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I am a beginner at go and we couldn't resolve this situation with my opponent. Neither of us want to play to these liberties because whoever plays loses their stones. Whose are these two intersections at the end of the game?

$$Bcm1 Whose are the points?
$$ |.....
$$ |XXX..
$$ |OOOX.
$$ |.OOX.
$$ |X.OX.
$$ +-----

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The White's are dead if the surrounding Black's are alive. The White's are two moves away from being captured by Black. White can make moves to prolong its dying but not prevent it.

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    This is right, but the essential thing to explain to a raw beginner is that if Black plays (e.g.) A2 and White captures the two stones, then Black can play back at A1 and then A2. Inexperienced players often worry too much about individual stones being captured and have to learn to sacrifice them to gain territory or (as they improve) influence, and this is the stage before that: sacrificing in order to capture, in its most basic form. Read more in Sensei’s Library at Two eyes.
    – PJTraill
    Commented Apr 13, 2020 at 15:12

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