A commentator named Oz proposed the following question: You have a box with n red balls and n blue balls. You take out each time a ball at random but, if the ball was red, you put it back in the box and take out a blue ball. If the ball was blue, you put it back in the box and take out a red ball.
You keep doing it until left only with balls of the same color. How many balls will be left (as a function of n)?
Peter Shor wrote in a comment “I’m fairly sure that there is not enough bias to get , but it intuitively seems far too much bias to still be . I want to say . At a wild guess, it’s either or , since those are the simplest exponents between and .” The comment followed by a heuristic argument of Kevin Kostelo and computer experiments by Lior Silberman that supported the answer .