There is no simple yes or no.
There is no Chess RULE which forces you to resign - neither for the referee to terminate the game claiming a win . But there is an ethical obligation, I said that many times. If one took a few lessons in chess, he should know that this is exactly the right moment to resign. With one possible exception: huge time trouble.
Huge time trouble here would be: less than 30 seconds. All players with rating > 1900 can mate with only one rook on the board when having 30 seconds left.
If you have less time in such a situation, your opponent can continue (and thus hope for a draw), I think this is hard to judge morally (it is, though, painful for the party with the rook, and even for the people who watch).
As far as I'm concerned, I would resign anyway.
By the way, this is the reason why many people are in favor for a time regulation with increment (10 seconds for instance, for each move), then such situations do not occur anymore.
A player with 2100 Elo will mate you in even less than 30 seconds with a rook, from every position.
I have another anecdote, not related to resigning attitude, but also to chess etiquette:
Once I saw a game with K +R vs. K+ R, in a small tournament in Missouri, in the B-group, with players all having less than 1900 rating.
One player was better in time (10 minutes), the other had about 3 minutes left and offered two times a draw which was rejected by the first!
The second player than indeed lost by time. In fact, it seemed to me that he did this deliberately, in order to show his ugly opponent that he was a moron!
He left the room calmly, but without looking at his opponent.
The first player after the game justified himself saying 'this was my only chance to win the B-group' (thx god, he didn't). I watched the game with my friend, a Czech mathematician, he told me 'when this would happen in my country, nobody would ever talk to that guy'.
In my opinion, the player with less time could have approached the referee claiming a draw. The rule says he (the referee) can fix a draw in such a situation.
Though I cannot remember wether such a rule already existed in 2001, when this happened.
at being called a bastard, for not playing in the manner expected by an earlier opponent lol. (I'm really glad I got him going) . Anyway, my point is, there was no point in playing on. There was no way he was going to make a similar blunder, and the game would be over very quickly. I would have only insulted his intelligence and my own by continuing.
I'm being invited back into this thread. I can resist. Oh no, I can't!
A simple question for you then, sir (mandelshtam):
In a King+Rook versus King situation: ought the player with the bare king to resign immediately upon reaching this situation, irrespective of any other consideration?
1. For instance, even if both players are learners, the one with the bare king should resign.
2. Or if a master has the bare king, and the learner has K+R, the master ought to resign.
3. Or if the player with the K+R is in time trouble, the player with the bare king still ought to resign.
I would like, if I may, to request a simple answer: either Yes or No.