The birthday paradox concerns the chance of 2 random elements in an entire set being the same. There's no set here, so there's no birthday paradox. http://en.wikipedia.org/wiki/Birthday_problem
So the chance of success after 2^32 acks is >0.999999999, not <0.5.
It takes about 2^60 acks before there's a significant chance of a mistake. That's a lot of acks, so it will take an insanely long time for a mistake to be made.
Comments
The birthday paradox concerns the chance of 2 random elements in an entire set being the same. There's no set here, so there's no birthday paradox. http://en.wikipedia.org/wiki/Birthday_problem
Hilariously, you got your equation right (which isn't the birthday paradox equation btw) but got your result wrong. http://www.wolframalpha.com/input/?i=%28%282%5E64-1%29%2F%28...
So the chance of success after 2^32 acks is >0.999999999, not <0.5.
It takes about 2^60 acks before there's a significant chance of a mistake. That's a lot of acks, so it will take an insanely long time for a mistake to be made.