I'd also like to mention that "exactly like normal chess in complexity" is false. How can you say that there are the same number of possible first moves in a standard game versus a fischer random game?
It's obvious that there are going to be exactly the same number of possible first moves plus or minus two. And what that has to do with the perceived complexity of the game, I haven't the slightest.
But you do not know the layout of the board in fischer random. And once you do the number of first moves is not even; the knights could be in the corners...