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draw

if you remain a bishop against a horse, should not it be a draw?
No. You need some remaining time to show that you avoid the possible mates (in the corner for example).
Kings without pawns and only one minor piece each, is a drawn game.

Even if you play until you run out of time, the position is a draw.
No. Not here and not at FIDE tournaments. K+minor piece each (except Bs of the same color) is „mate potential“.
There are other exceptions, although Lichess doesn't detect the forced draw:


A more realistic scenario: QxQ+ (with no other material left) where the king has no other escape square but to capture the queen.
@Vempele your example is no checkmate: Nxc3 draws.
Bb2 is a checkmate.
@tpr That's the point: it's a forced draw (how is black going to mate after the only legal move Nxc3?), but Lichess incorrectly awards black the win if white runs out of time. It's an exception to the general rule that minor vs minor is not a guaranteed draw, just as same-colored bishops are.
OK, this is an example where lichess has incorrectly implemented the FIDE rule. There is work in progress to cure this.
With what is left on the above chessboard, I think it's called a "dead position" and it should immediately have ended the game with insufficient material to checkmate.

To claim a win on time, see the Appendix A.4.3

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