1 - Is a bug, but I can't reproduce it.
2 - There is no arbiter and computing every move whether a threefold repetition can be _caused_ isn't very constructive. This rule is difficult to implement in online chess (the same with when time out with K + N can still be a win if in a forced mate sequence) and therefore is neglected.
lichess is supposed to support this. Maybe the takebacks confused it.
I can consistently reproduce 2. This is a real problem, because you have to pass the turn to your opponent, who might move, before you manage to claim.
On that note, maybe it's more practical to keep the button to claim draw there for an additional move (when I move, not when my opponent moves)?
Ah, perhaps simpler (and FIDE-rules appropriate) would be:
I just saw an inconsistent eval with 3-fold rep today : https://fr.lichess.org/M0eOwUgm#69
The local engine gives +6 with 35.Qf6 but the Lichess analyse gives 0 .
The local eval is right because it's only 2 times the same position.
I don't think it's quite correct to "keep the button to claim draw there for an additional move" since this could lead to angle shooting (in the form of a player seeing the opponent's winning move and then deciding to claim a draw in a position where threefold repetition no longer applies).
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I can consistently reproduce 2. This is a real problem, because you have to pass the turn to your opponent, who might move, before you manage to claim.