Sente, gote and endgame plays

[RBerenguel]

I have started Get Strong at the Endgame recently, I just got into the first endgame tesujis (prolems 43 and up). And I've found that most of them (well, most of the first 12) are 1-2 points better than the standard response, but the standard response usually is sente and the best (point-wise) response is gote.

My question is (and I know I could find a suitable answer in The Endgame, but I want something I can understand better and I have faith in the L19 community ): how do I order these moves? I just count double for sente? Count in half for gote? Count the best sequence as a gote play? Count the best sente sequence as sente play? Resign before yose?

[topazg]

In general, I think reverse sente is approximately worth double gote (as you're taking a gote sequence that your opponent could get for free, so for the remaining endgame points, if you take reverse sente you get one, and your opponent gets one, whereas if you take gote, your opponent takes the reverse sente as sente and then gets a gote point as well - effectively a free move of that value). Sente moves are just to be played really, ideally before the reverse sente if your opponent becomes their biggest move. Sente moves can be left as ko threats, but not left so late that you don't get them.

[p2501]

As far as I know: Count double for sente (because you can play on a equally big point after the sente sequence). Thus count 4 times the points for double-sente.

Then the order is simply pointwise.

[topazg]

As far as I know: Count double for sente (because you can play on a equally big point after the sente sequence). Thus count 4 times the points for double-sente.

Then the order is simply pointwise.

As far as I know, the value of sente and double sente is effectively infinite, as they are "free" plays and therefore don't lose initiative. Reverse sente is double gote because even though it's gote for you, it deprives your opponent of a move for your opponent and therefore forces him to lose one more initiative, and has double value for the reason that it removes one move from his next sequence.

Double sente should be played immediately unless there's something big enough that your opponent would ignore your move and allow you to follow up to get something even bigger - which is fairly rare outside of big group loss situations.

[Bill Spight]

Let's suppose that you have a position where you can move to a local count of G with gote or S with sente, and the your opponent can move to a local count of R with gote, and G > S > R (from your perspective).

Just looking at the local position, compare S with (G + R)/2. If the position is gote, then its count is (G + R)/2, and if it is sente its count is S. If S > (G + R)/2 then it is sente, if S < (G + R)/2 it is gote, and if S = (G + R)/2 it is ambiguous (See http://senseis.xmp.net/?AmbiguousPosition .) You can also compare G - S with S - R. If they are equal it is ambiguous, if G - S > S - R it is gote, and if S - R > G - S it is sente.

As for which option to play, you should normally play the sente option if the position is sente and the gote option if it is gote. But that is not always the case. If you can read the whole board out, that's cool. However, here is a rule of thumb. Suppose that the ambient temperature is T, i. e., that the gain from making the largest play elsewhere on the board is T. (Note that if the above position is gote, then the gain from playing it is (G - R)/2, not G - R, since you are starting from a position worth (G + R)/2.) Then we can estimate the gain from playing out the rest of the board as T/2. That gives us the following comparison:

S + T/2 >?< G - T/2 ,

or

T >?< G - S .

If T is larger, then make the sente play. If G - S is larger, then make the gote play.

Note: In the problems in the book where the gote is presented as correct while the other option is sente, the sente play should be a losing sente, i. e., G - S > S - R.

Edit: The above discussion is about which option to choose, not about playing a losing sente, which I discuss next.

[RBerenguel]

Although it looks odd, this makes sense Bill, thanks (and now I understand some of all that CGT gibberish I see in Senseis ). Indeed, the "wrong sente" I have checked are all losing sente, although they are sente plays they lose points against the best answers to the gote play (and it's usually not a gote play, but that they end in gote). Since they are local problems, a losing sente is bad (i.e. we have to assume T=0) and gote is good. Does this makes sense?

