Most chess games are already time constrained (though a ref can call it if someone in a non-winning position is trying to run out the opponents clock)
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I was imperfectly remembering the rules. If it is theoretically impossible (even with blunders on the player who is out of time's part) for the player with time left to win, then it is a draw.
In addition, a player with less than 2 minutes on the clock may request a draw; see Article 10.2 which includes this subsection:
> a. If the arbiter agrees the opponent is making no effort to win the game by normal means, or that it is not possible to win by normal means, then he shall declare the game drawn. Otherwise he shall postpone his decision or reject the claim.
I'm not super into chess, but I was under the impression that running out the clock was a totally legitimate tactic. I'm surprised to hear that a referee has discretion to end the game based on it.
The issue is when positions are completely equal and there is no reasonable way to progress. It might still be technically possible to win in such positions, but it would require someone to make extremely bad moves and almost certainly lose. If there is no rule that forces draws in such positions, then players will just keep moving pieces without purpose until either someone's time runs out or 50 moves without capture / threefold repetition happens.
An arbiter 100% cannot stop a game because of that. Time management is part of the game in speed chess anyway, and for longer time controls there is usually a delay/increment so running out the clock in a clearly lost position isn't viable.
I slightly misremembered; the player stops the clock and calls the arbiter; if the arbiter agrees that their opponent is not attempting to win by normal means, the arbiter may award a draw. There is a 2 minute bonus to the opponent if the arbiter disagrees with the player making this claim.
I am not a chess player but I have never heard of referees stopping the game if you don't "give up" in a losing position and have extra time. That sounds ridiculous but I would love to know if it applies in certain tournaments and the reasoning behind it.
You are allowed to keep thinking as long as you have time on your clock. Isn't really considered good sportsmanship but is legal.
Recent instances I saw was an adult was in an almost-lost position with over an hour on the clock while his opponent had 10 minutes. He let his clock run down to nothing and then played quickly before finally let the clock run to zero in a lost (mate in 2) position. He got mocked for this in the local forums.
Also common for a kid to do a blunder and then sit there sad/crying for an hour. You try to encourage them to resign though.
[edit]
I was imperfectly remembering the rules. If it is theoretically impossible (even with blunders on the player who is out of time's part) for the player with time left to win, then it is a draw.
In addition, a player with less than 2 minutes on the clock may request a draw; see Article 10.2 which includes this subsection:
> a. If the arbiter agrees the opponent is making no effort to win the game by normal means, or that it is not possible to win by normal means, then he shall declare the game drawn. Otherwise he shall postpone his decision or reject the claim.