Which kinds of problems count as endgame problems? Do they constitute just reduction/encroachment/defence problems, or do they also include capturing race problems? And if the latter, do all capturing race problems count or only certain kinds?

I think the general assumption is that a group isn't going to die, and that black (generally) needs to find the line that is most advantageous in terms of points and sente, including future followups. If a capturing race is only about the race, I would say it's not an endgame problem to capture unless it involves the cut and starting the race. It may be a problem in how to extract the most points out of the dead stones, though.

Here is a problem from Go no joshiki, by Kubomatsu Katsukiyo, 1929.



Black to play.

I think that we can classify it as an endgame problem, because it is not very big. OC, hot positions can arise in endgame fighting, too.

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Already 'endgame' as a word has multiple meanings, so one should not perceive endgame problems too tightly. In particular, endgame aspects already occur during opening and middle game, so problems discussing such aspects can be considered endgame problems, too. Do not restrict your own understanding by setting a too tight meaning.

Yose, in both Japanese and English, can refer to both endgame plays and plays that approach relatively settled territory at any stage of the game. IMO it is a mistake to equate yose and endgame, and to call a move in the opening an endgame play, except when you mean a mistake, i. e., a play that is made too early and should not be played before the endgame.

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The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I care more for English use of 'endgame' than for English use of 'yose'. Endgame can mean:

"1) Simplifying tradition sees the game as a sequence of the phases opening, middle game, endgame.

2) [...] Endgame aspects can be relevant also during the opening and middle game: all boundary plays must be optimal or prepare later optimal settling.

3) A 'local endgame' is a locale's part of the position, where all relevant local sequences consist of boundary plays only. Such sequences starting with Black and White are compared and evaluated. [...]

4) Sometimes, a sequence of boundary plays is called an 'endgame sequence'." [11]

Most go problems are simplifications where the solution purposely does not concern itself with other global considerations including endgame aspects other than that which the creator of the problem is looking for.
While moves in the opening and middlegame may have aspects which are relevant to the endgame, such is not the main concern for most people when they are focusing on solving problems designed to study endgame situations.
A simple math problem requiring a student to identify the sum of two amounts of money does not require further elaboration on how to spend the total sum of money thereafter.

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