Bags I go nth
You are in a lucky dip style competition. There is a bag with tickets in it. They are numbered 1 to 100. One of them wins tonight’s star prize, the others win nothing. It is equally likely that any one of the tickets is the winner. Only the host knows the lucky number. 100 people form a queue and in the order of their position in the queue, randomly take one of the tickets and show it to the host. If the number on the ticket is divisible by 3, it is put back into the bag, but you still get the prize. The winner isn’t announced until all of the contestants have selected a ticket (in fact, that’s irrelevant).
What is the optimum position to be standing in the queue to maximise your chance of winning the star prize?