The ultimate out-draw

I went 2-2 at club on Tuesday. It's the third time in four weeks I've finished with that record, and the other time I only played three games (2-1). In one of my recent losses (a supreme slaughter) my opponent drew all four esses, both blanks, the Z, Q, X, J and the K -- all the power tiles. I can't remember that ever happening to me before, neither on a board nor on-line. At the end of the game I made a play to empty the bag with a blank and an S unseen to me. I was hoping not to draw either of them, at that point, just so that the clean sweep of power tiles would be complete, and I would have the ultimate justification for complaining and feeling sorry for myself.

On the way home from club I figured out the probability of my opponent getting all 11 power tiles. It's pretty simple if you assume each player has a 50% chance of drawing any given tile, and draws are independent (both of which seem reasonable). The probability would be (1/2)^11 = 1/2048. This is not incredibly low, meaning that although I don't remember this ever happening to me before, it almost certainly has. I've played about 4100 games of Scrabble on-line and several hundred more in tournaments and at club. The probability that a clean sweep of the power tiles has never happened against me is only around 11%. So it probably has happened before, but it still sucked on Tuesday.