Originally Posted by issybird
I think the only wrinkle I'd like to add is that once a person has been book-picker, s/he is out of the running unless/until everyone has had a crack at it.
Of course. But you should trust the laws of probability a bit more. I was chosen one out of 6. That is 16%. To be chosen a second time it would be 1 in 36 (2,6%).
But do not worry, I will not volunteer again.