Values of moves

[Knotwilg]

Playing moves in order of their value (as in value of the move) will give the best possible result for both.

Insert "Usually,"

I will.

But, if modern endgame theory only applies "usually", then how is it a substantial improvement over traditional endgame theory, which we may assume to also work "usually", since it has worked for most players?

I would think that modern endgame theory works always, but includes uncertainty in its approach using probabilities.

[Bill Spight]

But, if modern endgame theory only applies "usually", then how is it a substantial improvement over traditional endgame theory, which we may assume to also work "usually", since it has worked for most players?

This part, without kos, infinitesimals, or difference games, is the same as traditional theory, except that it eschews the concept of local double sente, which has caused numerous errors, it has a more accurate way of determining local sente, and it uses how much a play gains (what O Meien calls the value of one move), which is what most players think that deiri counting means, but it doesn't, thus eliminating that source of confusion.

[RobertJasiek]

if modern endgame theory only applies "usually", then how is it a substantial improvement over traditional endgame theory, which we may assume to also work "usually", since it has worked for most players?

I would think that modern endgame theory works always

The mathematicians of combinatorial game theory and so on, Bill and I have not solved the endgame completely! We are making substantial contributions so that, from a practical perspective, we can now say "works much more often than before". Especially, during the early endgame, we are using simplifying models as (very good) approximations. For the large late endgame, we have solved some more useful classes of positions giving a good guide when real positions are similar but more complicated.

For modern endgame theory, the "usually" can be much tighter than it would be for traditional endgame theory. E.g., it is not always correct to play a gote with follow-up exactly in order of decreasing move values but it can sometimes be correct to play move values in an order resembling ...6, 5, 5.25, 4.... (I will give examples in a few months.) AFAIK, research under traditional endgame theory would simply overlook such anomalies involving small differences in move values.

Then there are many exceptions, such as unusual kos. Bill will tell you. See also the fine print of correct move order during the microendgame.

[Bill Spight]

Global gote is also local gote. If you have a global sente that is also a local gote, its reply is worth less than it is. So it would also be worth playing if it were the same size but not global sente. It doesn't matter what you call it.

As far as the value of a move goes, think in terms of gain.

Edit: Also, for sente it helps to think about how much the reply gains, which is not necessarily what the follow-up gains if your opponent plays elsewhere.

Sorry Bill, I don't understand anything of what you say here. I'm really willing to study the subject now, since I want to bridge the gap with those who don't want that, but do want to get insight in the value of modern endgame theory.

But your reply to my attempt at summary was:
- some joking remarks "except when ..." which mystified, not clarified

You were claiming too much.

- a helpful diagram on a topic that seemed complementary to my initial summary, in response to my attempt at interpreting mitsun's earlier try

For the illustration of figuring out whether a play was sente or not, I mostly had daal in mind. You don't have to go through mathematical contortions to find out whether a play is local sente or not.

Global gote is also local gote.

Maybe understand this. Missing definitions. Missing thought.

If you play a global gote, you are playing in a local region (which may be the only one left, in which case why bother with the distinction?). If your opponent doesn't answer locally, it is still a global gote. Global gote does not mean the last play of the game. It means the largest play on the board, one that is also a gote.

If you have a global sente that is also a local gote, its reply is worth less than it is.

Nope, not getting this.

We have already established that with alternating global play, the concepts of gote and sente do not have meaning unless we look at local regions. A global sente is a play that is the "best" play on the board, and is answered locally. If it is a local gote, that means that the answer is smaller that it is. Otherwise it would be local sente. So it is local gote, but it is answered, because its reply is the biggest play. Since it is even bigger, it would be played even if its reply were smaller.

It doesn't matter what you call it.

Mystifying. You and Robert seem careful about definitions, but now the terms don't matter.

A global play is the one that is best in some sense. (The theory is heuristic.) That is, it is chosen over other plays on the whole board. Sente and gote do not make global sense. A global gote does not get a local reply. A global sente does. (Assuming "best" play.) A local gote could get a local reply if the reply is the best play globally. That makes it a global sente.

You brought up the idea of global sente. I guess you had something else in mind.

Edit: Sorry, I checked.

Global sente means, the value of the follow-up move is bigger than anything else on the board.

That's the basic idea of what I was saying. Just one refinement.
Global sente means, the value of the reply is bigger than anything else on the board.

As far as the value of a move goes, think in terms of gain.

I don't know how to do that. I am as far as understanding "value of a position" and "value of a move" but don't know yet what "gain" means.

The value of the move should be how much it gains, on average. I thought you were indicating that you were having trouble with the value of a move.

Edit: Also, for sente it helps to think about how much the reply gains, which is not necessarily what the follow-up gains if your opponent plays elsewhere.

I'm trying to define and to reason, not to think about something that may help me. I though we were scanning the potential of precise calculations?

It may help you because it is correct. For instance, what if the follow-up is another sente? In that case it is the reverse sente, the reply, that matters.

[Bill Spight]

One more.

[Knotwilg]

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).

[Pio2001]

Thank you for your comments, Bill.

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.

$$c Black to play. A is a small sente, B is a big gote.
$$ ---------------------------
$$ | X X X X X O . . . . . . . |
$$ | 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 |
$$ | O O O O O O O O O O O O . |
$$ ---------------------------

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.

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" ?

[Bill Spight]

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.

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.

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.

[Bill Spight]

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.

[Pio2001]

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".

[Pio2001]

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.

[Bill Spight]

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.

[Bill Spight]

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.

[mitsun]

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: Select all

              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: Select all

             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: Select all

              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: Select all

             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?

[Bill Spight]

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.

Code: Select all

              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: Select all

             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. )

After pruning the branch which will never occur, we get the following simplified diagram:

Code: Select all

              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.

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: Select all

             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, 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!"