So where is the fair line?
I remember a game I played in the World Open where my 2300 opponent seemed to be very mad at me because I was not resigning even though I thought I still had reasonable chances. He was mad and playing fast and I saw some tricks that I might be able to get. I resigned as soon as I thought I had no reasonable chances left. Once I resigned he left without even saying anything and was obviously very upset. I personally thought I had great reason for playing on. First of all, there is a lot to learn from playing out a tough position. I want to be that 2300 player one day (hopefully soon). Second of all, when he got mad it gave me more incentive to play it out because he probably wasn’t going to play his best chess and it upset me that he had gotten so upset when I felt like I still had chances.
But there is another point which is probably even more important. When you continue to play (as mentioned by Tartakower) you have chances to win. There was another game mentioned in one of my blogs in which I went down a Queen for a piece and Rook. At this point many people would have resigned, but I kept fighting and later on got it back but it was still a losing endgame. It was a Bishop and Rook with some pawns versus Knight and Rook with some pawns. He had the Bishop and Rook and he was up a pawn with a better position. I was checking him and he brought his King down so he was still winning but he was in a dangerous position and he had to be careful. I knew that I had chances to trap the King. He wasn’t careful enough and I won in an endgame where you would think I would lose or at best draw. I had determined in that game that if he brought his King over instead of bringing it down that I would resign because I had no more reasonable chance of winning, but he didn’t do that so I knew I still had some reasonable chances. There are lots of examples of games like this. In the US Jr. Championship, there were a few games that appeared lost that finished differently: Parker Zhao vs. John Daniel Bryant and Ray Robson vs. Eric Rosen (Eric had mate in 12 at one point in the game). Sam Shankland admitted that it took some luck in his game against John Daniel Bryant, but if he had resigned that possibility would not have been there.
There are some games, however, where you have to pray for a miracle beyond miracles. These games you most likely should resign because there is almost no (if none at all) chance that you can learn something from those games. In the games where you are losing but still have reasonable chances then I think you should play it out to learn something, (if you are a Super GM, you can resign because there is probably not a whole lot you can learn), and then maybe you will luck out. Both Alex Lenderman and Sam Shankland have said that luck is part of chess. In the games where you think you are barely losing, I recommend fighting not resigning!! You could be wrong and even if you are right, you still most likely have good drawing chances.
So to me, the fair line is don’t play ridiculous positions out (I am still working on this a little bit), but if you feel like you have reasonable chances then it is your choice if you want to play it out or not. It is important to remember that you need to give respect to the players who have earned that respect through all their hard work and dedication. If you are playing a GM, you don’t need to be down a whole lot for it to be a ridiculous position to play out. However, I hope that GMs and IMs that are playing 12 year old kids who are not kids any more, but are still trying to learn and get better, will understand that sometimes they play a game out because they want to learn or maybe because they are mad at themselves for making a stupid move, but they are not trying to show disrespect.
Here's an example from the recent US Junior Championship where John Daniel Bryant should have resigned but played it out and lucked out (granted Parker Zhao was in time trouble):