Dieter Verhofstadt / Practical Endgame

Sub-page of DieterVerhofstadt

With modern endgame theory being developed and published by professionals like O Meien and Antti Tormanen, I've been reflecting on its practical use. For starters, let me discuss here the way I think about the endgame and apply these thoughts in actual games.

Table of contents

The Endgame

First, my definition of the endgame is:

the stage in the game where only border plays remain, i.e.

  • all (major) groups are in a stable state, which is either alive or dead,
  • and there are no more empty areas to develop, both Black and White have territories with relatively clearly defined borders


The endgame  

With B1-W2, Black has forced White to capture the circled chain, while in the sequence leading up to that, Black was still fighting for survival. Other places where 3 or more stones are dead, are marked with squares. Other major groups are alive.

There are no major territories to conquer, all are defined. The borders can still move up a few points in either direction. We say that "only border plays remain".

Disruptive border plays

A border play can be of two different natures

  • either it threatens to disrupt the above mentioned assumptions, i.e.
    • it threatens to kill a living opponent group, or revive one's own dead group
    • it threatens to considerably reshape the borders of the defined territories, mostly that of the opponent
  • or it doesn't

Examples of disruptive border plays

Diagram 1 - Disruptive border plays  

Black's disruptive border plays:

  • a threatens to revive 7 dead stones and kill White's upper right side doing so.
  • b threatens to cut off and kill White's lower right side
  • c threatens to enter White's central territory and redefine its shape
  • d threatens to revive 2 stones and kill 5 of White's

White's disruptive border plays

  • e threatens to revive 3 White stones and destroy much of Black's territory
  • f though not easy to see, if unanswered, White can jump to x and undermine the life of the Black corner (I believe it can be killed)

Such a disruptive border play is what we usually refer to as "(local) sente". A non-disruptive border play is then "(local) gote".

The more narrow definition for sente in the endgame is "a play that, if unanswered, gains more by following through, than it gains if answered". Although that may be more precise, I find it less helpful in order to determine in which order to play the moves.

Examples of non-disruptive border plays

Diagram 2 - Non-disruptive border plays  
  • Black a is not disrupting the borders. If White plays it, it threatens to reduce the area but not kill the corner, although there's a risk.
  • Black b catches a stone. White b saves that stone and threatens cutting off a Black stone. YOu could call it formation of a new territory but at this point of the endgame we don't see it as disruptive
  • Black c will later force White to capture three stones but in itself doesn't redefine the areas. A White play just prevents that.
  • Black d indents White's area, White d threatens to capture a stone.
  • Black e enlarges the edge territory. White e sets up shortage of liberties to catch a few more stones.

Later in the game, these captures and threats will become more significant and can be considered "disruptive".

The controversy caused by the term "sente"

The traditional understanding of sente is "a move which the opponent responds to locally, or eveb needs to respond to, hence keeping the initiative, often to play elsewhere". A gote move is then a move which doesn't provoke such answer, hence yielding the initiative to the opponent.

This notion of "need (not) to respond" is controversial. The opponent always has a choice and even if responding locally seems necessary, it is not guaranteed to give the best result globally.

However, the notion is practical: a disruptive border play is likely to be answered and keep the initiative. On the other hand we know that a move which locally is likely to be responded to, may still be ignored in favor of a larger move elsewhere.

Example: disruptive and sente

Diagram 3 - Disruptive and sente  

B1 is the only real sente on the board, i.e. that single move which (gains a point and) will be answered.

Another such move, but still not as hot as B1, is W4. Unlocking 3 stones would overhaul the territory and threaten the Black groups for life.

And W6 is so threatening that again Black only has B1 to postpone answering it.

Example: disruptive but not sente

Diagram 4 - Disruptive border plays but not sente  

While B1 is disruptive in the sense that it threatens to destroy most of White's centre territory, WHite's move W2 may pose a larger threat to Black, namely killing its entire corner. Black will likely answer, making W2 really sente and White can return to answering B1 with W6, since that has now become the largest move (protecting about 10 points), but first executes his own sente at W4.

Now why would White play W2 and W4 and Black not play his own undisputable sente?

Because Black's move is a 1 point sente and nothing else. White's move include more uncertainty: what if Black plays there? Should White answer? What's the value of those moves? There is a high likelihood Black will play B2 himself if White omits it. Same for B4.

