I am about to join my Computer Science Master’s course in around 10 days. One of the introductory and how-to mails I received mentioned that hostel rooms are allotted by drawing lots. One of the hostels is a newly constructed block, which has slightly better rooms than the others. This situation posed an interesting problem to me: how to maximize my chances of ending up in the new hostel?
Or, phrasing in a more general way:
There are p lots, out of which q are winning lots (0 < q ≤ p). Contestants draw their lots one after the other. After drawing his lot, the contestant publicizes the lot that he has got, i.e. whether it is a winning lot or not. A lot once drawn is not returned to the box. What is the ideal time to draw your lot, so as to maximize the winning probability?