Yeah, the way it seems to be working for me is I play the blackmail card, he discards, and then it is the next round.
When he plays, he lays down the blackmail card, I discard, he plays a card, and then it is the next round.
So when I do it, I don't get a chance to play another card.
I took one look at this and thought, "Wow, this looks like The Incredible Machine". TIM had a lot more fun contraptions, but this wasn't bad for a flash game.