Let's explore this some more

Opponent's perspective

Now switch to the opponent's perspective who will use the same or a close-by point as a border play. We call this the "opponent's border play". Likewise, this can be a disruptive or non-disruptive one. This gives 4 combinations:

  • both the border play AND the opponent's border play are disruptive: this we usually refer to as "double sente"
  • the border play is disruptive, but the opponent's border play isn't: this we call "sente"
  • the border play is not distruptive, but the opponent's is: this we call "reverse sente"
  • or neither is disruptive, which we call "(double) gote"
Diagram 5 - Black's perspective  
  • a is (big) reverse sente
  • b is (big) gote
  • c is (big) gote (with a sense of reverse sente)
  • d is (small) sente
  • e is (small) gote
  • f is (mid size) gote
  • g is (mid size) gote
  • h is (small) sente
  • i is reverse sente (with a sense of double sente)
  • j is (almost zero) sente
  • k is (small) sente

About double sente

Again, it is controversial whether "double sente" can really exist and how it then came about. With this wording, there is no such controversy: both plays are disruptive but whether both need to be answered is not conclusive, indeed questionable.

Diagram 6 - double sente  

a looks like double sente. It indeed threatens to disfigure the opponent's territory.

Mutual damage

A disruptive border play can remain unanswered, often if the opponent plays such a disruptive border play elsewhere. We call this mutual damage. The game then goes in a state of turmoil, eventually restoring the endgame assumptions along different lines (for example, both subsequently answer the alleged sente), or evolving to a breakdown for the player who apparently misjudged the need to answer a disruptive border play.

We can see this at work in diagram 4. If Black misjudges the need to answer W2 there and enters the centre, White may kill the corner.

Size of moves

As a rule of thumb, you play disruptive border plays before non-disruptive ones, trying to keep the initiative. On the other hand, disruptive border plays can be kept as ko threats. Black's dominant sente in our sample game is a clear example of that.

Among each category, the rule of thumb is to play the bigger move first. The size of a move is determined by evaluating the difference between the result of the border play and the result of the opponent border play (the swing) and the difference in number of moves played (the tally?).

Calculating the size of A

Black first  

Let's first see what happens if Black plays first. After B3, we draw borders at the square points, because it is equally likely for both to play there. Note that White will have to defend at a eventually.

We don't know how many points Black has made here but with some foreknowledge we can say he made the 6 circled points.

White first - the gote way  

Suppose Black leaves the situation after W3 and for the sake of the argument, secures his corner by playing the big gote of B4-W5-B6, then White makes another exchange W7-B8 which is surely sente. In comparison with Black first, White has made the 3 circled points, while Black's 6 points are indeed gone (Black will need to protect the cut).

The swing value is 9, the tally is 2 and so the size of the move is 4,5.

White first - the sente way  

If White plays W1 in order to keep sente and later follows up with what will be the sente exchange of W3 to B6, then White makes 2 points compared to Black first, while Black keeps 3 of his original points, losing 3. The swing value is 5 but the tally is 1 ans so the size of the move is 5.

Calculating the size of F

Black first  

After B1, Black executes a force to capture? with B3 to B6. Next a has some value (White can only destroy a point by destroying his own).

Let's count this as the zero position.

White first  

W1 turns all of the 6 circled points into territory, compared to Black first. Also White is slightly more likely to get b than Black, so we count it as 7 points.

The swing is 7, the tally is 2. The size of the move is 3,5

Calculating the size of B

Black first  

Again with foresight, Black makes the 5 circled points. White nothing.

White first  

White W1-B2-W3 makes 2-3 points for White, IF she gets a, which is a 50-50 chance, so let's say >1 point. Later she executes the sente sequence which is her prerogative, to destroy all point Black made when he'd go first.

The swing is 6+. The tally is 2. The size is slightly more than 3.

Calculating the size of C

Black first  

Black makes 2 points. (the 2-3 exchange is White's prerogative). Later, Black has a sente move at a.

White first - sente?  

W1 saves the stone but also threatens a, which makes an additional 7 points.

In the sente case, the swing is 2 and the tally 1, so the value is 2. In the gote case, the swing is 9 and the tally 3, so the value is 3. This makes it more likely for the move to be sente.

Calculating the size of G

Black first  

B1 makes the 2 circled points. Later, Black has a sente sequence B3-W6 and W8-B9 is White's prerogative. Overall we count this as 2 Black points.

White first  

W1 destroys 2 points and makes 2 extra. Later, W5-W7 gain her another 3 extra, with 50%. The count is 2+3/2 = 3,5. The swing is 5,5 and the tally is 2, so the value of this move is 2,75.

Calculating the size of I

Black first  

B1 makes the circled point, captures a stone and will eventually force White to play a. It leaves a ko worth -1/3 for Black. The reference score here is 2-1/3 = 5/3 for Black.

