A sente-sente (or double-sente) move is a move which is sente for either player. It is always important to grab these moves as soon as possible, because whoever plays them gets points for free - no move is lost by playing a double sente play, but it does give one points.
Note: However ... Double Sente is Relative.
The simplest sente-sente position is on the left. White can play and in sente. Compared to a black play (Black 1 at 3 etc.), White has two more points of territory, whereas Black has two fewer, i.e. a total of four points. This is said to be a four-point sente play for both sides. (The actual value of a double sente is a relatively large number.)
The "value" of four points is deceptive. Double sente plays should normally be played as soon as they arise on the board. The question is how large the threats for each player are, compared with other plays on the board.
For example, in this case, if Black does not answer with and , White can take a large chunk out of Black's territory.
In this diagram (assuming that there is white territory to the left and black to the right), is often a double sente move. If White does not answer, Black makes a huge incursion into White's territory. White can play the same move at 1, threatening to jump into Black's. White answers at , and Black can also play and in sente. White can exchange a for b later.
It is important to play this type of move before the opponent does so: Black has gained six points here compared to a white play at 1, at no cost of moves. Giving two of these, rather common, positions to your opponent already costs over 10 points - which can easily be the difference between win and loss even at moderate levels.
After the white corner stones are captured. White can now play a in sente to force Black into capturing. When immobilizes the black stones in the center, Black can likewise play a himself as a forcing move. The move is sente for both or double sente.
xela: Thanks, interesting example!
Question 1: Where does the KataGo analysis come into it? Did KataGo back up your judgement, or did it surprise you at all?
Question 2: If a is double sente, then I guess that means should be at a. How did the game actually continue? Did the players both get it right?
Question 3: If a is really double sente, then why was not at a?
kmr - Its 1987-10-12 game from 12th Kisei Touunament (black won by resignation). According to LZ, white 4 is pretty big mistake and it should be at 5, then after black forcing response, white should force again (on 1st line) then he can switch to 6. Apparently LZ judge white 4 as a too close to weak black stones and prefers to attack them indirectly (about 6% of WR loss).
xela: OK, if it looks obvious to me that should be at a, and LZ agrees, yet Otake played a different move -- what can we learn from Otake's thought process here?
kmr - i have 2 thoughts. 1st is that 4 looks solid, and if you read Kageyama book "Lessons in the Fundamentals of Go" it may add up, that japanese pros in such a positions tends to play solid (and top bots usually disagrees with such a solid play, for them its too solid :) ). 2nd - top bots frequently disagrees with pros with ko threats - they play it out as a forcing moves, and pros tends to save them.
xela: As general principles, both of those make sense, but I don't see how they apply to the current position. If is solid, then surely forcing at a followed by is even more solid? And you can't save as a ko threat: if you don't play there right away, then black will take the sente move instead (as happened in the game). That's why it's called double sente :-)