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Black's group with a one-point eye has eight physical liberties ().

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White needed eight moves to capture Black's group. Black has eight effective liberties.

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Here, Black's group has a larger eye. Again, there are eight physical liberties ().

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Black gets some breathing room by capturing White's two stones inside his larger eye, answering White's move at .

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White needed nine (effective) moves to capture Black's group. Black has nine effective liberties.

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Here, we have the additional, and shared, ko in the centre. Again, there are eight physical liberties ().

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White captures the ko "late".

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And connects. For the calculation here, a ko-fight makes no sense.

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White needed nine (effective) moves to capture Black's group. Black has nine effective liberties. This is the same as with the larger Black eye.