This post is based on a comment by Oz to our question about balls with two colors:
“There is an interesting (and more difficult) variation I once heard but can’t recall where:
You have a box with n red balls and n blue balls. You take out each time a ball at random as before. 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 as before until left only with balls of the same color. How many balls will be left (as a function of n)?
1) Roughly εn for some ε>0.
2) Roughly ?
3) Roughly log n?
4) Roughly a constant?
5) Some other behavior