How many possible Othello boards are there?

Factual Questions
1

Don’t ask me why, but my brother and I started talking about this tonight and now I can’t stop wondering, but I’m not sure how to figure it out.

It’s an 8x8 board with three possible states for most of the squares: white, black, or empty (the four spaces in the middle start out filled, so they can only be white or black). Some boards are duplicates (since if you rotate the board it’s the same) and a bunch more aren’t possible.

So I challenge the math wizards here at the SDMB. How many are there?

2

Approximately 10^28, according to Wikipedia.

http://en.wikipedia.org/wiki/Reversi

3

There are 3[sup]64[/sup] possible Othello boards. Now, the question of how many valid, distinguishable boards there are is more difficult to answer.