Middlegame
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In chess, the middlegame refers to the portion of the game that happens immediately after the opening (usually the first move after the procession of moves that make up a standard opening) and blends somewhat with the endgame. During this time, players will attempt to strengthen their positions while weakening their opponent's, both by careful arrangement of the pieces for prepared attacks and defenses and by whittling away at their opponent's numbers. Often, the middlegame involves a good deal of trading; studying how to trade successfully is important.
There are a number of elementary tactics that help with taking your opponent's pieces. Examples include forking, skewering, pinning, and discovered attacks, though there are more. Most of them involve checking the king (or, conversely, by making it so that he cannot move in a certain way to prevent being checked), which will force your opponent to move the king instead of taking your piece.
In addition, there are strategies that are useful, which usually revolve around having pieces in spots that are well defended, attacking other squares that your opponent would like to move to and thus preventing him from doing so. On the other hand, it involves setting up your pieces so that they will be useful there later in the game, despite the fact that they may not be useful when you first put a piece there.
Good players will use good tactics that usually resolve with good trades, but also a strong position during the middlegame.
Finally, the last thing that happens in the middlegame is the setup for endgame. Since many endgames involve the promotion of a pawn, it's usually good to keep that in mind when making trades during the middlegame.
Chess computers are widely considered to be weakest (as compared to human opponents) in the middlegame. During the opening the computer can rely on an extensive stored library of standard openings, and during the endgame the complexity is low enough that the computer can calculate the game very far ahead, and extend its reach using endgame tablebases. In contrast, during the middlegame, extensive heuristics are required, exactly what the human brain excels at.