How did Akagi know which three tiles to take to make a 4 Shan Ten hand? That's easy. Fake Akagi simply didn't shuffle them all that thoroughly, Akagi just memorized them and watched them as they were being shuffled. It's obvious that it wasn't MAGIC, because he stole the correct tiles from the pond anyway, as a safeguard.
I've done a lot of thinking about this stuff because I've watched the Fake Akagi wager episodes about a hundred billion times and it's pretty much my favourite thing ever.