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Your opinion: time is up but win is forced

I am an arbiter. The game would be declared a draw if an arbiter were present.

White obviously can't win, he failed to make his move on time. But as there is no series of legal moves with which black could win (the only series of legal moves is 1.Bg7#), the game would be declared a draw.
@Neverness
There is something similar to premoves in OTB games and you can frequently see that in blitz games: you make your move after your opponent has left the piece on the board but before s/he switched the clock.
This "feature" is the reason why I prefer OTB bullet to online: there is no gambling involved in pre-moving because you can see opponent's last move and you save your time.

Back to the main thread, I agree with @Scarblac: the game should be adjudicated a draw because white's only legal move is Bg7# so there is no way for black to win this game. Just like with insufficient mating material there is no way to win on time
Doesn't the player have to call an arbiter before his time flags? Can he do it after he lost?
Normally you cannot call the arbiter without any time on the clock. In this case I guess it would be black to call the arbiter as white would not accept a loss and black would like to win. So black would call the arbiter to claim the win and the arbiter should record a draw in this particular position
Wow! So many interesting ideas and oppinions...

The comment from Scarblac gives me new input.
So the Fide rules care about a position that is not winable even when time is up. So as a arbiter you have this rule to justify the decission to draw such a game.
Maybe Fide never noticed that there are positions which only can be continued by checkmating the opponent.
The idea to draw a game even in a situation the time is over lead me to the thought there is space for a rule in future to give the full point for an absolut forced checkmate position. If there is only one legal move not to checkmate the position is not won..
Hmm have to think more about it :-)
By the way.. I've got the spirit of my chess club. For some years I was on a small blitz tournament and the person next to me (I learned a lot about blitz games from him) said while playing the opponent: "damn! plan b". And I asked him what was plan a and he said to win by time. And so i asked him for plan b and he said "to win by position". I have to say that he is a really strong player (on of the strongest in club).
So I'm a friend of wining by time and think it is important to give power to the clock... but in a situation that is impossible no to win?
I've made my point already, but if this kind of situation ever came in play, i would be surprised. putting this stuff in the rules when it will matter basically never strikes me as needless complication which should be avoided in the rules. but then, I'm not FIDE, so who knows what they would do.
I tried to build a more realistic example:

http://de.lichess.org/analysis/6rk/6p1/8/8/8/6q1/7K/7R_w_-_-
what about blacks queen was on g6 and now played Qg3+. Let's say black was in hurry and forget his pawn on g7.. and in reality the rook is not helping the queen to mate the queen is for free.
What a blunder... which forces his opponent to take and mate.. 1. ...Kg3:#

Aaah.. what was the rule? somebody said it already?
Black can only claim on his move? So Checkmate ends a game? So white can play Kg3# without having time and end the game and the reclamation from black are "too late"?
Wasn't there such a rule?
But I feel we're comming closer :-)
When the clock runs out, the game is over.

The same thing happened some years ago in football: referee Clive Thomas blew the final whistle in a game at the 1978 World Cup between Sweden and Brazil. A corner, taken by the legendary Zico, went into the net, but the whistle had gone and the goal didn't stand.

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