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The goal here, albeit heterodox, is to bring the game into a position with few pieces on the board, where yourself as a player has forced the other to trade all your major pieces, leaving both in a position that is likely to draw.

Which chess openings illustrate this strategy best?

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    there isn't an opening that can force the trade of a lot of material. The berlin defense, however, gets into an endgame.
    – CognisMantis
    Commented Nov 23, 2015 at 3:44
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    Some variations in the Scotch lead to exchange of Q and N, with near 50% draw in database. Of course as @CognisMantis said, you can't force it.
    – jf328
    Commented Nov 26, 2015 at 9:09

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in the gurgenidze variation of the accelerated dragon, all pieces are exchanged off except white's two bishops, and typically a bishop and a knight for black. white has a nice space advantage, but blacks structure is very solid and he should be able to draw. however, there are no winning chances for black.

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For black, I would recommend the Queen's Gambit accepted against d4 and the Scandinavian Defense against e4. Sure, it may only be one pawn, but you'll immediately notice how much your position opens up with just that trade. For white, you can play e4, and openings you might like may include the Ruy Lopez exchange, which is drawish from the outset. However, when many people say they are trying to play for a draw, they lack aggression and make defensive mistakes, which can make it quite easy to lose in the end. One one hand, you will learn something with whatever opening repertoire you happen to choose. On the other hand, this most likely isn't going to be where you'll spend the rest of your chess career.

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I recommend the Exchange Variation of the Ruy Lopez. The "classic game" for this opening was played in 1914 between world champion Emmanuel Lasker and future world champion J.R. Capablanca.

It leads to an early exchange of queens, and hence an early endgame. In "Chess Fundamentals," Capablanca noted that immediately after the queen exchange, "The reader should note that if all the pieces were exchanged, White would be practically a pawn ahead and therefore have a won game."

Black's compensation for this was the "Bishop pair," which was not enough in this game.

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For Black 1.d4 d5 2.c4 c5! to clear the c and d files.

Another idea 1.d4 d6 2.c4 e5 to invite 3.dxe5 dxe5 4.Qxd8+.

Similarly 1.e4 d6 2.d4 Nf6 3.Nc3 e5 to invite 4.dxe5 dxe5 5.Qxd8+.

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