[Bill Spight]

Although it looks odd, this makes sense Bill, thanks (and now I understand some of all that CGT gibberish I see in Senseis ). Indeed, the "wrong sente" I have checked are all losing sente, although they are sente plays they lose points against the best answers to the gote play (and it's usually not a gote play, but that they end in gote). Since they are local problems, a losing sente is bad (i.e. we have to assume T=0) and gote is good. Does this makes sense?

First, in an endgame book you should assume that T = 0 only for whole board problems. For instance, we might classify a local position as sente, which is how it is normally played, but if T = 0 and G > S, then you play it as a gote.

Second, the book should show a sequence up to the point where the local temperature drops. (Or sometimes where it stays the same, as with ambiguous plays.) However, endgame books have many mistakes where that is not the case. In part that is because they were ghost written by amateurs, in part because the pro author goofed. These errors are biased towards the sequences being too long.

I remember when I found a play that the book said was sente but I calculated it as gote. It should not normally have been answered. I was feeling pleased with myself. Then a couple of weeks later I saw the play in one of Sakata's games (against Fujisawa Hideyuki I think). It was not answered. So the top pros knew it was gote, but the books still said it was sente.

[RBerenguel]

First, in an endgame book you should assume that T = 0 only for whole board problems. For instance, we might classify a local position as sente, which is how it is normally played, but if T = 0 and G > S, then you play it as a gote.

But... if the "correct play" is a gote move (because the equivalent sente is losing sente), doesn't that mean that T=0? Because the correct move is G, because G>S. Hmmm....

[Bill Spight]

First, in an endgame book you should assume that T = 0 only for whole board problems. For instance, we might classify a local position as sente, which is how it is normally played, but if T = 0 and G > S, then you play it as a gote.

But... if the "correct play" is a gote move (because the equivalent sente is losing sente), doesn't that mean that T=0? Because the correct move is G, because G>S. Hmmm....

The sente option is a losing sente when G - S > S - R. That says nothing about T.

I should not have made the comment about playing the sente "even if it is a losing sente" because, while true, it is irrelevant. The sente will not be a losing sente. (More later.)

[RBerenguel]

This is why there is "research" on endgames Waiting for more

[Bill Spight]

Sente option or Gote option?

Suppose that you have a position where you have two options of play, one sente (ending at a count of S) and one gote (ending at a count of G), while your opponent has one gote option (ending at a count of R), with G > S > R (from your point of view). How to play it?

OC, if you can read the board out, go ahead. If you can't here are the basic rules of thumb.

First, let's classify the position. Is it sente or gote? If it is sente, then normal play is to choose the sente option, if it is gote, normal play is to choose the gote option. As mentioned earlier, if G - S > S - R the position is gote, and that is normally the option to choose, while if S - R > G - S the position is sente, and that is normally the option to choose.

The great majority of the time, normal play is correct, but there are exceptions. Exceptions depend on the ambient temperature, T, which is how much a play somewhere else on the board gains. An example of a play that gains T is one where if Black takes it the resulting position has a local count of T while if White takes it the result position has a count of -T (from Black's point of view).

Exception 1: In a sente position to play the gote option.

Condition: G - S > T.

Exception 2: In a gote position to play the sente option.

This exception requires a large gote (ending in a local count of A if you play, B if your opponent plays, A > B). We also need to know the size of the sente threat. If you play the sente and your opponent ignores it, and you play again, let the resulting local count be H (for huge ).

Case 1. The sente threat is at least as large as the other gote: H - S >= A - B.

Conditions:

1) S - R > T

2) A - B > G - S + T

Case 2. The sente threat is smaller than the other gote: A - B > H - S

Conditions:

1) H - G > T

2) H - R > A - B + T

[RobertJasiek]

Let's suppose that you have a position where you can move to a local count of G with gote or S with sente, and the your opponent can move to a local count of R with gote, and G > S > R (from your perspective).

