Resign;my opponent might get busy with life issues and timeout, but I don't want to win that way..
Would You Resign in Positions Like These?

I'd resign every single game in that position - White has literally no hope, not even for a cheapo, and I have much better ways to spend my time than playing lost positions.

Sure, in low-level chess (below rating 1000), you can reasonably expect there to be a chance for your opponent to stalemate you. If both you and your opponent are rated higher than 1400, however, you're basically insulting them by implying he can't convert a complicationless endgame where he's a bishop and two pawns up.

A note - I feel like this is something that goes unnoticed by a lot of people, and it's why resignation is considered so strange by others.
Chess is fundamentally not like other sports, where you play to have the most points or goals or the least strokes. In chess, you play on one board, for one point - there is no "score". In baseball, you can always try to score more runs. In soccer, you can always try to score more goals. In chess, you can't try to "score" anything if you're losing, because the score will be the same: 1-0. In the same way, there are no degrees of winning or losing in chess: you didn't get crushed, put up a fight or (heaven forbid) last a long time. You just won or lost.
Secondly, playing a losing chess game is far less enjoyable than playing a losing game of any other sport, because unlike in other sports, where the gameplay doesn't depend on the score, in chess, it does, to such an extent that the impact of an extra piece can usually be felt all over the board the moment it is captured. People resign in chess games not just because defending lost positions is pointless, but because it actually hurts to look at them and have to play them.
Thirdly, the way the outcome is determined in chess is different from every other sport. Games of most sports are not objectively won, lost or drawn, except perhaps in the final minutes. Chess is. If you're down 4-0 in a hockey game in the first period, it won't mean anything if you play well. If you're down four points of material in the opening of a chess game, you're usually just lost, and barring some lucky tactic, your position will just slowly fall apart.
Lastly, most people consider forfeiting a game in other sports disrespectful and value perseverance, but in chess, often not resigning is disrespectful, and though perseverance is valued, chess players also believe that there's a difference between persevering and wasting time.
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People resign in chess games not just because defending lost positions is pointless, but because it actually hurts to look at them and have to play them.
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Maybe some do, but it should really be the other way around: if it's pointless, resign, if not, don't - in particular if playing on will be difficult and painful.
Lastly, most people consider forfeiting a game in other sports disrespectful and value perseverance, but in chess, often not resigning is disrespectful
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Very often people take a notion of fair play they picked up in an entirely different, not chess related context and apply it to chess. Just thinking of the countless variations of the theme "they refused to give me a rematch". *sigh*

I've never been lucky enough to win on time or by stalemate in a game like this but I certainly have been on the other end of the spectrum. Case in point: https://www.chess.com/daily/game/145781410
Literally a mate in 1 in a 5 day game and I timeouted. Never give up!
you had mate in 1 too

A note - I feel like this is something that goes unnoticed by a lot of people, and it's why resignation is considered so strange by others.
Chess is fundamentally not like other sports, where you play to have the most points or goals or the least strokes. In chess, you play on one board, for one point - there is no "score". In baseball, you can always try to score more runs. In soccer, you can always try to score more goals. In chess, you can't try to "score" anything if you're losing, because the score will be the same: 1-0. In the same way, there are no degrees of winning or losing in chess: you didn't get crushed, put up a fight or (heaven forbid) last a long time. You just won or lost.
Secondly, playing a losing chess game is far less enjoyable than playing a losing game of any other sport, because unlike in other sports, where the gameplay doesn't depend on the score, in chess, it does, to such an extent that the impact of an extra piece can usually be felt all over the board the moment it is captured. People resign in chess games not just because defending lost positions is pointless, but because it actually hurts to look at them and have to play them.
Thirdly, the way the outcome is determined in chess is different from every other sport. Games of most sports are not objectively won, lost or drawn, except perhaps in the final minutes. Chess is. If you're down 4-0 in a hockey game in the first period, it won't mean anything if you play well. If you're down four points of material in the opening of a chess game, you're usually just lost, and barring some lucky tactic, your position will just slowly fall apart.
Lastly, most people consider forfeiting a game in other sports disrespectful and value perseverance, but in chess, often not resigning is disrespectful, and though perseverance is valued, chess players also believe that there's a difference between persevering and wasting time.
Those are all good points. But just like my opinion, it's just how you personally feel about it. I agree chess is not like any other sport, because it's not like any sport. It's not a sport at all. I think it's more like poker or maybe Monopoly, where if you feel like the other side is going to win, you just give up.
I think it's really easy to take ones own personal view and believe everyone should play by that belief. Not everyone plays games for the same reasons. When you say playing a losing game is far less enjoyable, according to who? Who decides what is enjoyable and what isn't? I say it's the person playing who decides, not a third party.
As I said before, who wins or loses is of far less importance to me than the game itself and the company of the person I'm playing. I think many people believe resigning is done when they feel like there is little or no chance of winning or drawing. But those are not the only reasons to play the game. Maybe they just take it far more seriously than I do, and cannot understand that other people dont take it equally as seriously.
I understand why people resign, and I dont think it's wrong if they do. It's their choice and I wouldn't try to convince them otherwise. I just think it's disrespectful to quit, especially when the opponent is so close to winning. I totally understand if other people have a different point of view, but it doesn't change my point of view. I think the feelings people have on whether someone should resign or not probably come from the reasons they play the game. If the reasons are totally different, it might be difficult to understand the other point of view.
POST NUMBER 69 hahahahahaha