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Originally Posted by CoccoBill
Should I hunt down his remaining pieces, defend against their pawns or attack with mine.
I mean, all of the above. There's always an optimal move, and that might be an attacking move, a defending move or even a waiting move. I guess the easiest way to approach "balanced" endgames is to try to control more space, that will usually mean a superior position, so moves that either increase your control of the board or restrict your opponent's are what we want to play.
If the game is truly balanced, a theoretical draw, then our ideal moves are ones where our opponent has few good replies and many bad replies, increasing the chances of him blundering. Of course we also need to ensure our position is solid so we're not giving him winning chances, that's your priority in theoretically drawn endgame, but we do want to be thinking about making it as difficult as possible for our opponent to find the right moves to secure his half point. If you think you have a better position in a balanced endgame then avoid trades (edit - unnecessary trades, if it wins a pawn then go for it) and try to control more space, if you're under pressure in balanced endgames then seek to trade off pieces and blockade dangerous pawns or create a fortress for your king.
That's general advice and won't always apply, chess is wonderful in that it has its quirks. Sometimes logical assumptions in chess (controlling more space is good etc), they fail us. But it's rare.
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