Re: More proof
"The odds of winning without having bought a ticket (perhaps finding the winning ticket on the ground or being left one in a will or something) are pretty similar to winning after having bought a ticket."
No, it's a world of difference. 0 in X, for any nonzero X, is always zero. 1 in X may be infinitesimally small, but it's still not zero. An infinitesimally small chance is always preferable to no chance at all.