A birthday puzzle

[jason_t]

This is a spin on a classic problem from probability. If you're familiar with that problem, this won't be that difficult but is still interesting.

The manager of a movie theatre announces that a free ticket will be given to the first person in line whose birthday is the same as someone else who has already purchased a ticket. You can get in line at any time. The birthdays are distributed uniformly at random over 365 days. Which position in line should you take?