Consider an urn with r red balls and b blue balls. In every turn, one ball is drawn. When a red ball is drawn, it is put back in the urn together with some extra R red balls. When a blue ball is drawn, it is left outside the urn. The questions are: 1. What is the expectation value of the number of blue balls outside the urn, B(n), after n turns? 2. What is the expected number of turns needed to get all the blue balls out of the urn? 3. What minimal value must the penalty have, the number R, to get this number of expected turns to infinity?