Game #2
Research on Radioactive Toys
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Is opening important in 960 chess? Is it worth to spend time analysing the initial position? Yes, of course!
Game #1, 3 days per move
I've found a good article about opening http://www.chess.com/article/view/chess960-the-opening-makes-a-comeback2
So, in addition to common rules of the opening as in standard chess you can add:
-improve your queen, especially on a1 / h1 (a8 / h8 as black) - in standard chess d1 is a very comfortable square for queen therefore there's no need to concentrate on this particular thing
-search for weaknesses in the initial position - undefended pawns and pieces that allow some tactical threats (every position has its own "f2/f7")
-consider localization of pieces - if both opponent's knights are at the opposite site of the board they will not threaten your king soon
-how easily are central pawns attacked / defended and by what? Answering that question will help you make a choice if you wish to play sharp or positional opening (like difference between 1.e4 / 1.d4 in standard chess)
-try to find moves that force opponent's response (like 1.e4 e5 2.Nf3 in standard position, kind of forcing Nc6)
Going back to initial position in the game above; as we can see a- and h-pawns are undefended, the same as bishops on a-file and rooks on c-file. There is also quite unique weakness of the d-pawn as it may be pinned to king and / or rook along diagonals, and moving it prematurely may just expose these pieces. Moreover, developing knight from b1 / b8 will remove the only defender of that pawn. It appears that white is most likely to have some weaknesses on the dark squares and black will have those on the light squares. Moving e-pawn first enables queen and bishop to have a lot of scope, while moving d-pawn does nothing except grabbing space. Therefore after 1.e4 e5 white is unable to play 2.b4 at the moment (unless he's willing to play a gambit, which is promising in my opinion), but after 2.b3 there occurs a mentioned complex of weakened dark squares. That's why white handed initiative to black as quickly as on the third move and allowed him to gain an advantage.