Just looking at the local position, compare S with (G + R)/2. If the position is gote, then its count is (G + R)/2, and if it is sente its count is S. If S > (G + R)/2 then it is sente, if S < (G + R)/2 it is gote, and if S = (G + R)/2 it is ambiguous

While I admire the elegance of these conditions because of their independence of move values, the gote / sente unequations are wrong. The conditions 1 below are correct, according to the proofs below.


Consider a local endgame and a player, here Black, having a gote sequence resulting in the count G or a sente sequence resulting in the count S and the opponent having a gote (or reverse sente) sequence resulting in the count R.


Conditions 1:
The local endgame is
a local gote if S > (G + R) / 2,
Black's local sente if S < (G + R) / 2,
ambiguous if S = (G + R) / 2.


The initial position's tentative 'gote' move value is MA = (G - R) / 2.

With GB and GW being the counts of G's followers, we have
S = GW, // From the initial position, Black moves to G, then White moves to GW.
the count G = (GB + GW) / 2,
the move value MG = (GB - GW) / 2.


The following conditions define local gote or sente according to de-/increasing move values.

Conditions 2:
The local endgame of the initial position is
a local gote if MA > MG, // decreasing tentative 'gote' move values
Black's local sente if MA < MG, // increasing tentative 'gote' move values
ambiguous if MA = MG.


Proof of equivalence of the "ambiguous" conditions 1 and 2:

MA = MG <=> (G - R) / 2 = (GB - GW) / 2 <=> G - R = GB - GW <=>(*1) G - R = (2G - GW) - GW <=> G - R = 2G - 2GW <=> -G - R = -2GW <=> G + R = 2GW <=> (G + R) / 2 = GW <=> (G + R) / 2 = S.

Proof of equivalence of the "gote" conditions 1 and 2:

MA > MG <=> (G - R) / 2 > (GB - GW) / 2 <=> G - R > GB - GW <=>(*1) G - R > (2G - GW) - GW <=> G - R > 2G - 2GW <=> -G - R > -2GW <=>(*2) G + R < 2GW <=> (G + R) / 2 < GW <=> (G + R) / 2 < S.

Proof of equivalence of the "sente" conditions 1 and 2:

MA < MG <=> (G - R) / 2 < (GB - GW) / 2 <=> G - R < GB - GW <=>(*1) G - R < (2G - GW) - GW <=> G - R < 2G - 2GW <=> -G - R < -2GW <=>(*2) G + R > 2GW <=> (G + R) / 2 > GW <=> (G + R) / 2 > S.

(*1) This transformation is possible because of G = (GB + GW) / 2 <=> 2G = GB + GW <=> 2G - GW = GB.

(*2) Multiplication by -1 inverts the unequality sign, as can be seen in this example transformation: 2 < 3 <=> -2 > -3.


Note:

If the local endgame is sente, we replace the tentative 'gote' count (G + R) / 2 and tentative 'gote' move value (G - R) / 2 by the sente count S and sente move value S - R.

[Bill Spight]

Let's suppose that you have a position where you can move to a local count of G with gote or S with sente, and the your opponent can move to a local count of R with gote, and G > S > R (from your perspective).

Just looking at the local position, compare S with (G + R)/2. If the position is gote, then its count is (G + R)/2, and if it is sente its count is S. If S > (G + R)/2 then it is sente, if S < (G + R)/2 it is gote, and if S = (G + R)/2 it is ambiguous

While I admire the elegance of these conditions because of their independence of move values, the gote / sente unequations are wrong.

The conditions are not, repeat, not independent of move values. The sente condition depends upon the miai value of the threat, which must be greater than S - R.

Consider a local endgame and a player, here Black, having a gote sequence resulting in the count G or a sente sequence resulting in the count S and the opponent having a gote (or reverse sente) sequence resulting in the count R.

Whether the gote sequence is a gote or the sente sequence is a sente depends upon the the intermediate positions having a higher local temperature than the original position. Move values are relevant. I am sorry if I did not make that clear in the earlier text.

[RobertJasiek]

The conditions are not, repeat, not independent of move values.

