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This black group can always make two eyes.
Black has two alternative places to make two eyes: A and B.
 
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Diagram
 
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To see whole sequence move by move, use arrows near the diagram!
 
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Diagram
 
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White can reduce black to single eye, if white plays first.
 
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Diagram
 
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Making or preventing two eyes can get very difficult. When learning it is good to play out any unclear situations. Reading out all positions can be difficult.
 
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Bigger Territories
 
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White cannot play to A, because white stone would not have liberties.
Also white cannot play to B, because again white stone would not have liberties.
So white cannot start killing at all.
 
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Eventually black is reduced to one liberty, and white can capture black stones.
 
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If black plays, black is left with just one liberty, and white can capture black.
 
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The only way to prevent making two eyes is to play white 1.
 
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If black can play first, black can make two eyes.
 
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This black group can make eyes if its blacks turn to play. If white is to play, white can reduce the group to one eye.
 
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Diagram
 
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Making two eyes
 
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One eye is not enought for living.
 
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Now black has only one liberty, and white can capture black with next move.
 
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Diagram
 
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This black group has only one eye. White can capture the group.
 
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