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I heard about a popular chess variant called Chess960, which uses randomized home ranks for the pieces. Which are the basic principles we can adapt there in Chess960?

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The first is to know it completely. Many people even don't know that it's possible to castle in Chess960 or they don't know how to castle. A good starting point is to get familiar to its rules, read this wiki.

The pieces in Chess960 set randomized so the known opening moves and variants aren't valid anymore. BUT, the opening principles and rules are still valid. Occupying center, controlling more open lines and diagonals, developing pieces rapidly, protecting the king, connecting the rooks... you should learn opening strategies and principles.

In Chess960 memorizing the opening moves like a machine doesn't useful anymore. By playing this kind of chess you're stepping in the unknown and wonder land of openings.

A bad practice is trying to make opening positions as same as known positions and wasting moves for simulating normal chess variants.

“Chess960 is healthy and good for your chess. If you get into it and not just move the pieces to achieve known positions it really improves your chess vision.” -- GM Levon Aronian.

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