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Why did this game end in draw?

Three-fold repetition. And judging by the way you were trying to win, I don't think you would have succeeded anyways. The correct way to tackle Queen vs Pawn endgames is to post your queen in front of the pawn and bring your king closer. If that's not possible (in the case of the drawish a-pawn), try to achieve this position (lichess.org/analysis/8/8/8/8/8/1K6/3Q4/qk6_b_-_-) with either side to move, and the white queen on d2, e2, f2, g2, or h2.
Sorry but how is this a three-fold repition?

My plan was to just check him until his clock expired (since we were way below the 50 move rule) and I made sure not to make the same move three times in a row?
It‘s not the moves themselves it‘s the position and the possibilities to move. Three times the same position.

Always the same:

-Why draw? (three times repetition)
-Why not draw? (time-out with only a enemy light piece remaining)
I was going to raise this question in a separate thread but doesn't "threefold repetition" mean that a position should occur four times? The first time a position occurs is not a repetition. 2nd time = first repetition, 3rd time 2nd repetition, 4th time third repetition. Or is it just a misnomer?
@leonelmrjvr With 4 minutes left on your clock, you should have been able to win. If you really wanted to time-out your opponent, playing 48. Qa1 followed by premoving the king randomly around the board made much more sense.
Yeah, three times the same position means it occurs once and is repeated two further times.

Forget about this „three-times move repetion“. My rule of thumb: three times the same FEN - it even includes ep, castling and the player to move.
FIDE Laws of Chess:
"The game is drawn, upon a correct claim by a player having the move, when the same position for at least the third time (not necessarily by a repetition of moves):
is about to appear, if he first writes his move, which cannot be changed, on his scoresheet and declares to the arbiter his intention to make this move, or
has just appeared, and the player claiming the draw has the move.
Positions are considered the same if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same. Thus positions are not the same if:
at the start of the sequence a pawn could have been captured en passant.
a king or rook had castling rights, but forfeited these after moving. The castling rights are lost only after the king or rook is moved."
My opponent says he didn't get the option to claim a draw (it happened automatically), isn't that what's supposed to happen in a threefold repitition sitch?
There's a setting for that: "Game behavior" -> "Claim draw on threefold repetition automatically". Options: "Never", "Always" and "When time remaining < 30 seconds".

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