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What's the best strategy against the so-called Hippopotamus opening or defense, in which White or Black pushes almost all of her pawns on the 3rd or 6th rank, except perhaps the a and h pawns, and then possibly moves her Knights and Bishops on the 2nd or 7th rank? Would you try a breakthrough with the d or the e Pawns, or something else?

4

In my opinion, against these openings, the best strategy is to maintain the tension. Move around your pieces building up threats, and prevent the opponent's pawn breaks. Against these positions usually there is no forced win, but it is very hard to play them because of the cramped position, so your opponent will sooner or later make some mistake, and then his/her position will collapse.

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3

Check out this extremely useful video: How to Fight the Hippopotamus Defense

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3

The Hippo does not do well against a 3 pawn center. For example, d4, e4, f4. Then with Nf3, Bd3 and 0-0 White can play f5 breaking the position. Tiger Hillarp Persson wrote a couple books on the Modern defense, where has a chapter on the Hippo. In the book he warns against using it when White can get 3 pawns in the center and has great explanations.

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2

Make a pawn break on a flank and bring a minor piece into the now weakened square.

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1

The Hippo does not do well against a large pawn center, since White can rip up the position before Black castles. Also, White can trade off the g7-bishop and take advantage of the weaknesses caused on the f6-square for occupation with a piece.

If you look at the engine evaluation of Black's position, then you can see that White has a large advantage.

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