My girlfriend and I had a discussion about probability as it relates to a weekly lottery draw. She argued that the probablity of winning remains the same from draw to draw, and because of this anyone who plays the lottery more than once stands no greater chance of winning than someone who only plays it on one occasion. Against this, I argued that because any lottery operates with a finite series of numbers, given enough draws all possible combinations will eventually have appeared at least once, and as such someone who plays more than once stands a greater chance of winning. I also claimed that the probability relating to each draw is different from that which relates to a succession of draws (again because of the finite series of numbers). Which of us is right?