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Learn to resign

To reply to the OP: you play a ton of bullet. You're a strong player who plays chess for diversion and entertainment; knock yourself out.

If you're a serious player reading this and wondering the answer to the question, remember that when you play a game with a longer time control you are no longer wasting seconds at a time, you're wasting minutes or hours at a time.

When you think of chess, do you want to think of minutes and hours wasted, or success and improvement?

You only have so much time to devote to chess in a lifetime...
Try checkmating with only these black pieces :
Kd7,Re7
White pieces on
Kd2,Qe2
Its not easy.White to play first or else it is a draw.

So this means even thought you have a losing position as black, you should play on, because maybe the opponent time will run out or the player does not know how to check mate or figures it can turn into a draw. (White starts and in 28 moves white will checkmate.) Make a few wrong choice and you break the 50 move rule.
lichess.org/analysis/8/3kr3/8/8/8/8/3KQ3/8_w_KQkq_-

That's a position which requires solid heuristic and technical memorization. Black is down four points of material. I would always play this out in a tournament against someone.

If I lost a piece on move five in a tournament--three points of material--I would resign if there were no compensation.

Applying the standard of "reasonableness" to any position is fruitful.
just because you end up winning a lost position doesn't mean its not rude to keep playing.

imagine sitting across from a real person/friend and playing out every lost endgame, you think they would still want to play with you after a few games?
There is no rudeness in chess, only in personal behaviour, like making noises during a game.
Resign when you are ready to give up hope.

A player should only resign when they submit to the fact that their opponent won that round. It is like wrestling, when you had enough, you say or show that you give up.

The aim of the game is to checkmate the king, like a dual, may the best person win. For some it is a war and they fight to the very end.

We play to checkmated or be checkmated. To be or not to be is the real question. If we do not want to be checkmated we resign early. A forced checkmate should be enough for any player to resign. Unrefined chess players will play on. When we are new at chess, we are unrefined. As we gain knowledge,
we learn when to resign.

Without structure, the game crumbles.
Does this mean it is over? It depends on the position. Hope goes a long way. If the game is hopeless, then it is rude to continue.

If only one player is missing the tools to checkmate, should that person lacking the tools resign? From a refined cultural point of view, yes.

Leaving a game deliberately unfinished is rude. Resigning is the answer.

Is it rude if a player lacks the training, knowledge or skill to checkmate a king? Obviously not for a newbie. Will they ever master the game? If not, don't expect them to resign.
@68
There is not always rudeness is not resigning, especially in one minute chess. Just because you feel offended, does not mean you are justifiably so. Comparing playing someone otb and online chess is apples and oranges and if you feel so easily offended then the harsh world of internet is not for you :) The player I played did not give up and was rewarded . He fought on because he correctly knows there are people like me who can blunder such situations. He deserved the win as much as I deserved the loss.
You are under no obligation to Resign it does not matter weather you are playing speed or a slow game.
If someone asks you to resign it is probably because they do not know how to win or they see their weakness and hope you do not.
Example a player elsewhere played a 5 minute game and complained his opponent would not resign. Out of his last 10 moves the complainer missed mate in one 9 times No body should resign to him he can not mate and his clock might run out first.

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