ThrillerFan: Thanks for your comment. Strictly speaking, it doesn't guarantee that best moves will be the same (even in the case of symmetrical rooks!). This is cuz the pseudo-symmetry doesn't exchange short and long castlings. In your example, the short castling in QBBRNKNR will give *****RK* but U can't obtain *KR***** with the long castling in the pseudo-symmetrical RNKNRBBQ.
Correct.
@ThrillerFan
Counter-example. U can castle immediately in RNBQNKRB:
but not in its pseudo-symmetrical version BRKNQBNR:
U can try as hard as U can. 
Good project. Just so I understand, what are the scores? Is that the best opening move by White for each Fischer position?
Does this mean that for each game, you are testing the (usually) 20 openings? That would be about 480 x 20 = 9600 openings to analyze, right?
Once you finish learning the best 480 openings, it would be interesting (for the best) to see if Black can equalize with his next move.
Good project. Just so I understand, what are the scores? Is that the best opening move by White for each Fischer position?
Does this mean that for each game, you are testing the (usually) 20 openings? That would be about 480 x 20 = 9600 openings to analyze, right?
Once you finish learning the best 480 openings, it would be interesting (for the best) to see if Black can equalize with his next move.
Hehe ... 20 openings / position would be too many at the moment. 
Now, I calculate only the 1 "best" move with its evaluation using the Explorer (Stockfish 8) at depth d=20 plies. 
Oh, now I understand. You let Stockfish find the best opening. I'm not too familiar with all the abilities of Stockfish. I've played games against it, but very rarely have I used it to evaluate positions. I think your research is good for the understanding of variant games. For example it will help us understand how much the game needs to be modified, to make a game significantly different. Good work.
Darn, I like 1.O-O 
Darn, I like 1.O-O
Yeah, that's a funny option in some Fischer's positions.
All right, I decided to post not only "best" first moves but, actually, "best" openings in 5 moves chosen by the Explorer at d=20. The very first such opening is really nice and crazy with a gambit and a counter-gambit :
The test game for position #25 is also crazy, against all opening rules , with d-pawn going to d6:
After 3. d4 white threatened with 4. Qe3+, annoying for black, and the crazy pawn advance is a consequence of this entanglement.
Endure Clive, the Italian Stalion Sicilian Spaghetti Dragon....Endure = E4 Clive = C5...i have to work deeper in the variations...
Finally, we have position #27 that might be refutable. Two white's knights can start the immediate attack at the king's flank. So, black is obliged to exchange its LSB. Nevertheless, white has a significant advantage.
try this link, i think it is the one i used that was free in the end.
Estimated chessmates;
Some advices for playing Fischer's chess:
1. The most important thing to not taking risks is to care as much as possible of the pawn structure.
2. Quick development of minor (trying not to create blockage among our own pieces)
3. In some positions there are unprotected or very weak pawns that can be exploited by our opponent's: identify them and take care of them!
4. Our mind usually works easier with patterns: the nearer you approach it to classical chess, the better! Of course it will depend in the position.
5. Calculation overall! This variation was made to not fall in theoretical memorization!
Hey, thanks for your good advices! It was not intended for the theoretical memorization but it's possible, at some extent.
Bobby Fischer is rolling around in his grave right now!
Yes, he's happy that his chess variant has gained such a popularity.
And also, where do you get that RNKNRBBQ castles to *KR*****? King moves 2 squares. Hence in a case like NRKQBBNR, if you castle to the left, the Rook wouldn't even move, the King would just jump the b-Rook to a1.
So shouldn't your example be KR******, not *KR*****, in the case of RNKNRBBQ?