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.
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First, my definition of the endgame is:
the stage in the game where only border plays remain, i.e.
With -, 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".
A border play can be of two different natures
Black's disruptive border plays:
White's disruptive border plays
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.
Later in the game, these captures and threats will become more significant and can be considered "disruptive".
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.
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 , is . Unlocking 3 stones would overhaul the territory and threaten the Black groups for life.
And is so threatening that again Black only has to postpone answering it.
While is disruptive in the sense that it threatens to destroy most of White's centre territory, WHite's move may pose a larger threat to Black, namely killing its entire corner. Black will likely answer, making really sente and White can return to answering with , since that has now become the largest move (protecting about 10 points), but first executes his own sente at .
Now why would White play and 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 himself if White omits it. Same for .
Let's explore this some more
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:
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.
a looks like double sente. It indeed threatens to disfigure the opponent's territory.
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 there and enters the centre, White may kill the corner.
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?).
Let's first see what happens if Black plays first. After , 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.
Suppose Black leaves the situation after and for the sake of the argument, secures his corner by playing the big gote of --, then White makes another exchange - 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.
If White plays in order to keep sente and later follows up with what will be the sente exchange of to , 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.
After , Black executes a force to capture? with to . Next a has some value (White can only destroy a point by destroying his own).
Let's count this as the zero position.
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
White -- 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.
Black makes 2 points. (the 2-3 exchange is White's prerogative). Later, Black has a sente move at a.
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.
makes the 2 circled points. Later, Black has a sente sequence - and - is White's prerogative. Overall we count this as 2 Black points.
destroys 2 points and makes 2 extra. Later, - 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.
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.
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
We calculated the sizes of the major moves and can conclude the following
In the endgame, sente seems to have the following meanings, concentrically:
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".
Now let's turn to the following questions:
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.
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.