I just know I am in WAY over my head. I have been attempting to calculate the number of possible positions in chess. I started by taking the number of squares in a chess board.

8 x 8 = 64 tiles on a chess board.

Each players has a total of 16 peices, so we would do 32x64 = 2048 possible positions. But that is exlcuding mutual positioning and invalid moves. We know that pawns cannot move backward, so we can take the total, without pawns, x 16 away from the total. Bishops, also can only move to 32 squares each on the board. The mutual positioning is the hardest to kink out. Every time I think I have it, I find a flaw in my math. Does anyone know of a good resource that will aid me here today?

PS: If someone has already calculated this, please do not post the link. I want to figure this out (mostly) on my own.

PSS: I am still in the process of working this out, I may figure something out later. In other words, I have not been crushed by such a problem yet.