The conditions themselves depend on G, S and R, which are counts. So evaluating the conditions can be done independently of move values; we do not need to calculate move values to decide whether we have a local gote or local sente. At least, that is how I interpret and want to apply the conditions.

Of course, the conditions are also related to move values and, in this sense, they are not independent of them.

If for the moment we restrict ourselves to Black playing to G, you seem to have stated that the local endgame is
a local gote if S < (G + R)/2,
Black's local sente if S > (G + R)/2.
Contrarily, I say
a local gote if S > (G + R) / 2,
Black's local sente if S < (G + R) / 2.

Please confirm which unequations are right.

I applied your conditions to an example, which obviously is a local sente and got your condition's statement to have a local gote. So I tried to prove. At first I made a mistake in the proofs, having forgotten my school maths that multiplication by a negative number inverts the unequation sign. When correcting the proof, suddenly the example made sense when identified as a local sente.

$$B Black's local sente
$$ -----------
$$ | X X X O .
$$ | . O O O .
$$ | . O . . .
$$ | X O O O O
$$ | X X X X X
$$ | . . . . .

Click Here To Show Diagram Code

[go]$$B Black's local sente
$$ -----------
$$ | X X X O .
$$ | . O O O .
$$ | . O . . .
$$ | X O O O O
$$ | X X X X X
$$ | . . . . .[/go]

G = -3
S = GW = -6
R = -7

S < (G + R) / 2 <=> -6 < (-3 + (-7)) / 2 <=> -6 < -5. We have Black's local sente according to my conditions.

The sente condition depends upon the value of the threat, which must be greater than S - R.

I guess this is so but we do not need to calculate the value of the threat. Simply applying the conditions, it is sufficient to calculate the counts G, S and R. Of course, the value of the threat is hidden in these values and in particular the count G = (GB + GW) / 2. We do not, however, need to explicitly calculate the value of the threat to decide whether we have a local gote or local sente.

Whether the gote sequence is a gote or the sente sequence is a sente depends upon the the intermediate positions having a higher local temperature than the original position. Move values are relevant. I am sorry if I did not make that clear in the earlier text.

Nevertheless, according to my current understanding, we need not calculate these move values to decide if we have a local gote or local sente...! We may calculate them and apply conditions 2, but the short method for distinguishing local gote / sente is using conditions 1, that is, just calculating the counts.

[Bill Spight]

The conditions are not, repeat, not independent of move values.

The conditions themselves depend on G, S and R, which are counts.

They also depend upon the threat carried by the sente, which is not shown. My bad, I guess. I simply posited that S was the result of sente, without spelling the threat out.

So evaluating the conditions can be done independently of move values; we do not need to calculate move values to decide whether we have a local gote or local sente. At least, that is how I interpret and want to apply the conditions.

I did not make what I meant clear, then.

I applied your conditions to an example, which obviously is a local sente and got your condition's statement to have a local gote. So I tried to prove. At first I made a mistake in the proofs, having forgotten my school maths that multiplication by a negative number inverts the unequation sign. When correcting the proof, suddenly the example made sense when identified as a local sente.

$$B Black's local sente
$$ -----------
$$ | X X X O .
$$ | . O O O .
$$ | . O . . .
$$ | X O O O O
$$ | X X X X X
$$ | . . . . .

Click Here To Show Diagram Code

[go]$$B Black's local sente
$$ -----------
$$ | X X X O .
$$ | . O O O .
$$ | . O . . .
$$ | X O O O O
$$ | X X X X X
$$ | . . . . .[/go]

That is not an example of what I was talking about, because there is only a sente option for Black, but no gote option. There is no G, only S.

Here is what I was talking about.

Code: Select all

                   P
               /  / \
              G  /   R
                Q
               / \
             BIG  S

Black has two options in P, one to G in gote and one to S in sente (through Q). White has one option, to R. BIG is big enough to make the play to Q sente.