I dunno...
Standard position in 960

When 500 960-games are played, the chance that one of them is a standard is about 40,6%. For 1000 960-games this chance is about 64,7%.

Isn't the exact mirror image of the standard opening position--queens "off color," on e1 and e8, and kings on d1 and d8--also the same as the standard position? Everything is the same, only reversed left to right, so standard chess opening theory would still apply, just as a mirror image, e.g.: Spanish/Ruy 1 d4 d5 2 Nc3 Nf6 3 Bg5; Queen's Gambit, Slav Defense: 1 e4 e5 2 f4 f6.
It seems to me that this would double the chances of having a 960 game that takes place in very familiar haunts. Of course, this would still be a rare occurrence indeed.
Isn't the exact mirror image of the standard opening position--queens "off color," on e1 and e8, and kings on d1 and d8--also the same as the standard position? Everything is the same, only reversed left to right, so standard chess opening theory would still apply, just as a mirror image, e.g.: Spanish/Ruy 1 d4 d5 2 Nc3 Nf6 3 Bg5; Queen's Gambit, Slav Defense: 1 e4 e5 2 f4 f6.
It seems to me that this would double the chances of having a 960 game that takes place in very familiar haunts. Of course, this would still be a rare occurrence indeed.
The mirror image wouldn't be exactly the same as castling would be different. For example, to be identical you would need the king on d1 to move to b1 when castling, but in Chess960 it would in fact move to c1.

Thank you, Malcolm. You are right; of course, according to the rules of 960 that would indeed be the case.
Of course, on the rare occasions when the mirror-image starting position would occur, the players would be able to draw on orthodox opening theory and decide how any particular opening line is affected by the difference in castling.

In chess960, the rooks should always be in the corner, the king restricted to d1 or e1, bishops on opposite colors, and the knights and queen scrambled. Also, the positions should NOT mirror each other

In chess960, the rooks should always be in the corner, the king restricted to d1 or e1, bishops on opposite colors, and the knights and queen scrambled. Also, the positions should NOT mirror each other
This would significantly reduce the number of positions. I don't remember the exact number, but it's small.
Would you leave in positions where castling to one side or the other doesn't move the King?
Its funny when it happens. You automatically lose 3-5 seconds going "WTH" and checking to make sure you picked the correct game mode.
Has anybody encountered the standard position while playing Chess 960? Or is the standard position somehow blocked so we're actually playing Chess 959 here?