Beating the odds

We had an early Christmas gift exchange yesterday. There were ten of us, and we picked slips of paper to determine whose present we would receive. Before picking a paper, the first person hesitated and asked, what if I pick my own name? We said, you'll just pick again! Besides, it won't happen, there are ten of us here, what are the chances? (ten percent, to be exact)

And... she picked her own name. What a lucky girl! :P