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Well, I have the project of classification of ALL Fischer's random chess games and everybody is welcome to join!
I explain here some basic features that I have discovered.
U can look at my posts in the chess960 forum for some classifications.
The most important thing is the presence or absence of a QxB-pair (Q stands for "queen" and B for " bishop"). Definition : a Fischer's game is of QxB-type if the queen and one of bishops are separated by 1 square.
The significance come from the fact that the pawn located between Q and B opens the way to both of them. So typically "best" openings are those when U move that QxB-pawn! Example :
So, basically, QxB-games are divided in 4 types : QKB, QRB, QBB and QNB (K stands for "king" etc.).
Pliz notice that the usual chess is a QKB-game, that's why the QxB-opening 1. e4 is the "best" in this particular case.
There are following openings in such games after 2 moves :
A) Two knights games. Example :
B) Three knights games :
C) Bishop's openings :
D) Trompowsky attack :
E) Queen's attack :