White first  

W1 makes the 3 circled points. Later a is Black's prerogative. The swing is 3+5/3 = 14/3. The tally is 1, so the value is 14/3 = 4,67

Summary of how to play

How to play - Black's perspective  

We calculated the sizes of the major moves and can conclude the following

  • a is a 5 point move (and reverse sente), it's the biggest move on the board and will be played first. Next, it's White to move.
  • i, is a 4,67 point move, and is White's best choice
  • c is a 2 point sente move, which White executes next (not sure, the follower is 6/2=3 which is smaller than Black's b)
  • f is 3,5 and White takes gote here
  • b is 3+ for Black
  • g is 2,75 and will be White's
  • d, h, j, k are all 1 point sente and probably kept in reserve
  • e is (small) gote

Better terminology

In the endgame, sente seems to have the following meanings, concentrically:

  1. The one move that must absolutely be answered or the game is lost. I call this the "dominant move" or "dominant sente" because whichever move the opponent plays, the owner of the dominant move can be assured that the dominant move will be answered or else he wins the game. When the dominant move has been played out, another move will become the dominant move. In the sample game, diagram 5, k is the dominant move. After that, d is the dominant sente, but 'there's something funny about d. If Black plays it, White can postpone answering and answer locally with c. So, d is not dominant strictly speaking. If Black gets c first, then d is dominant. But that doesn't make c dominant at all. This makes d a very unattractive move to play. It's a kind of "negative sente".
  2. A move that threatens to change the assumptions of the endgame, as indicated above, which I call a "disruptive border play". The main feature of a disruptive border play is that it increases uncertainty about the score. In extreme cases (like the dominant sente) it's clear that the game is decided, even without calculating the proceedings. In diagram 5, d, j and k are Black's disruptive border plays; a and i are White's.
  3. A border play whose follow-up has a larger gain that its own. This is the traditional meaning of endgame sente: if answered, the move represents a certain gain (or, as the advocates of sente gains nothing would say, the gain represented by forestalling the move, i.e. the reverse sente) and if not answered, one can play a move which represents a higher gain. Apart from above mentioned "disruptive border plays", in diagram 5 c is such a move. Its gain if answered is 2 points, if unanswered White can follow up with a 3-pointer (6/2=3). The major difference with what I call a "disruptive border play" is that we can quite accurately calculate the gain if the move is unanswered and that gain is moderate. While thinking of a shorter name, I'll call this "border play with larger follower"

I find it instructive to think about these three categories with different terms and I tend to remove "sente" from the wording, since that term has such a strong sense of "keeping the initiative", which is in fact only guaranteed with the dominant move. Using "sente" for disruptive border plays and border plays with higher follower, may mislead players into thinking they have to answer these moves, or put them off guard if their alleged sente is locally unanswered.

The word I like best for the superset of these moves, as an alternative for "sente", is "prerogative". The above categories then become "dominant move", "disruptive border play" and "prerogative". A reverse sente is a "forestalling move".

Order of play

Now let's turn to the following questions:

  1. Should you play out your dominant move?
  2. Should you play your distruptive border plays? In which order?
  3. Should you play your prerogatives? In which order?
  4. And when does it make sense to forestall the opponent's prerogatives?

From the sample game, we can see that k, the dominant move, is a classic 1 point sente. What happens if Black plays it right away? What happens if he doesn't? And what happens if White plays it?

In that position, it's Black's turn.

  • If Black plays k, White will answer and it's Black's turn again. Black has thus avoided White taking that point ever, at the expense of losing a ko threat, should a ko occur later in the game.
  • If Black does not play k and plays a instead, as he probably should, the initiative shifts to White. White can now forestall at k, play a disruptive border play i, or play another prerogative like c.
    • If White plays k, she gains a point but the initiative shifts back to Black who can take f, as he has no real prerogatives left. In terms of value, Black has gained 5 + 3,5 while White has gained 1. This is unlikely to be the best course of action for White
    • With a gone, White has only i for a disruptive border play. If she plays it, Black will answer (or choose to inject k). If she doesn't, she leaves a play with value 4,67 to Black, which is much harder to overcome by plays elsewhere than Black's dominant move with value 1.

In the end it's all about the value of a move. A 1 point sente, even if it's the dominant move, can be played at will, because the opponent is unlikely to forestall it. Keeping it in reserve as a ko threat is proper gamesmanship. A 4,67 sente should be played much sooner.

Dieter Verhofstadt / Practical Endgame last edited by Dieter on June 1, 2019 - 22:42
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