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system should set draw

I lost my last game on time although there was no material left to checkmate.
I played the daily Blitz-tournament. In the last round my oppenent had a bishop and i had a pawn and a knight. With his last move my opponent took the last pawn and after that i lost on time. However there was only a white knight and a black bishop and the two kings left on the board. This is of course a draw, but the system let me loose on time. Even if there are theoretical mates this should be set to draw, because if not you could always flag the opponent in the endgame bishop vs knight. That does not sound reasonable to me.
I hope you could change this setting.
The current rules are that if the opponent can mate, a timeout counts as a loss.

Changing the rule would require drawing the line somewhere else -- what about K+P winning on time versus K+Q+R+R? What about K+R versus K+R, or K+P (rook pawn) versus K blocking the pawn?
Also, it should be noted that that is a loss under FIDE rules also, so it's not like some arbitrary thing that lichess came up with.

It's an arbitrary thing FIDE came up with :)
however you can always claim it a draw concerning to FIDE rules, dont? K+P vs K you can at least make mistakes and a pawn could always promote. But the Bishop only can't mate, can he?
In your game, it is possible for your opponent to construct a checkmate.
This one special case, K + N or B versus K + N or B could be automatically given draw as well on lichess, like it is done with K + N or B versus K.

Reason: Even if a mate is possible in theory, it is impossible to achieve in practice if the opponent is not braindead, which separates it clearly from other endgames of that type, for example K + R versus K + R where it regulary happens that one player drops a rook. But in this endgame a player can even drop his piece and it is a draw.

In my database (5,5 million OTB games) there are 1350 games with this end position. Only seven of these games (three were internet games) are won by a player, all on time, not one by mate.

It is true that according to FIDE rules it is a win if the player does not claim and loses on time, but if he claims, the referee will agree. He will also do so in other endgames. For example i once successfully claimed in K + R versus K + R.

I even know two cases where the referee gave it draw under dubious circumstances. One was an endgame K + P versus K + N and the player with the pawn lost on time without claiming before. The referee decided for draw. Another was an endgame K + Q versus K + Q where one player did not correctly claim by stopping the clock first, then dropped his queen and THEN successfully claimed a draw, arguing that he had made clear his intention before and that the (formally correct) non-communication by his opp had irritated him. This was also given draw. Both referee decisions were formally not correct but were not undone by FIDE. Which shows that in edge cases the FIDE leaves the decision to the referee.

So Lichess could do that as well and declare this endgame draw, assuming that no player is that dumb to run into the mate (i wonder if this mate has actually ever happened in the history of chess). This says yes to the common case and no to the clock trolls.
Why isn't K+P versus K+Q+R+R also a "special case", or K+R versus K+R, or any of the other hundreds of endgames where one player is highly unlikely to mate?

Also, what about special cases of your special cases, where a player is likely to mate against random moves? Should that player be denied a win because their opponent's random moves might not have lost?
The rules are the rules, live by them.
If you do not like losing on time, then play with increment.
Dont get me wrong, i want the following types of positions to be a draw:

K + N or B vs K + N or B.
I would even suggest K + N or B vs K + any pieces except pawns.

Because in all of those piece constellations there exist no won postition (except the mate) for the K + N or B party where it is the opponents move.

However, i wouldnt go so far to include KNN vs K. Draw only if the player not losing on time has just a bishop or knight left and the other player has no pawns.

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