A weak color complex is a group of squares of the same colour that one side can no longer adequately defend, frequently because the bishop of that colour has been traded or lost.
Pawns can only ever guard one colour of square — a pawn on a light square attacks dark squares, and vice versa. When a player's pawns are fixed on one colour and the bishop that covered the other colour is gone, the squares of that other colour become permanently weak.
The classic cause is trading or losing the 'good' bishop: with the dark-squared bishop off, for instance, the dark squares around your king or in your camp have no proper defender, and enemy pieces — especially a knight or the remaining bishop — can occupy them with impunity.
Treat a weak colour complex as a long-term target. Aim your knight and bishop at those squares, plant a piece on a hole, and remember that the side suffering the complex should avoid trading the one bishop that still patrols it.
Usually fixing your pawns on one colour and then losing or trading the bishop that guarded the other colour. Those other-coloured squares are left with no good defender.
Route your pieces — especially a knight — onto the weak squares, where pawns can't challenge them, and avoid trading your remaining piece that controls that colour while pressing on the holes.
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