nachtrabe: I've noticed a lot of discussion on this point and something confuses me. Isn't, by definition, all of sente relative and dependent on the temperature? How is this different from sente, where an opponent might completely ignore an expected-to-be-sente move to either play somewhere else along a different line or to make a counterthreat worth an equal-or-greater amount?
The page on sente says that: "This is theoretical rather than practical: after all one can only say what ought to be answered, not what will be." It also of course always depends on the surrounding conditions. Is this any different from what is meant by the "Double Sente is Relative" point? Thanks for helping clarify this :)
Bill: Theoretical sente is defined in terms of temperature. That does not mean that it is relative. It does not depend upon surrounding conditions. Practical sente is defined according to whether it gets a local reply. Whether that is correct or not depends upon the rest of the board, which is not part of its definition.
As for double sente, there is no such thing theoretically. There is only double sente in the practical sense, which depends upon the rest of the board.
Part of your problem stems from different wording by different authors. I restrict the term, theoretical to sente based upon calculation. If a play is sente in that sense, you cannot even say that it ought to be answered. Apparently the author of the quote on the sente page uses the term theoretical to cover correct play.
(I use the term to cover correct play, too, but for a different theory, that does not talk about sente or gote or temperature.)
Let me give an example to disentangle some of these different senses of sente. Suppose that there are only two plays left on the board, and that their game trees look like this. (/ indicates a Black move, \ indicates a White move, and letters indicate non-negative scores.)
A B / \ / \ a -a C -b / \ c 0
A is, OC, gote, with a miai value of a.
1) sente if c > 2b, with a miai value of b;
2) gote if c < 2b, with a miai value of (b/2 + c/4);
3) ambiguous if c = 2b, with a miai value of b.
Practically, B could be sente, gote, or ambiguous. B is
1) sente if c > 2a;
2) gote if c < 2a;
3) ambiguous if c = 2a.
Note that the theoretical sense of sente depends only upon the play itself, with no regard for any other play, while the practical sense depends upon the whole situation.
What about correct play?
Black to play should play A or B depending on the comparison,
2a >?< b + c .
White to play should make the comparison,
2a >?< b .
Sente or gote is not part of that question. They are useful concepts to help guide us when, as usual, things are complicated.