Check and checkmate are normal because it's just way too hard to checkmate the king with dual threats.
I can't beat Alpha Beta 3 yet either. If anyone starts beating 4 I'll put some effort into optimizing the search so it can go deeper. Going 10 ply deep is pretty standard for a chess engine, so it's pretty embarrassing for humanity that nobody is beating the 3-ply setting. I think this game actually favors computers over humans more than regular chess does.
Implied Chess:
Rule 1: Chess
Rule 2: You can't capture normally
Rule 3: Any piece threatened by two enemy pieces is captured (except kings)
Rule 4: The player who just moved captures first
Rule 5: No En Passant (it just doesn't make sense)
Rule 6: Check and checkmate are normal
http://noisyowl.com/chess/