 1-10 come from our example, quoted by lightvector :

Quote:
Usually play your sente moves (even though they gain you nothing after considering the opponent's reply) during a time when the biggest other moves for your opponent are worth between the reverse-sente value (1 in the above case) and the threat value (10 in the above case)


Since I am supposed to play this "when the biggest other moves [of my] opponent are worth between [1 and 10]", my question was what does the word "worth" mean ? The value or the gain ?

Then you said "I don't worry about any distinction".

But what if the biggest other move of my opponent is a sente move with a value per excess move equal to 5 and a gain equal to 20 ? (example not considered so far).

Would this move "worth between 1 and 10" or not ?
If so, it is time to play the sente, if not, it is too soon.

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Post #12 Posted: Sun Jul 28, 2019 2:54 pm 
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Pio2001 wrote:
Bill Spight wrote:
Edit: Where do you get value of 5 and the gain of 20? Where does the range, 1 - 10 come from? Aren't those the gains of the reverse sente and the reply to the sente? Are you introducing another sente into the mix?


The values 1-10 come from our example, quoted by lightvector :

Quote:
Usually play your sente moves (even though they gain you nothing after considering the opponent's reply) during a time when the biggest other moves for your opponent are worth between the reverse-sente value (1 in the above case) and the threat value (10 in the above case)


Since I am supposed to play this "when the biggest other moves [of my] opponent are worth between [1 and 10]", my question was what does the word "worth" mean ? The value or the gain ?

Then you said "I don't worry about any distinction".

But what if the biggest other move of my opponent is a sente move with a value per excess move equal to 5 and a gain equal to 20 ? (example not considered so far).

Would this move "worth between 1 and 10" or not ?
If so, it is time to play the sente, if not, it is too soon.


The heuristic is to consider the gain of the reverse sente as the value. So, yes, we would consider the reverse sente for White as lying in the range between 1 and 10.

Is it time to play the sente? We know, from previous consideration, that it is not the time to play the gote. So the question is sente vs. reverse sente. To get the right answer with assurance we have to read the play out.

Here are the plays.

A = {4|0}
B = {16||15|-5}
C = {40|0||-5} (plus some constant)

If C were a gote with a gain of 5, we know that the sente would be correct. So let's start with that. We play from B to {15|-5}.

Since 20 > 10 and both the threat and the largest gote are simple gote, we know that Black should play in C. The rest is obvious. White replies in C, Black replies in B, and then White takes A. Result: 0 + 15 + 0 = 15 plus some constant.

1st variation:

White plays the reverse sente, then Black replies in A and White plays B with sente. Result: -5 + 4 + 15 = 14 plus the same constant. This is one point better than playing the sente first.

2d variation:

White plays the reverse sente, then Black plays in B and White plays in A. Result: 0 - 5 + 16 = 11, plus the same constant. This is three points worse for Black than the 1st variation, so Black should reply in A.

Reading tells us that White should take the reverse sente, gaining 5 pts. It's right to play the largest play first. How about that? :cool: ;-)

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This post by Bill Spight was liked by: Pio2001
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 Post subject: Re: Engame move values vs endgame move gains
Post #13 Posted: Sun Jul 28, 2019 3:17 pm 
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Now it is clear ! :)

Thanks.
And thanks lightvector too for the tedomari explanation.

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 Post subject: Re: Engame move values vs endgame move gains
Post #14 Posted: Mon Aug 05, 2019 9:29 am 
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Pio2001 wrote:
Let's apply all this to the following example, White to play :
Attachment:
Endgame.png
[...]
If I follow the explanation of Robert Jasiek in his book Endgame 2 - Values [...]
Quote:
usually, play a move with the largest move value

Which gives the wrong sequence !


The book principle is a rough guideline for the middle game and early endgame, and says "usually" because it does not always apply. In particular, there is better theory if we also consider the temperature (discussion with Bill Spight in other threads, to be explained in a later book) and other theory for the late endgame. Your example belongs to the late endgame, for which we apply the theory of the microendgame!

The mentioned books do not make a mistake but you interpret them wrongly by trying to apply their theory for the middle game and early endgame. For your example, instead we must apply the theory of the microendgame. It says, e.g., on p. 187 of aforementioned book to play a simple sente at B with move value 1 and larger follow-up move value Y before a simple gote at A with a smaller move value X < Y. In the example, Y = 10 and X = 2.

***

Please write "move value" instead of "value" because there are different kinds of values. "Move value" does not create ambiguity which kind of value is being meant.

***

For the mentioned theory (guideline, temperature theory, microendgame), we need the move value and do not need the gain (unless it equals the move value, such as in simple gotes). (Antti's book speaks of value of a move when meaning gain. For this confusing usage of the words, we do not need it for the mentioned theory for the plays of the sente sequence of a local sente.)

We might need gains to
- judge the impact of an ignored ko threat or
- assess long local sequences consisting of 3 or more moves (see Endgame 3 - Accurate Local Evaluation, we need move values and gains then).

***

Temperature theory for local sente (applied during the middle game or early endgame): it differs for low and high temperature, the sente and the reverse sente players, and for the sente player and low temperature also needs the second largest move value in the environment.

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