Yes, I would accept a draw. But there is no problem here - after the repetition of the same position three times you can just claim the draw whether white agrees or not. So just play the repetitions, claim the draw, and move on.
To Accept or Not?
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I honestly thought this position was dead drawn when i first looked at it and indeed when I was analyzing it, I could not see any resources or tricks for either side(!)
Then I gave up on the position, making sure my buddy houdini here supported my analysis, and guess what i found: a truly amazing tactical shot with 42.Qa2!!, which looks to be so unspectacular at first glance
but since white missed this tricky move, it turns out to be dead drawn really.
If you were interested, after 42.Qa2, you might ask, what is so good about white's position?
Well let's go through some (not all of them stated i bothered to analyze) of black's moves. Black can play Qc1, Qb4, or defend the e6 pawn with Kf7, and play the cool headed Bd7/ Kh7
, saying to white "What are you going to do?"
I didn't go through all of the lines, as that would take a very long time, but as you can see, we see this repeating pattern of trickiness with Qa2/Be2/Qa1 (Qb1)/ with decisive effect. In the Qa1 stuff, white's threats are incredibly obvious, but unstoppable. d5 happens next, or Qh1 sometimes, and with Qb1, white has Qh1 stuff and even more deadly Qb8 with a winning position.
I do consider this a study, where the trickiness of the Queen is revealed. It is very difficult to notice!
Would you accept a draw here as white?
I offered a draw every turn after the queen exchange. My opponent refused. The repetition seems like something a computer would do. No, I'm really not accusing something, but it seemed like mindlessness to continue the game.